diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml index cffef64b0..20d5f9a68 100644 --- a/.github/workflows/build.yml +++ b/.github/workflows/build.yml @@ -7,26 +7,18 @@ on: jobs: build: - strategy: - matrix: - os: [ macOS-latest, windows-latest ] - runs-on: ${{matrix.os}} - timeout-minutes: 40 + runs-on: windows-latest + timeout-minutes: 20 steps: - - uses: actions/checkout@v3.0.0 - - uses: actions/setup-java@v3.0.0 + - uses: actions/checkout@v3 + - uses: actions/setup-java@v3.5.1 with: - java-version: 11 - distribution: liberica - - name: Cache konan - uses: actions/cache@v3.0.1 - with: - path: ~/.konan - key: ${{ runner.os }}-gradle-${{ hashFiles('*.gradle.kts') }} - restore-keys: | - ${{ runner.os }}-gradle- + java-version: '11' + distribution: 'liberica' + cache: 'gradle' - name: Gradle Wrapper Validation uses: gradle/wrapper-validation-action@v1.0.4 - - uses: gradle/gradle-build-action@v2.1.5 + - name: Gradle Build + uses: gradle/gradle-build-action@v2.3.2 with: - arguments: build + arguments: test jvmTest diff --git a/CHANGELOG.md b/CHANGELOG.md index feb925436..1b3ab75fd 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,11 +2,15 @@ ## [Unreleased] ### Added +- Type-aliases for numbers like `Float64` - 2D optimal trajectory computation in a separate module `kmath-trajectory` - Autodiff for generic algebra elements in core! - Algebra now has an obligatory `bufferFactory` (#477). ### Changed +- Tensor operations switched to prefix notation +- Row-wise and column-wise ND shapes in the core +- Shape is read-only - Major refactor of tensors (only minor API changes) - Kotlin 1.7.20 - `LazyStructure` `deffered` -> `async` to comply with coroutines code style @@ -16,6 +20,7 @@ ### Deprecated ### Removed +- Polynomials moved to https://github.com/SciProgCentre/kmath-polynomial ### Fixed diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BufferBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BufferBenchmark.kt index 41b9005e4..c2616303b 100644 --- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BufferBenchmark.kt +++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BufferBenchmark.kt @@ -6,34 +6,75 @@ package space.kscience.kmath.benchmarks import kotlinx.benchmark.Benchmark +import kotlinx.benchmark.Blackhole import kotlinx.benchmark.Scope import kotlinx.benchmark.State import space.kscience.kmath.complex.Complex +import space.kscience.kmath.complex.ComplexField import space.kscience.kmath.complex.complex +import space.kscience.kmath.operations.invoke +import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.DoubleBuffer -import space.kscience.kmath.structures.MutableBuffer +import space.kscience.kmath.structures.getDouble +import space.kscience.kmath.structures.permute @State(Scope.Benchmark) internal class BufferBenchmark { - @Benchmark - fun genericDoubleBufferReadWrite() { - val buffer = DoubleBuffer(size) { it.toDouble() } + @Benchmark + fun doubleArrayReadWrite(blackhole: Blackhole) { + val buffer = DoubleArray(size) { it.toDouble() } + var res = 0.0 (0 until size).forEach { - buffer[it] + res += buffer[it] } + blackhole.consume(res) } @Benchmark - fun complexBufferReadWrite() { - val buffer = MutableBuffer.complex(size / 2) { Complex(it.toDouble(), -it.toDouble()) } - - (0 until size / 2).forEach { - buffer[it] + fun doubleBufferReadWrite(blackhole: Blackhole) { + val buffer = DoubleBuffer(size) { it.toDouble() } + var res = 0.0 + (0 until size).forEach { + res += buffer[it] } + blackhole.consume(res) + } + + @Benchmark + fun bufferViewReadWrite(blackhole: Blackhole) { + val buffer = DoubleBuffer(size) { it.toDouble() }.permute(reversedIndices) + var res = 0.0 + (0 until size).forEach { + res += buffer[it] + } + blackhole.consume(res) + } + + @Benchmark + fun bufferViewReadWriteSpecialized(blackhole: Blackhole) { + val buffer = DoubleBuffer(size) { it.toDouble() }.permute(reversedIndices) + var res = 0.0 + (0 until size).forEach { + res += buffer.getDouble(it) + } + blackhole.consume(res) + } + + @Benchmark + fun complexBufferReadWrite(blackhole: Blackhole) = ComplexField { + val buffer = Buffer.complex(size / 2) { Complex(it.toDouble(), -it.toDouble()) } + + var res = zero + (0 until size / 2).forEach { + res += buffer[it] + } + + blackhole.consume(res) } private companion object { private const val size = 100 + private val reversedIndices = IntArray(size){it}.apply { reverse() } } } diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt index 141d0433b..3d39e89a5 100644 --- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt +++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt @@ -13,10 +13,8 @@ import org.jetbrains.kotlinx.multik.api.Multik import org.jetbrains.kotlinx.multik.api.ones import org.jetbrains.kotlinx.multik.ndarray.data.DN import org.jetbrains.kotlinx.multik.ndarray.data.DataType -import space.kscience.kmath.nd.BufferedFieldOpsND -import space.kscience.kmath.nd.StructureND -import space.kscience.kmath.nd.ndAlgebra -import space.kscience.kmath.nd.one +import space.kscience.kmath.misc.UnsafeKMathAPI +import space.kscience.kmath.nd.* import space.kscience.kmath.nd4j.nd4j import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.tensors.core.DoubleTensor @@ -69,9 +67,10 @@ internal class NDFieldBenchmark { blackhole.consume(res) } + @OptIn(UnsafeKMathAPI::class) @Benchmark fun multikInPlaceAdd(blackhole: Blackhole) = with(multikAlgebra) { - val res = Multik.ones(shape, DataType.DoubleDataType).wrap() + val res = Multik.ones(shape.asArray(), DataType.DoubleDataType).wrap() repeat(n) { res += 1.0 } blackhole.consume(res) } @@ -86,7 +85,7 @@ internal class NDFieldBenchmark { private companion object { private const val dim = 1000 private const val n = 100 - private val shape = intArrayOf(dim, dim) + private val shape = ShapeND(dim, dim) private val specializedField = DoubleField.ndAlgebra private val genericField = BufferedFieldOpsND(DoubleField) private val nd4jField = DoubleField.nd4j diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/TensorAlgebraBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/TensorAlgebraBenchmark.kt index 3ed7163b3..c4382374a 100644 --- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/TensorAlgebraBenchmark.kt +++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/TensorAlgebraBenchmark.kt @@ -13,6 +13,8 @@ import space.kscience.kmath.linear.linearSpace import space.kscience.kmath.linear.matrix import space.kscience.kmath.linear.symmetric import space.kscience.kmath.operations.DoubleField +import space.kscience.kmath.tensors.core.symEigJacobi +import space.kscience.kmath.tensors.core.symEigSvd import space.kscience.kmath.tensors.core.tensorAlgebra import kotlin.random.Random @@ -27,11 +29,11 @@ internal class TensorAlgebraBenchmark { @Benchmark fun tensorSymEigSvd(blackhole: Blackhole) = with(Double.tensorAlgebra) { - blackhole.consume(matrix.symEigSvd(1e-10)) + blackhole.consume(symEigSvd(matrix, 1e-10)) } @Benchmark fun tensorSymEigJacobi(blackhole: Blackhole) = with(Double.tensorAlgebra) { - blackhole.consume(matrix.symEigJacobi(50, 1e-10)) + blackhole.consume(symEigJacobi(matrix, 50, 1e-10)) } } \ No newline at end of file diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt index 25ce8410a..90f3cb765 100644 --- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt +++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt @@ -10,7 +10,7 @@ import kotlinx.benchmark.Blackhole import kotlinx.benchmark.Scope import kotlinx.benchmark.State import org.jetbrains.bio.viktor.F64Array -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND import space.kscience.kmath.nd.ndAlgebra import space.kscience.kmath.nd.one @@ -49,7 +49,7 @@ internal class ViktorBenchmark { private companion object { private const val dim = 1000 private const val n = 100 - private val shape = Shape(dim, dim) + private val shape = ShapeND(dim, dim) // automatically build context most suited for given type. private val doubleField = DoubleField.ndAlgebra diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt index ea417e564..4ec4605ed 100644 --- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt +++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt @@ -10,7 +10,7 @@ import kotlinx.benchmark.Blackhole import kotlinx.benchmark.Scope import kotlinx.benchmark.State import org.jetbrains.bio.viktor.F64Array -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.ndAlgebra import space.kscience.kmath.nd.one import space.kscience.kmath.operations.DoubleField @@ -49,7 +49,7 @@ internal class ViktorLogBenchmark { private companion object { private const val dim = 1000 private const val n = 100 - private val shape = Shape(dim, dim) + private val shape = ShapeND(dim, dim) // automatically build context most suited for given type. private val doubleField = DoubleField.ndAlgebra diff --git a/build.gradle.kts b/build.gradle.kts index 120b0f35d..e03bec9af 100644 --- a/build.gradle.kts +++ b/build.gradle.kts @@ -15,7 +15,7 @@ allprojects { } group = "space.kscience" - version = "0.3.1-dev-4" + version = "0.3.1-dev-7" } subprojects { @@ -79,9 +79,9 @@ ksciencePublish { github("kmath", "SciProgCentre") space( if (isInDevelopment) { - "https://maven.pkg.jetbrains.space/mipt-npm/p/sci/dev" + "https://maven.pkg.jetbrains.space/spc/p/sci/dev" } else { - "https://maven.pkg.jetbrains.space/mipt-npm/p/sci/release" + "https://maven.pkg.jetbrains.space/spc/p/sci/maven" } ) sonatype() diff --git a/docs/templates/ARTIFACT-TEMPLATE.md b/docs/templates/ARTIFACT-TEMPLATE.md index 1bac2a8ff..a3e47e693 100644 --- a/docs/templates/ARTIFACT-TEMPLATE.md +++ b/docs/templates/ARTIFACT-TEMPLATE.md @@ -3,10 +3,12 @@ The Maven coordinates of this project are `${group}:${name}:${version}`. **Gradle:** -```gradle +```groovy repositories { maven { url 'https://repo.kotlin.link' } mavenCentral() + // development and snapshot versions + maven { url 'https://maven.pkg.jetbrains.space/spc/p/sci/dev' } } dependencies { @@ -18,6 +20,8 @@ dependencies { repositories { maven("https://repo.kotlin.link") mavenCentral() + // development and snapshot versions + maven("https://maven.pkg.jetbrains.space/spc/p/sci/dev") } dependencies { diff --git a/examples/build.gradle.kts b/examples/build.gradle.kts index 1d224bace..da645f012 100644 --- a/examples/build.gradle.kts +++ b/examples/build.gradle.kts @@ -18,7 +18,6 @@ dependencies { implementation(project(":kmath-commons")) implementation(project(":kmath-complex")) implementation(project(":kmath-functions")) - implementation(project(":kmath-polynomial")) implementation(project(":kmath-optimization")) implementation(project(":kmath-stat")) implementation(project(":kmath-viktor")) diff --git a/examples/src/main/kotlin/space/kscience/kmath/fit/chiSquared.kt b/examples/src/main/kotlin/space/kscience/kmath/fit/chiSquared.kt index e32b97136..febf55283 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/fit/chiSquared.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/fit/chiSquared.kt @@ -18,10 +18,10 @@ import space.kscience.kmath.optimization.FunctionOptimizationTarget import space.kscience.kmath.optimization.optimizeWith import space.kscience.kmath.optimization.resultPoint import space.kscience.kmath.optimization.resultValue +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.real.DoubleVector import space.kscience.kmath.real.map import space.kscience.kmath.real.step -import space.kscience.kmath.stat.RandomGenerator import space.kscience.plotly.* import space.kscience.plotly.models.ScatterMode import space.kscience.plotly.models.TraceValues diff --git a/examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt b/examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt index 73fca8a38..c7eefa6b9 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt @@ -19,9 +19,9 @@ import space.kscience.kmath.optimization.QowOptimizer import space.kscience.kmath.optimization.chiSquaredOrNull import space.kscience.kmath.optimization.fitWith import space.kscience.kmath.optimization.resultPoint +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.real.map import space.kscience.kmath.real.step -import space.kscience.kmath.stat.RandomGenerator import space.kscience.plotly.* import space.kscience.plotly.models.ScatterMode import kotlin.math.abs diff --git a/examples/src/main/kotlin/space/kscience/kmath/functions/polynomials.kt b/examples/src/main/kotlin/space/kscience/kmath/functions/polynomials.kt deleted file mode 100644 index 8228983e2..000000000 --- a/examples/src/main/kotlin/space/kscience/kmath/functions/polynomials.kt +++ /dev/null @@ -1,399 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("LocalVariableName") - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.expressions.symbol -import space.kscience.kmath.operations.algebra -import space.kscience.kmath.operations.invoke - - -/** - * Shows [ListPolynomial]s' and [ListRationalFunction]s' capabilities. - */ -fun listPolynomialsExample() { - // [ListPolynomial] is a representation of a univariate polynomial as a list of coefficients from the least term to - // the greatest term. For example, - val polynomial1: ListPolynomial = ListPolynomial(listOf(2, -3, 1)) - // represents polynomial 2 + (-3) x + x^2 - - // There are also shortcut fabrics: - val polynomial2: ListPolynomial = ListPolynomial(2, -3, 1) - println(polynomial1 == polynomial2) // true - // and even - val polynomial3: ListPolynomial = 57.asListPolynomial() - val polynomial4: ListPolynomial = ListPolynomial(listOf(57)) - println(polynomial3 == polynomial4) // true - - val polynomial5: ListPolynomial = ListPolynomial(3, -1) - // For every ring there can be provided a polynomial ring: - Int.algebra.listPolynomialSpace { - println(-polynomial5 == ListPolynomial(-3, 1)) // true - println(polynomial1 + polynomial5 == ListPolynomial(5, -4, 1)) // true - println(polynomial1 - polynomial5 == ListPolynomial(-1, -2, 1)) // true - println(polynomial1 * polynomial5 == ListPolynomial(6, -11, 6, -1)) // true - } - // You can even write - val x: ListPolynomial = ListPolynomial(0.0, 1.0) - val polynomial6: ListPolynomial = ListPolynomial(2.0, -3.0, 1.0) - Double.algebra.listPolynomialSpace { - println(2 - 3 * x + x * x == polynomial6) - println(2.0 - 3.0 * x + x * x == polynomial6) - } - - // Also there are some utilities for polynomials: - println(polynomial1.substitute(Int.algebra, 1) == 0) // true, because 2 + (-3) * 1 + 1^2 = 0 - println(polynomial1.substitute(Int.algebra, polynomial5) == polynomial1) // true, because 2 + (-3) * (3-x) + (3-x)^2 = 2 - 3x + x^2 - println(polynomial1.derivative(Int.algebra) == ListPolynomial(-3, 2)) // true, (2 - 3x + x^2)' = -3 + 2x - println(polynomial1.nthDerivative(Int.algebra, 2) == 2.asListPolynomial()) // true, (2 - 3x + x^2)'' = 2 - - // Lastly, there are rational functions and some other utilities: - Double.algebra.listRationalFunctionSpace { - val rationalFunction1: ListRationalFunction = ListRationalFunction(listOf(2.0, -3.0, 1.0), listOf(3.0, -1.0)) - // It's just (2 - 3x + x^2)/(3 - x) - - val rationalFunction2 : ListRationalFunction = ListRationalFunction(listOf(5.0, -4.0, 1.0), listOf(3.0, -1.0)) - // It's just (5 - 4x + x^2)/(3 - x) - - println(rationalFunction1 + 1 == rationalFunction2) - } -} - -/** - * Shows [NumberedPolynomial]s' and [NumberedRationalFunction]s' capabilities. - */ -fun numberedPolynomialsExample() { - // Consider polynomial - // 3 + 5 x_2 - 7 x_1^2 x_3 - // Consider, for example, its term -7 x_1^2 x_3. -7 is a coefficient of the term, whereas (2, 0, 1, 0, 0, ...) is - // description of degrees of variables x_1, x_2, ... in the term. Such description with removed leading zeros - // [2, 0, 1] is called "signature" of the term -7 x_1^2 x_3. - - val polynomial1: NumberedPolynomial - with(Int.algebra) { - // [NumberedPolynomial] is a representation of a multivariate polynomial, that stores terms in a map with terms' - // signatures as the map's keys and terms' coefficients as corresponding values. For example, - polynomial1 = NumberedPolynomial( - mapOf( - listOf() to 3, - listOf(0u, 1u) to 5, - listOf(2u, 0u, 1u) to -7, - ) - ) - // represents polynomial 3 + 5 x_2 - 7 x_1^2 x_3 - - // This `NumberedPolynomial` function needs context of either ring of constant (as `Int.algebra` in this example) - // or space of NumberedPolynomials over it. To understand why it is like this see documentations of functions - // NumberedPolynomial and NumberedPolynomialWithoutCheck - - // There are also shortcut fabrics: - val polynomial2: NumberedPolynomial = NumberedPolynomial( - listOf() to 3, - listOf(0u, 1u) to 5, - listOf(2u, 0u, 1u) to -7, - ) - println(polynomial1 == polynomial2) // true - // and even - val polynomial3: NumberedPolynomial = 57.asNumberedPolynomial() // This one actually does not algebraic context! - val polynomial4: NumberedPolynomial = NumberedPolynomial(listOf() to 57) - println(polynomial3 == polynomial4) // true - - numberedPolynomialSpace { - // Also there is DSL for constructing NumberedPolynomials: - val polynomial5: NumberedPolynomial = NumberedPolynomialDSL1 { - 3 {} - 5 { 1 inPowerOf 1u } - -7 with { 0 pow 2u; 2 pow 1u } - // `pow` and `inPowerOf` are the same - // `with` is omittable - } - println(polynomial1 == polynomial5) // true - - // Unfortunately the DSL does not work good in bare context of constants' ring, so for now it's disabled and - // works only in NumberedPolynomialSpace and NumberedRationalFunctionSpace - } - } - - val polynomial6: NumberedPolynomial = Int.algebra { - NumberedPolynomial( - listOf() to 7, - listOf(0u, 1u) to -5, - listOf(2u, 0u, 1u) to 0, - listOf(0u, 0u, 0u, 4u) to 4, - ) - } - // For every ring there can be provided a polynomial ring: - Int.algebra.numberedPolynomialSpace { - println( - -polynomial6 == NumberedPolynomial( - listOf() to -7, - listOf(0u, 1u) to 5, - listOf(2u, 0u, 1u) to 0, - listOf(0u, 0u, 0u, 4u) to (-4), - ) - ) // true - println( - polynomial1 + polynomial6 == NumberedPolynomial( - listOf() to 10, - listOf(0u, 1u) to 0, - listOf(2u, 0u, 1u) to -7, - listOf(0u, 0u, 0u, 4u) to 4, - ) - ) // true - println( - polynomial1 - polynomial6 == NumberedPolynomial( - listOf() to -4, - listOf(0u, 1u) to 10, - listOf(2u, 0u, 1u) to -7, - listOf(0u, 0u, 0u, 4u) to -4, - ) - ) // true - - polynomial1 * polynomial6 // Multiplication works too - } - - Double.algebra.numberedPolynomialSpace { - // You can even write - val x_1: NumberedPolynomial = NumberedPolynomial(listOf(1u) to 1.0) - val x_2: NumberedPolynomial = NumberedPolynomial(listOf(0u, 1u) to 1.0) - val x_3: NumberedPolynomial = NumberedPolynomial(listOf(0u, 0u, 1u) to 1.0) - val polynomial7: NumberedPolynomial = NumberedPolynomial( - listOf() to 3.0, - listOf(0u, 1u) to 5.0, - listOf(2u, 0u, 1u) to -7.0, - ) - Double.algebra.listPolynomialSpace { - println(3 + 5 * x_2 - 7 * x_1 * x_1 * x_3 == polynomial7) - println(3.0 + 5.0 * x_2 - 7.0 * x_1 * x_1 * x_3 == polynomial7) - } - } - - Int.algebra.numberedPolynomialSpace { - val x_4: NumberedPolynomial = NumberedPolynomial(listOf(0u, 0u, 0u, 4u) to 1) - // Also there are some utilities for polynomials: - println(polynomial1.substitute(mapOf(0 to 1, 1 to -2, 2 to -1)) == 0.asNumberedPolynomial()) // true, - // because it's substitution x_1 -> 1, x_2 -> -2, x_3 -> -1, - // so 3 + 5 x_2 - 7 x_1^2 x_3 = 3 + 5 * (-2) - 7 * 1^2 * (-1) = 3 - 10 + 7 = 0 - println( - polynomial1.substitute(mapOf(1 to x_4)) == NumberedPolynomial( - listOf() to 3, - listOf(0u, 1u) to 5, - listOf(2u, 0u, 1u) to -7, - ) - ) // true, because it's substitution x_2 -> x_4, so result is 3 + 5 x_4 - 7 x_1^2 x_3 - println( - polynomial1.derivativeWithRespectTo(Int.algebra, 1) == - NumberedPolynomial(listOf() to 5) - ) // true, d/dx_2 (3 + 5 x_2 - 7 x_1^2 x_3) = 5 - } - - // Lastly, there are rational functions and some other utilities: - Double.algebra.numberedRationalFunctionSpace { - val rationalFunction1: NumberedRationalFunction = NumberedRationalFunction( - NumberedPolynomial( - listOf() to 2.0, - listOf(1u) to -3.0, - listOf(2u) to 1.0, - ), - NumberedPolynomial( - listOf() to 3.0, - listOf(1u) to -1.0, - ) - ) - // It's just (2 - 3x + x^2)/(3 - x) where x = x_1 - - val rationalFunction2: NumberedRationalFunction = NumberedRationalFunction( - NumberedPolynomial( - listOf() to 5.0, - listOf(1u) to -4.0, - listOf(2u) to 1.0, - ), - NumberedPolynomial( - listOf() to 3.0, - listOf(1u) to -1.0, - ) - ) - // It's just (5 - 4x + x^2)/(3 - x) where x = x_1 - - println(rationalFunction1 + 1 == rationalFunction2) - } -} - -/** - * Shows [LabeledPolynomial]s' and [LabeledRationalFunction]s' capabilities. - */ -fun labeledPolynomialsExample() { - val x by symbol - val y by symbol - val z by symbol - val t by symbol - - // Consider polynomial - // 3 + 5 y - 7 x^2 z - // Consider, for example, its term -7 x^2 z. -7 is a coefficient of the term, whereas matching (x -> 2, z -> 3) is - // description of degrees of variables x_1, x_2, ... in the term. Such description is called "signature" of the - // term -7 x_1^2 x_3. - - val polynomial1: LabeledPolynomial - with(Int.algebra) { - // [LabeledPolynomial] is a representation of a multivariate polynomial, that stores terms in a map with terms' - // signatures as the map's keys and terms' coefficients as corresponding values. For example, - polynomial1 = LabeledPolynomial( - mapOf( - mapOf() to 3, - mapOf(y to 1u) to 5, - mapOf(x to 2u, z to 1u) to -7, - ) - ) - // represents polynomial 3 + 5 y - 7 x^2 z - - // This `LabeledPolynomial` function needs context of either ring of constant (as `Int.algebra` in this example) - // or space of LabeledPolynomials over it. To understand why it is like this see documentations of functions - // LabeledPolynomial and LabeledPolynomialWithoutCheck - - // There are also shortcut fabrics: - val polynomial2: LabeledPolynomial = LabeledPolynomial( - mapOf() to 3, - mapOf(y to 1u) to 5, - mapOf(x to 2u, z to 1u) to -7, - ) - println(polynomial1 == polynomial2) // true - // and even - val polynomial3: LabeledPolynomial = 57.asLabeledPolynomial() // This one actually does not algebraic context! - val polynomial4: LabeledPolynomial = LabeledPolynomial(mapOf() to 57) - println(polynomial3 == polynomial4) // true - - labeledPolynomialSpace { - // Also there is DSL for constructing NumberedPolynomials: - val polynomial5: LabeledPolynomial = LabeledPolynomialDSL1 { - 3 {} - 5 { y inPowerOf 1u } - -7 with { x pow 2u; z pow 1u } - // `pow` and `inPowerOf` are the same - // `with` is omittable - } - println(polynomial1 == polynomial5) // true - - // Unfortunately the DSL does not work good in bare context of constants' ring, so for now it's disabled and - // works only in NumberedPolynomialSpace and NumberedRationalFunctionSpace - } - } - - val polynomial6: LabeledPolynomial = Int.algebra { - LabeledPolynomial( - mapOf() to 7, - mapOf(y to 1u) to -5, - mapOf(x to 2u, z to 1u) to 0, - mapOf(t to 4u) to 4, - ) - } - // For every ring there can be provided a polynomial ring: - Int.algebra.labeledPolynomialSpace { - println( - -polynomial6 == LabeledPolynomial( - mapOf() to -7, - mapOf(y to 1u) to 5, - mapOf(x to 2u, z to 1u) to 0, - mapOf(t to 4u) to -4, - ) - ) // true - println( - polynomial1 + polynomial6 == LabeledPolynomial( - mapOf() to 10, - mapOf(y to 1u) to 0, - mapOf(x to 2u, z to 1u) to -7, - mapOf(t to 4u) to 4, - ) - ) // true - println( - polynomial1 - polynomial6 == LabeledPolynomial( - mapOf() to -4, - mapOf(y to 1u) to 10, - mapOf(x to 2u, z to 1u) to -7, - mapOf(t to 4u) to -4, - ) - ) // true - - polynomial1 * polynomial6 // Multiplication works too - } - - Double.algebra.labeledPolynomialSpace { - // You can even write - val polynomial7: LabeledPolynomial = LabeledPolynomial( - mapOf() to 3.0, - mapOf(y to 1u) to 5.0, - mapOf(x to 2u, z to 1u) to -7.0, - ) - Double.algebra.listPolynomialSpace { - println(3 + 5 * y - 7 * x * x * z == polynomial7) - println(3.0 + 5.0 * y - 7.0 * x * x * z == polynomial7) - } - } - - Int.algebra.labeledPolynomialSpace { - // Also there are some utilities for polynomials: - println(polynomial1.substitute(mapOf(x to 1, y to -2, z to -1)) == 0.asLabeledPolynomial()) // true, - // because it's substitution x -> 1, y -> -2, z -> -1, - // so 3 + 5 y - 7 x^2 z = 3 + 5 * (-2) - 7 * 1^2 * (-1) = 3 - 10 + 7 = 0 - println( - polynomial1.substitute(mapOf(y to t.asPolynomial())) == LabeledPolynomial( - mapOf() to 3, - mapOf(t to 1u) to 5, - mapOf(x to 2u, z to 1u) to -7, - ) - ) // true, because it's substitution y -> t, so result is 3 + 5 t - 7 x^2 z - println( - polynomial1.derivativeWithRespectTo(Int.algebra, y) == LabeledPolynomial(mapOf() to 5) - ) // true, d/dy (3 + 5 y - 7 x^2 z) = 5 - } - - // Lastly, there are rational functions and some other utilities: - Double.algebra.labeledRationalFunctionSpace { - val rationalFunction1: LabeledRationalFunction = LabeledRationalFunction( - LabeledPolynomial( - mapOf() to 2.0, - mapOf(x to 1u) to -3.0, - mapOf(x to 2u) to 1.0, - ), - LabeledPolynomial( - mapOf() to 3.0, - mapOf(x to 1u) to -1.0, - ) - ) - // It's just (2 - 3x + x^2)/(3 - x) - - val rationalFunction2: LabeledRationalFunction = LabeledRationalFunction( - LabeledPolynomial( - mapOf() to 5.0, - mapOf(x to 1u) to -4.0, - mapOf(x to 2u) to 1.0, - ), - LabeledPolynomial( - mapOf() to 3.0, - mapOf(x to 1u) to -1.0, - ) - ) - // It's just (5 - 4x + x^2)/(3 - x) - - println(rationalFunction1 + 1 == rationalFunction2) - } -} - -fun main() { - println("ListPolynomials:") - listPolynomialsExample() - println() - - println("NumberedPolynomials:") - numberedPolynomialsExample() - println() - - println("ListPolynomials:") - labeledPolynomialsExample() - println() -} diff --git a/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt b/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt index 8fc6e1b06..4a5d783e1 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt @@ -8,14 +8,14 @@ package space.kscience.kmath.operations import space.kscience.kmath.commons.linear.CMLinearSpace import space.kscience.kmath.linear.matrix import space.kscience.kmath.nd.DoubleBufferND -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.Structure2D import space.kscience.kmath.nd.ndAlgebra import space.kscience.kmath.viktor.ViktorStructureND import space.kscience.kmath.viktor.viktorAlgebra fun main() { - val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.structureND(Shape(2, 2)) { (i, j) -> + val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.structureND(ShapeND(2, 2)) { (i, j) -> if (i == j) 2.0 else 0.0 } diff --git a/examples/src/main/kotlin/space/kscience/kmath/series/analyzeDif.kt b/examples/src/main/kotlin/space/kscience/kmath/series/analyzeDif.kt new file mode 100644 index 000000000..c1b0c056e --- /dev/null +++ b/examples/src/main/kotlin/space/kscience/kmath/series/analyzeDif.kt @@ -0,0 +1,49 @@ +package space.kscience.kmath.series + + +import kotlinx.html.FlowContent +import kotlinx.html.h1 +import space.kscience.kmath.operations.DoubleBufferOps +import space.kscience.kmath.operations.algebra +import space.kscience.kmath.operations.bufferAlgebra +import space.kscience.kmath.operations.toList +import space.kscience.kmath.stat.KMComparisonResult +import space.kscience.kmath.stat.ksComparisonStatistic +import space.kscience.kmath.structures.Buffer +import space.kscience.kmath.structures.slice +import space.kscience.plotly.* +import kotlin.math.PI + +fun main() = with(Double.algebra.bufferAlgebra.seriesAlgebra()) { + fun FlowContent.plotSeries(buffer: Buffer) { + val ls = buffer.labels + plot { + scatter { + x.numbers = ls + y.numbers = buffer.toList() + } + layout { + xaxis { + range(0.0..100.0) + } + } + } + } + + + val s1 = series(100) { sin(2 * PI * it / 100) + 1.0 } + val s2 = s1.slice(20..50).moveTo(40) + + val s3: Buffer = s1.zip(s2) { l, r -> l + r } //s1 + s2 + val s4 = DoubleBufferOps.ln(s3) + + val kmTest: KMComparisonResult = ksComparisonStatistic(s1, s2) + + Plotly.page { + h1 { +"This is my plot" } + plotSeries(s1) + plotSeries(s2) + plotSeries(s4) + }.makeFile() + +} \ No newline at end of file diff --git a/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionBenchmark.kt b/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionBenchmark.kt index bdbf42797..2576e9222 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionBenchmark.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionBenchmark.kt @@ -10,6 +10,7 @@ import kotlinx.coroutines.async import kotlinx.coroutines.runBlocking import org.apache.commons.rng.sampling.distribution.BoxMullerNormalizedGaussianSampler import org.apache.commons.rng.simple.RandomSource +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.samplers.GaussianSampler import java.time.Duration import java.time.Instant diff --git a/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionDemo.kt b/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionDemo.kt index 3de9b6f34..8e6d096ed 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionDemo.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/stat/DistributionDemo.kt @@ -9,6 +9,7 @@ import kotlinx.coroutines.runBlocking import space.kscience.kmath.chains.Chain import space.kscience.kmath.chains.combineWithState import space.kscience.kmath.distributions.NormalDistribution +import space.kscience.kmath.random.RandomGenerator private data class AveragingChainState(var num: Int = 0, var value: Double = 0.0) diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt index 48d14cb4c..ba8f047a8 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt @@ -29,7 +29,7 @@ fun main() { Nd4j.zeros(0) val dim = 1000 val n = 1000 - val shape = Shape(dim, dim) + val shape = ShapeND(dim, dim) // specialized nd-field for Double. It works as generic Double field as well. diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt index 4aa420305..67c9b421f 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt @@ -17,11 +17,11 @@ import java.util.stream.IntStream * A demonstration implementation of NDField over Real using Java [java.util.stream.DoubleStream] for parallel * execution. */ -class StreamDoubleFieldND(override val shape: IntArray) : FieldND, +class StreamDoubleFieldND(override val shape: ShapeND) : FieldND, NumbersAddOps>, ExtendedField> { - private val strides = DefaultStrides(shape) + private val strides = ColumnStrides(shape) override val elementAlgebra: DoubleField get() = DoubleField override val zero: BufferND by lazy { structureND(shape) { zero } } override val one: BufferND by lazy { structureND(shape) { one } } @@ -31,17 +31,19 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND.buffer: DoubleBuffer get() = when { !shape.contentEquals(this@StreamDoubleFieldND.shape) -> throw ShapeMismatchException( this@StreamDoubleFieldND.shape, shape ) - this is BufferND && this.indices == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer + + this is BufferND && indices == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) } } - override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): BufferND { + override fun structureND(shape: ShapeND, initializer: DoubleField.(IntArray) -> Double): BufferND { val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset -> val index = strides.index(offset) DoubleField.initializer(index) @@ -109,4 +111,4 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND): BufferND = arg.map { atanh(it) } } -fun DoubleField.ndStreaming(vararg shape: Int): StreamDoubleFieldND = StreamDoubleFieldND(shape) +fun DoubleField.ndStreaming(vararg shape: Int): StreamDoubleFieldND = StreamDoubleFieldND(ShapeND(shape)) diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/StructureReadBenchmark.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/StructureReadBenchmark.kt index a64ac7280..e3e7daaae 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/structures/StructureReadBenchmark.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/structures/StructureReadBenchmark.kt @@ -5,16 +5,19 @@ package space.kscience.kmath.structures +import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.nd.BufferND -import space.kscience.kmath.nd.DefaultStrides +import space.kscience.kmath.nd.ColumnStrides +import space.kscience.kmath.nd.ShapeND import kotlin.system.measureTimeMillis @Suppress("ASSIGNED_BUT_NEVER_ACCESSED_VARIABLE") +@OptIn(PerformancePitfall::class) fun main() { val n = 6000 val array = DoubleArray(n * n) { 1.0 } val buffer = DoubleBuffer(array) - val strides = DefaultStrides(intArrayOf(n, n)) + val strides = ColumnStrides(ShapeND(n, n)) val structure = BufferND(strides, buffer) measureTimeMillis { diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/StructureWriteBenchmark.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/StructureWriteBenchmark.kt index ce5301a7b..14c058417 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/structures/StructureWriteBenchmark.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/structures/StructureWriteBenchmark.kt @@ -5,16 +5,23 @@ package space.kscience.kmath.structures +import space.kscience.kmath.nd.BufferND +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND -import space.kscience.kmath.nd.mapToBuffer +import space.kscience.kmath.operations.mapToBuffer import kotlin.system.measureTimeMillis +private inline fun BufferND.mapToBufferND( + bufferFactory: BufferFactory = BufferFactory.auto(), + crossinline block: (T) -> R, +): BufferND = BufferND(indices, buffer.mapToBuffer(bufferFactory, block)) + @Suppress("UNUSED_VARIABLE") fun main() { val n = 6000 - val structure = StructureND.buffered(intArrayOf(n, n), Buffer.Companion::auto) { 1.0 } - structure.mapToBuffer { it + 1 } // warm-up - val time1 = measureTimeMillis { val res = structure.mapToBuffer { it + 1 } } + val structure = StructureND.buffered(ShapeND(n, n), Buffer.Companion::auto) { 1.0 } + structure.mapToBufferND { it + 1 } // warm-up + val time1 = measureTimeMillis { val res = structure.mapToBufferND { it + 1 } } println("Structure mapping finished in $time1 millis") val array = DoubleArray(n * n) { 1.0 } diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/OLSWithSVD.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/OLSWithSVD.kt index d0b24de70..2c570ea34 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/tensors/OLSWithSVD.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/OLSWithSVD.kt @@ -5,16 +5,17 @@ package space.kscience.kmath.tensors -import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.contentEquals import space.kscience.kmath.operations.invoke import space.kscience.kmath.tensors.core.DoubleTensor import space.kscience.kmath.tensors.core.DoubleTensorAlgebra - +import space.kscience.kmath.tensors.core.randomNormal +import space.kscience.kmath.tensors.core.randomNormalLike import kotlin.math.abs // OLS estimator using SVD -@OptIn(PerformancePitfall::class) fun main() { //seed for random val randSeed = 100500L @@ -23,10 +24,10 @@ fun main() { DoubleTensorAlgebra { // take coefficient vector from normal distribution val alpha = randomNormal( - intArrayOf(5), + ShapeND(5), randSeed ) + fromArray( - intArrayOf(5), + ShapeND(5), doubleArrayOf(1.0, 2.5, 3.4, 5.0, 10.1) ) @@ -34,27 +35,29 @@ fun main() { // also take sample of size 20 from normal distribution for x val x = randomNormal( - intArrayOf(20, 5), + ShapeND(20, 5), randSeed ) // calculate y and add gaussian noise (N(0, 0.05)) val y = x dot alpha - y += y.randomNormalLike(randSeed) * 0.05 + y += randomNormalLike(y, randSeed) * 0.05 // now restore the coefficient vector with OSL estimator with SVD - val (u, singValues, v) = x.svd() + val (u, singValues, v) = svd(x) // we have to make sure the singular values of the matrix are not close to zero println("Singular values:\n$singValues") // inverse Sigma matrix can be restored from singular values with diagonalEmbedding function - val sigma = diagonalEmbedding(singValues.map{ if (abs(it) < 1e-3) 0.0 else 1.0/it }) + val sigma = diagonalEmbedding(singValues.map { if (abs(it) < 1e-3) 0.0 else 1.0 / it }) val alphaOLS = v dot sigma dot u.transposed() dot y - println("Estimated alpha:\n" + - "$alphaOLS") + println( + "Estimated alpha:\n" + + "$alphaOLS" + ) // figure out MSE of approximation fun mse(yTrue: DoubleTensor, yPred: DoubleTensor): Double { @@ -62,7 +65,7 @@ fun main() { require(yTrue.shape contentEquals yPred.shape) val diff = yTrue - yPred - return diff.dot(diff).sqrt().value() + return sqrt(diff.dot(diff)).value() } println("MSE: ${mse(alpha, alphaOLS)}") diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/PCA.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/PCA.kt index 1768be283..fb774a39d 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/tensors/PCA.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/PCA.kt @@ -5,8 +5,8 @@ package space.kscience.kmath.tensors -import space.kscience.kmath.tensors.core.tensorAlgebra -import space.kscience.kmath.tensors.core.withBroadcast +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.tensors.core.* // simple PCA @@ -16,12 +16,12 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast { // work in context with // assume x is range from 0 until 10 val x = fromArray( - intArrayOf(10), + ShapeND(10), DoubleArray(10) { it.toDouble() } ) // take y dependent on x with noise - val y = 2.0 * x + (3.0 + x.randomNormalLike(seed) * 1.5) + val y = 2.0 * x + (3.0 + randomNormalLike(x, seed) * 1.5) println("x:\n$x") println("y:\n$y") @@ -30,34 +30,34 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast { // work in context with val dataset = stack(listOf(x, y)).transposed() // normalize both x and y - val xMean = x.mean() - val yMean = y.mean() + val xMean = mean(x) + val yMean = mean(y) - val xStd = x.std() - val yStd = y.std() + val xStd = std(x) + val yStd = std(y) - val xScaled = (x - xMean) / xStd - val yScaled = (y - yMean) / yStd + val xScaled: DoubleTensor = (x - xMean) / xStd + val yScaled: DoubleTensor = (y - yMean) / yStd // save means ans standard deviations for further recovery val mean = fromArray( - intArrayOf(2), + ShapeND(2), doubleArrayOf(xMean, yMean) ) println("Means:\n$mean") val std = fromArray( - intArrayOf(2), + ShapeND(2), doubleArrayOf(xStd, yStd) ) println("Standard deviations:\n$std") // calculate the covariance matrix of scaled x and y - val covMatrix = cov(listOf(xScaled, yScaled)) + val covMatrix = covariance(listOf(xScaled.asDoubleTensor1D(), yScaled.asDoubleTensor1D())) println("Covariance matrix:\n$covMatrix") // and find out eigenvector of it - val (_, evecs) = covMatrix.symEig() + val (_, evecs) = symEig(covMatrix) val v = evecs.getTensor(0) println("Eigenvector:\n$v") @@ -68,7 +68,7 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast { // work in context with // we can restore original data from reduced data; // for example, find 7th element of dataset. val n = 7 - val restored = (datasetReduced.getTensor(n) dot v.view(intArrayOf(1, 2))) * std + mean + val restored = (datasetReduced.getTensor(n) dot v.view(ShapeND(1, 2))) * std + mean println("Original value:\n${dataset.getTensor(n)}") println("Restored value:\n$restored") } diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/dataSetNormalization.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/dataSetNormalization.kt index 6d72fd623..45c2ff120 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/tensors/dataSetNormalization.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/dataSetNormalization.kt @@ -5,6 +5,8 @@ package space.kscience.kmath.tensors +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.tensors.core.randomNormal import space.kscience.kmath.tensors.core.tensorAlgebra import space.kscience.kmath.tensors.core.withBroadcast @@ -13,17 +15,17 @@ import space.kscience.kmath.tensors.core.withBroadcast fun main() = Double.tensorAlgebra.withBroadcast { // work in context with broadcast methods // take dataset of 5-element vectors from normal distribution - val dataset = randomNormal(intArrayOf(100, 5)) * 1.5 // all elements from N(0, 1.5) + val dataset = randomNormal(ShapeND(100, 5)) * 1.5 // all elements from N(0, 1.5) dataset += fromArray( - intArrayOf(5), + ShapeND(5), doubleArrayOf(0.0, 1.0, 1.5, 3.0, 5.0) // row means ) // find out mean and standard deviation of each column - val mean = dataset.mean(0, false) - val std = dataset.std(0, false) + val mean = mean(dataset, 0, false) + val std = std(dataset, 0, false) println("Mean:\n$mean") println("Standard deviation:\n$std") @@ -35,8 +37,8 @@ fun main() = Double.tensorAlgebra.withBroadcast { // work in context with broad // now we can scale dataset with mean normalization val datasetScaled = (dataset - mean) / std - // find out mean and std of scaled dataset + // find out mean and standardDiviation of scaled dataset - println("Mean of scaled:\n${datasetScaled.mean(0, false)}") - println("Mean of scaled:\n${datasetScaled.std(0, false)}") + println("Mean of scaled:\n${mean(datasetScaled, 0, false)}") + println("Mean of scaled:\n${std(datasetScaled, 0, false)}") } \ No newline at end of file diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/linearSystemSolvingWithLUP.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/linearSystemSolvingWithLUP.kt index 64cc138d7..238696cf9 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/tensors/linearSystemSolvingWithLUP.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/linearSystemSolvingWithLUP.kt @@ -5,6 +5,7 @@ package space.kscience.kmath.tensors +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.tensors.core.DoubleTensor import space.kscience.kmath.tensors.core.tensorAlgebra import space.kscience.kmath.tensors.core.withBroadcast @@ -15,13 +16,13 @@ fun main() = Double.tensorAlgebra.withBroadcast {// work in context with linear // set true value of x val trueX = fromArray( - intArrayOf(4), + ShapeND(4), doubleArrayOf(-2.0, 1.5, 6.8, -2.4) ) // and A matrix val a = fromArray( - intArrayOf(4, 4), + ShapeND(4, 4), doubleArrayOf( 0.5, 10.5, 4.5, 1.0, 8.5, 0.9, 12.8, 0.1, @@ -40,7 +41,7 @@ fun main() = Double.tensorAlgebra.withBroadcast {// work in context with linear // solve `Ax = b` system using LUP decomposition // get P, L, U such that PA = LU - val (p, l, u) = a.lu() + val (p, l, u) = lu(a) // check P is permutation matrix println("P:\n$p") @@ -64,7 +65,7 @@ fun main() = Double.tensorAlgebra.withBroadcast {// work in context with linear // this function returns solution x of a system lx = b, l should be lower triangular fun solveLT(l: DoubleTensor, b: DoubleTensor): DoubleTensor { val n = l.shape[0] - val x = zeros(intArrayOf(n)) + val x = zeros(ShapeND(n)) for (i in 0 until n) { x[intArrayOf(i)] = (b[intArrayOf(i)] - l.getTensor(i).dot(x).value()) / l[intArrayOf(i, i)] } diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/neuralNetwork.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/neuralNetwork.kt index 84d6dcd22..8fd5ae5ad 100644 --- a/examples/src/main/kotlin/space/kscience/kmath/tensors/neuralNetwork.kt +++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/neuralNetwork.kt @@ -5,12 +5,11 @@ package space.kscience.kmath.tensors +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.contentEquals import space.kscience.kmath.operations.asIterable import space.kscience.kmath.operations.invoke -import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra -import space.kscience.kmath.tensors.core.DoubleTensor -import space.kscience.kmath.tensors.core.DoubleTensorAlgebra -import space.kscience.kmath.tensors.core.toDoubleTensor +import space.kscience.kmath.tensors.core.* import kotlin.math.sqrt const val seed = 100500L @@ -49,7 +48,7 @@ fun reluDer(x: DoubleTensor): DoubleTensor = DoubleTensorAlgebra { class ReLU : Activation(::relu, ::reluDer) fun sigmoid(x: DoubleTensor): DoubleTensor = DoubleTensorAlgebra { - 1.0 / (1.0 + (-x).exp()) + 1.0 / (1.0 + exp((-x))) } fun sigmoidDer(x: DoubleTensor): DoubleTensor = DoubleTensorAlgebra { @@ -68,12 +67,12 @@ class Dense( private val weights: DoubleTensor = DoubleTensorAlgebra { randomNormal( - intArrayOf(inputUnits, outputUnits), + ShapeND(inputUnits, outputUnits), seed ) * sqrt(2.0 / (inputUnits + outputUnits)) } - private val bias: DoubleTensor = DoubleTensorAlgebra { zeros(intArrayOf(outputUnits)) } + private val bias: DoubleTensor = DoubleTensorAlgebra { zeros(ShapeND(outputUnits)) } override fun forward(input: DoubleTensor): DoubleTensor = BroadcastDoubleTensorAlgebra { (input dot weights) + bias @@ -83,7 +82,7 @@ class Dense( val gradInput = outputError dot weights.transposed() val gradW = input.transposed() dot outputError - val gradBias = outputError.mean(dim = 0, keepDim = false) * input.shape[0].toDouble() + val gradBias = mean(structureND = outputError, dim = 0, keepDim = false) * input.shape[0].toDouble() weights -= learningRate * gradW bias -= learningRate * gradBias @@ -116,7 +115,7 @@ class NeuralNetwork(private val layers: List) { onesForAnswers[intArrayOf(index, label)] = 1.0 } - val softmaxValue = yPred.exp() / yPred.exp().sum(dim = 1, keepDim = true) + val softmaxValue = exp(yPred) / exp(yPred).sum(dim = 1, keepDim = true) (-onesForAnswers + softmaxValue) / (yPred.shape[0].toDouble()) } @@ -174,7 +173,6 @@ class NeuralNetwork(private val layers: List) { } -@OptIn(ExperimentalStdlibApi::class) fun main() = BroadcastDoubleTensorAlgebra { val features = 5 val sampleSize = 250 @@ -182,17 +180,17 @@ fun main() = BroadcastDoubleTensorAlgebra { //val testSize = sampleSize - trainSize // take sample of features from normal distribution - val x = randomNormal(intArrayOf(sampleSize, features), seed) * 2.5 + val x = randomNormal(ShapeND(sampleSize, features), seed) * 2.5 x += fromArray( - intArrayOf(5), + ShapeND(5), doubleArrayOf(0.0, -1.0, -2.5, -3.0, 5.5) // row means ) // define class like '1' if the sum of features > 0 and '0' otherwise val y = fromArray( - intArrayOf(sampleSize, 1), + ShapeND(sampleSize, 1), DoubleArray(sampleSize) { i -> if (x.getTensor(i).sum() > 0.0) { 1.0 diff --git a/gradle.properties b/gradle.properties index 0d1506980..da5867ea4 100644 --- a/gradle.properties +++ b/gradle.properties @@ -3,13 +3,15 @@ # Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. # kotlin.code.style=official -kotlin.jupyter.add.scanner=false kotlin.mpp.stability.nowarn=true kotlin.native.ignoreDisabledTargets=true kotlin.incremental.js.ir=true org.gradle.configureondemand=true -org.gradle.parallel=true org.gradle.jvmargs=-Xmx4096m -toolsVersion=0.13.0-kotlin-1.7.20-Beta +toolsVersion=0.13.1-kotlin-1.7.20 + + +org.gradle.parallel=true +org.gradle.workers.max=4 diff --git a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/random/CMRandomGeneratorWrapper.kt b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/random/CMRandomGeneratorWrapper.kt index c7a23ebc4..32962659f 100644 --- a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/random/CMRandomGeneratorWrapper.kt +++ b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/random/CMRandomGeneratorWrapper.kt @@ -6,12 +6,12 @@ package space.kscience.kmath.commons.random import kotlinx.coroutines.runBlocking -import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.samplers.GaussianSampler import space.kscience.kmath.misc.toIntExact -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator +import space.kscience.kmath.samplers.GaussianSampler import space.kscience.kmath.stat.next + public class CMRandomGeneratorWrapper( public val factory: (IntArray) -> RandomGenerator, ) : org.apache.commons.math3.random.RandomGenerator { diff --git a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/transform/Transformations.kt b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/transform/Transformations.kt index 2243dc5d9..a77da2d2f 100644 --- a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/transform/Transformations.kt +++ b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/transform/Transformations.kt @@ -10,28 +10,18 @@ import kotlinx.coroutines.flow.Flow import kotlinx.coroutines.flow.map import org.apache.commons.math3.transform.* import space.kscience.kmath.complex.Complex -import space.kscience.kmath.operations.SuspendBufferTransform +import space.kscience.kmath.operations.BufferTransform import space.kscience.kmath.streaming.chunked import space.kscience.kmath.streaming.spread -import space.kscience.kmath.structures.Buffer -import space.kscience.kmath.structures.DoubleBuffer -import space.kscience.kmath.structures.VirtualBuffer -import space.kscience.kmath.structures.asBuffer - +import space.kscience.kmath.structures.* /** - * Streaming and buffer transformations + * Streaming and buffer transformations with Commons-math algorithms */ public object Transformations { - private fun Buffer.toArray(): Array = + private fun Buffer.toCmComplexArray(): Array = Array(size) { org.apache.commons.math3.complex.Complex(get(it).re, get(it).im) } - private fun Buffer.asArray() = if (this is DoubleBuffer) { - array - } else { - DoubleArray(size) { i -> get(i) } - } - /** * Create a virtual buffer on top of array */ @@ -43,70 +33,67 @@ public object Transformations { public fun fourier( normalization: DftNormalization = DftNormalization.STANDARD, direction: TransformType = TransformType.FORWARD, - ): SuspendBufferTransform = { - FastFourierTransformer(normalization).transform(it.toArray(), direction).asBuffer() + ): BufferTransform = BufferTransform { + FastFourierTransformer(normalization).transform(it.toCmComplexArray(), direction).asBuffer() } public fun realFourier( normalization: DftNormalization = DftNormalization.STANDARD, direction: TransformType = TransformType.FORWARD, - ): SuspendBufferTransform = { - FastFourierTransformer(normalization).transform(it.asArray(), direction).asBuffer() + ): BufferTransform = BufferTransform { + FastFourierTransformer(normalization).transform(it.toDoubleArray(), direction).asBuffer() } public fun sine( normalization: DstNormalization = DstNormalization.STANDARD_DST_I, direction: TransformType = TransformType.FORWARD, - ): SuspendBufferTransform = { - FastSineTransformer(normalization).transform(it.asArray(), direction).asBuffer() + ): BufferTransform = DoubleBufferTransform { + FastSineTransformer(normalization).transform(it.array, direction).asBuffer() } public fun cosine( normalization: DctNormalization = DctNormalization.STANDARD_DCT_I, direction: TransformType = TransformType.FORWARD, - ): SuspendBufferTransform = { - FastCosineTransformer(normalization).transform(it.asArray(), direction).asBuffer() + ): BufferTransform = BufferTransform { + FastCosineTransformer(normalization).transform(it.toDoubleArray(), direction).asBuffer() } public fun hadamard( direction: TransformType = TransformType.FORWARD, - ): SuspendBufferTransform = { - FastHadamardTransformer().transform(it.asArray(), direction).asBuffer() + ): BufferTransform = DoubleBufferTransform { + FastHadamardTransformer().transform(it.array, direction).asBuffer() } } /** * Process given [Flow] with commons-math fft transformation */ -@FlowPreview -public fun Flow>.FFT( +public fun Flow>.fft( normalization: DftNormalization = DftNormalization.STANDARD, direction: TransformType = TransformType.FORWARD, ): Flow> { val transform = Transformations.fourier(normalization, direction) - return map { transform(it) } + return map(transform::transform) } -@FlowPreview @JvmName("realFFT") -public fun Flow>.FFT( +public fun Flow>.fft( normalization: DftNormalization = DftNormalization.STANDARD, direction: TransformType = TransformType.FORWARD, ): Flow> { val transform = Transformations.realFourier(normalization, direction) - return map(transform) + return map(transform::transform) } /** * Process a continuous flow of real numbers in FFT splitting it in chunks of [bufferSize]. */ -@FlowPreview @JvmName("realFFT") -public fun Flow.FFT( +public fun Flow.fft( bufferSize: Int = Int.MAX_VALUE, normalization: DftNormalization = DftNormalization.STANDARD, direction: TransformType = TransformType.FORWARD, -): Flow = chunked(bufferSize).FFT(normalization, direction).spread() +): Flow = chunked(bufferSize).fft(normalization, direction).spread() /** * Map a complex flow into real flow by taking real part of each number diff --git a/kmath-commons/src/test/kotlin/space/kscience/kmath/commons/optimization/OptimizeTest.kt b/kmath-commons/src/test/kotlin/space/kscience/kmath/commons/optimization/OptimizeTest.kt index b1b7b3ed7..7c8ba7d27 100644 --- a/kmath-commons/src/test/kotlin/space/kscience/kmath/commons/optimization/OptimizeTest.kt +++ b/kmath-commons/src/test/kotlin/space/kscience/kmath/commons/optimization/OptimizeTest.kt @@ -13,12 +13,11 @@ import space.kscience.kmath.expressions.Symbol.Companion.x import space.kscience.kmath.expressions.Symbol.Companion.y import space.kscience.kmath.expressions.chiSquaredExpression import space.kscience.kmath.expressions.symbol -import space.kscience.kmath.operations.map +import space.kscience.kmath.operations.DoubleBufferOps.Companion.map import space.kscience.kmath.optimization.* -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.structures.DoubleBuffer import space.kscience.kmath.structures.asBuffer -import kotlin.math.pow import kotlin.test.Test internal class OptimizeTest { diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt index 5804e47c1..7bf8af4e8 100644 --- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt +++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt @@ -193,7 +193,6 @@ public object ComplexField : * @property re The real part. * @property im The imaginary part. */ -@OptIn(UnstableKMathAPI::class) public data class Complex(val re: Double, val im: Double) { public constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble()) public constructor(re: Number) : this(re.toDouble(), 0.0) diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt index 42914ed5b..06f6cad85 100644 --- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt +++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt @@ -5,6 +5,7 @@ package space.kscience.kmath.complex +import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.nd.* import space.kscience.kmath.operations.* @@ -20,6 +21,7 @@ import kotlin.contracts.contract public sealed class ComplexFieldOpsND : BufferedFieldOpsND(ComplexField.bufferAlgebra), ScaleOperations>, ExtendedFieldOps>, PowerOperations> { + @OptIn(PerformancePitfall::class) override fun StructureND.toBufferND(): BufferND = when (this) { is BufferND -> this else -> { @@ -57,7 +59,7 @@ public sealed class ComplexFieldOpsND : BufferedFieldOpsND, NumbersAddOps> { @@ -69,12 +71,12 @@ public class ComplexFieldND(override val shape: Shape) : public val ComplexField.ndAlgebra: ComplexFieldOpsND get() = ComplexFieldOpsND -public fun ComplexField.ndAlgebra(vararg shape: Int): ComplexFieldND = ComplexFieldND(shape) +public fun ComplexField.ndAlgebra(vararg shape: Int): ComplexFieldND = ComplexFieldND(ShapeND(shape)) /** * Produce a context for n-dimensional operations inside this real field */ public inline fun ComplexField.withNdAlgebra(vararg shape: Int, action: ComplexFieldND.() -> R): R { contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) } - return ComplexFieldND(shape).action() + return ComplexFieldND(ShapeND(shape)).action() } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSAlgebra.kt index fa8bf5e58..e7ade4f66 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSAlgebra.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSAlgebra.kt @@ -268,7 +268,7 @@ public open class DSRing( protected fun DS.mapData(block: A.(T) -> T): DS { require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" } - val newData: Buffer = data.map(valueBufferFactory) { + val newData: Buffer = data.mapToBuffer(valueBufferFactory) { algebra.block(it) } return DS(newData) @@ -276,7 +276,7 @@ public open class DSRing( protected fun DS.mapDataIndexed(block: (Int, T) -> T): DS { require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" } - val newData: Buffer = data.mapIndexed(valueBufferFactory, block) + val newData: Buffer = data.mapIndexedToBuffer(valueBufferFactory, block) return DS(newData) } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/specialExpressions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/specialExpressions.kt index 8cfa1b353..59dfeb8ea 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/specialExpressions.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/specialExpressions.kt @@ -11,6 +11,8 @@ import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.indices import kotlin.jvm.JvmName +//TODO move to stat + /** * Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic * differentiation. diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt index 361d59be1..5976b67b1 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt @@ -6,9 +6,7 @@ package space.kscience.kmath.linear import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.BufferedRingOpsND -import space.kscience.kmath.nd.as2D -import space.kscience.kmath.nd.asND +import space.kscience.kmath.nd.* import space.kscience.kmath.operations.* import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.VirtualBuffer @@ -23,7 +21,7 @@ public class BufferedLinearSpace>( private val ndAlgebra = BufferedRingOpsND(bufferAlgebra) override fun buildMatrix(rows: Int, columns: Int, initializer: A.(i: Int, j: Int) -> T): Matrix = - ndAlgebra.structureND(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D() + ndAlgebra.structureND(ShapeND(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D() override fun buildVector(size: Int, initializer: A.(Int) -> T): Point = bufferAlgebra.buffer(size) { elementAlgebra.initializer(it) } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt index e2f81d84e..4e7ab55ef 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt @@ -6,9 +6,7 @@ package space.kscience.kmath.linear import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.DoubleFieldOpsND -import space.kscience.kmath.nd.as2D -import space.kscience.kmath.nd.asND +import space.kscience.kmath.nd.* import space.kscience.kmath.operations.DoubleBufferOps import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.operations.invoke @@ -23,7 +21,7 @@ public object DoubleLinearSpace : LinearSpace { rows: Int, columns: Int, initializer: DoubleField.(i: Int, j: Int) -> Double - ): Matrix = DoubleFieldOpsND.structureND(intArrayOf(rows, columns)) { (i, j) -> + ): Matrix = DoubleFieldOpsND.structureND(ShapeND(rows, columns)) { (i, j) -> DoubleField.initializer(i, j) }.as2D() diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/VirtualMatrix.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/VirtualMatrix.kt index eb5e20856..55b970f4a 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/VirtualMatrix.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/VirtualMatrix.kt @@ -5,6 +5,9 @@ package space.kscience.kmath.linear +import space.kscience.kmath.nd.ShapeND + + /** * The matrix where each element is evaluated each time when is being accessed. * @@ -16,7 +19,7 @@ public class VirtualMatrix( public val generator: (i: Int, j: Int) -> T, ) : Matrix { - override val shape: IntArray get() = intArrayOf(rowNum, colNum) + override val shape: ShapeND get() = ShapeND(rowNum, colNum) override operator fun get(i: Int, j: Int): T = generator(i, j) } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/misc/annotations.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/misc/annotations.kt index f7b486850..7da333a45 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/misc/annotations.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/misc/annotations.kt @@ -29,3 +29,16 @@ public annotation class UnstableKMathAPI public annotation class PerformancePitfall( val message: String = "Potential performance problem", ) + +/** + * Marks API that is public, but should not be used without clear understanding what it does. + */ +@MustBeDocumented +@Retention(value = AnnotationRetention.BINARY) +@RequiresOptIn( + "This API is unsafe and should be used carefully", + RequiresOptIn.Level.ERROR, +) +public annotation class UnsafeKMathAPI( + val message: String = "Unsafe API", +) diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt index 101f90160..d53f5488a 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt @@ -25,7 +25,7 @@ public interface AlgebraND>: Algebra> { /** * Produces a new [StructureND] using given initializer function. */ - public fun structureND(shape: Shape, initializer: C.(IntArray) -> T): StructureND + public fun structureND(shape: ShapeND, initializer: C.(IntArray) -> T): StructureND /** * Maps elements from one structure to another one by applying [transform] to them. diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt index 4025ba548..781d2e367 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt @@ -12,11 +12,11 @@ import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.operations.* public interface BufferAlgebraND> : AlgebraND { - public val indexerBuilder: (IntArray) -> ShapeIndexer + public val indexerBuilder: (ShapeND) -> ShapeIndexer public val bufferAlgebra: BufferAlgebra override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra - override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): BufferND { + override fun structureND(shape: ShapeND, initializer: A.(IntArray) -> T): BufferND { val indexer = indexerBuilder(shape) return BufferND( indexer, @@ -26,6 +26,7 @@ public interface BufferAlgebraND> : AlgebraND { ) } + @OptIn(PerformancePitfall::class) public fun StructureND.toBufferND(): BufferND = when (this) { is BufferND -> this else -> { @@ -46,7 +47,7 @@ public interface BufferAlgebraND> : AlgebraND { zipInline(left.toBufferND(), right.toBufferND(), transform) public companion object { - public val defaultIndexerBuilder: (IntArray) -> ShapeIndexer = ::Strides + public val defaultIndexerBuilder: (ShapeND) -> ShapeIndexer = ::Strides } } @@ -98,24 +99,24 @@ internal inline fun > BufferAlgebraND.zipInline( @OptIn(PerformancePitfall::class) public open class BufferedGroupNDOps>( override val bufferAlgebra: BufferAlgebra, - override val indexerBuilder: (IntArray) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, + override val indexerBuilder: (ShapeND) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, ) : GroupOpsND, BufferAlgebraND { override fun StructureND.unaryMinus(): StructureND = map { -it } } public open class BufferedRingOpsND>( bufferAlgebra: BufferAlgebra, - indexerBuilder: (IntArray) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, + indexerBuilder: (ShapeND) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, ) : BufferedGroupNDOps(bufferAlgebra, indexerBuilder), RingOpsND public open class BufferedFieldOpsND>( bufferAlgebra: BufferAlgebra, - indexerBuilder: (IntArray) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, + indexerBuilder: (ShapeND) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, ) : BufferedRingOpsND(bufferAlgebra, indexerBuilder), FieldOpsND { public constructor( elementAlgebra: A, - indexerBuilder: (IntArray) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, + indexerBuilder: (ShapeND) -> ShapeIndexer = BufferAlgebraND.defaultIndexerBuilder, ) : this(BufferFieldOps(elementAlgebra), indexerBuilder) @OptIn(PerformancePitfall::class) @@ -130,7 +131,7 @@ public val > BufferAlgebra.nd: BufferedFieldOpsND ge public fun > BufferAlgebraND.structureND( vararg shape: Int, initializer: A.(IntArray) -> T, -): BufferND = structureND(shape, initializer) +): BufferND = structureND(ShapeND(shape), initializer) public fun , A> A.structureND( initializer: EA.(IntArray) -> T, diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt index 1eb08fa8c..55e8bbcf8 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt @@ -5,10 +5,9 @@ package space.kscience.kmath.nd +import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.structures.Buffer -import space.kscience.kmath.structures.BufferFactory import space.kscience.kmath.structures.MutableBuffer -import space.kscience.kmath.structures.MutableBufferFactory /** * Represents [StructureND] over [Buffer]. @@ -22,32 +21,33 @@ public open class BufferND( public open val buffer: Buffer, ) : StructureND { + @PerformancePitfall override operator fun get(index: IntArray): T = buffer[indices.offset(index)] - override val shape: IntArray get() = indices.shape + override val shape: ShapeND get() = indices.shape override fun toString(): String = StructureND.toString(this) } -/** - * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [BufferND] - */ -public inline fun StructureND.mapToBuffer( - factory: BufferFactory, - crossinline transform: (T) -> R, -): BufferND = if (this is BufferND) - BufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) }) -else { - val strides = DefaultStrides(shape) - BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) }) -} - -/** - * Transform structure to a new structure using inferred [BufferFactory] - */ -public inline fun StructureND.mapToBuffer( - crossinline transform: (T) -> R, -): BufferND = mapToBuffer(Buffer.Companion::auto, transform) +///** +// * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [BufferND] +// */ +//public inline fun StructureND.mapToBuffer( +// factory: BufferFactory, +// crossinline transform: (T) -> R, +//): BufferND = if (this is BufferND) +// BufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) }) +//else { +// val strides = ColumnStrides(shape) +// BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) }) +//} +// +///** +// * Transform structure to a new structure using inferred [BufferFactory] +// */ +//public inline fun StructureND.mapToBuffer( +// crossinline transform: (T) -> R, +//): BufferND = mapToBuffer(Buffer.Companion::auto, transform) /** * Represents [MutableStructureND] over [MutableBuffer]. @@ -60,22 +60,24 @@ public open class MutableBufferND( strides: ShapeIndexer, override val buffer: MutableBuffer, ) : MutableStructureND, BufferND(strides, buffer) { + + @PerformancePitfall override fun set(index: IntArray, value: T) { buffer[indices.offset(index)] = value } } -/** - * Transform structure to a new structure using provided [MutableBufferFactory] and optimizing if argument is [MutableBufferND] - */ -public inline fun MutableStructureND.mapToMutableBuffer( - factory: MutableBufferFactory = MutableBufferFactory(MutableBuffer.Companion::auto), - crossinline transform: (T) -> R, -): MutableBufferND { - return if (this is MutableBufferND) - MutableBufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) }) - else { - val strides = DefaultStrides(shape) - MutableBufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) }) - } -} \ No newline at end of file +///** +// * Transform structure to a new structure using provided [MutableBufferFactory] and optimizing if argument is [MutableBufferND] +// */ +//public inline fun MutableStructureND.mapToMutableBuffer( +// factory: MutableBufferFactory = MutableBufferFactory(MutableBuffer.Companion::auto), +// crossinline transform: (T) -> R, +//): MutableBufferND { +// return if (this is MutableBufferND) +// MutableBufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) }) +// else { +// val strides = ColumnStrides(shape) +// MutableBufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) }) +// } +//} \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt index aab137321..b5ed64108 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt @@ -14,15 +14,25 @@ import kotlin.contracts.contract import kotlin.math.pow import kotlin.math.pow as kpow +/** + * A simple mutable [StructureND] of doubles + */ public class DoubleBufferND( indexes: ShapeIndexer, override val buffer: DoubleBuffer, -) : MutableBufferND(indexes, buffer) +) : MutableBufferND(indexes, buffer), MutableStructureNDOfDouble{ + override fun getDouble(index: IntArray): Double = buffer[indices.offset(index)] + + override fun setDouble(index: IntArray, value: Double) { + buffer[indices.offset(index)] = value + } +} public sealed class DoubleFieldOpsND : BufferedFieldOpsND(DoubleField.bufferAlgebra), ScaleOperations>, ExtendedFieldOps> { + @OptIn(PerformancePitfall::class) override fun StructureND.toBufferND(): DoubleBufferND = when (this) { is DoubleBufferND -> this else -> { @@ -64,7 +74,7 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND(D transform: DoubleField.(Double, Double) -> Double, ): BufferND = zipInline(left.toBufferND(), right.toBufferND()) { l, r -> DoubleField.transform(l, r) } - override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND { + override fun structureND(shape: ShapeND, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND { val indexer = indexerBuilder(shape) return DoubleBufferND( indexer, @@ -179,7 +189,7 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND(D } @OptIn(UnstableKMathAPI::class) -public class DoubleFieldND(override val shape: Shape) : +public class DoubleFieldND(override val shape: ShapeND) : DoubleFieldOpsND(), FieldND, NumbersAddOps>, ExtendedField> { @@ -221,7 +231,8 @@ public class DoubleFieldND(override val shape: Shape) : public val DoubleField.ndAlgebra: DoubleFieldOpsND get() = DoubleFieldOpsND -public fun DoubleField.ndAlgebra(vararg shape: Int): DoubleFieldND = DoubleFieldND(shape) +public fun DoubleField.ndAlgebra(vararg shape: Int): DoubleFieldND = DoubleFieldND(ShapeND(shape)) +public fun DoubleField.ndAlgebra(shape: ShapeND): DoubleFieldND = DoubleFieldND(shape) /** * Produce a context for n-dimensional operations inside this real field @@ -229,5 +240,5 @@ public fun DoubleField.ndAlgebra(vararg shape: Int): DoubleFieldND = DoubleField @UnstableKMathAPI public inline fun DoubleField.withNdAlgebra(vararg shape: Int, action: DoubleFieldND.() -> R): R { contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) } - return DoubleFieldND(shape).run(action) + return DoubleFieldND(ShapeND(shape)).run(action) } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/IntRingND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/IntRingND.kt index ac01239a9..f46defeee 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/IntRingND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/IntRingND.kt @@ -20,7 +20,7 @@ public class IntBufferND( public sealed class IntRingOpsND : BufferedRingOpsND(IntRing.bufferAlgebra) { - override fun structureND(shape: Shape, initializer: IntRing.(IntArray) -> Int): IntBufferND { + override fun structureND(shape: ShapeND, initializer: IntRing.(IntArray) -> Int): IntBufferND { val indexer = indexerBuilder(shape) return IntBufferND( indexer, @@ -35,7 +35,7 @@ public sealed class IntRingOpsND : BufferedRingOpsND(IntRing.buffe @OptIn(UnstableKMathAPI::class) public class IntRingND( - override val shape: Shape + override val shape: ShapeND ) : IntRingOpsND(), RingND, NumbersAddOps> { override fun number(value: Number): BufferND { @@ -46,5 +46,5 @@ public class IntRingND( public inline fun IntRing.withNdAlgebra(vararg shape: Int, action: IntRingND.() -> R): R { contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) } - return IntRingND(shape).run(action) + return IntRingND(ShapeND(shape)).run(action) } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/PermutedStructureND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/PermutedStructureND.kt new file mode 100644 index 000000000..e4ba72cec --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/PermutedStructureND.kt @@ -0,0 +1,50 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.nd + +import space.kscience.kmath.misc.PerformancePitfall + + +public class PermutedStructureND( + public val origin: StructureND, + public val permutation: (IntArray) -> IntArray, +) : StructureND { + + override val shape: ShapeND + get() = origin.shape + + @OptIn(PerformancePitfall::class) + override fun get(index: IntArray): T { + return origin[permutation(index)] + } +} + +public fun StructureND.permute( + permutation: (IntArray) -> IntArray, +): PermutedStructureND = PermutedStructureND(this, permutation) + +public class PermutedMutableStructureND( + public val origin: MutableStructureND, + override val shape: ShapeND = origin.shape, + public val permutation: (IntArray) -> IntArray, +) : MutableStructureND { + + + @OptIn(PerformancePitfall::class) + override fun set(index: IntArray, value: T) { + origin[permutation(index)] = value + } + + @OptIn(PerformancePitfall::class) + override fun get(index: IntArray): T { + return origin[permutation(index)] + } +} + +public fun MutableStructureND.permute( + newShape: ShapeND = shape, + permutation: (IntArray) -> IntArray, +): PermutedMutableStructureND = PermutedMutableStructureND(this, newShape, permutation) \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Shape.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Shape.kt deleted file mode 100644 index c5d04c9de..000000000 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Shape.kt +++ /dev/null @@ -1,35 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.nd - -/** - * An exception is thrown when the expected and actual shape of NDArray differ. - * - * @property expected the expected shape. - * @property actual the actual shape. - */ -public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) : - RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.") - -public class IndexOutOfShapeException(public val shape: Shape, public val index: IntArray) : - RuntimeException("Index ${index.contentToString()} is out of shape ${shape.contentToString()}") - -public typealias Shape = IntArray - -public fun Shape(shapeFirst: Int, vararg shapeRest: Int): Shape = intArrayOf(shapeFirst, *shapeRest) - -public interface WithShape { - public val shape: Shape - - public val indices: ShapeIndexer get() = DefaultStrides(shape) -} - -internal fun requireIndexInShape(index: IntArray, shape: Shape) { - if (index.size != shape.size) throw IndexOutOfShapeException(index, shape) - shape.forEachIndexed { axis, axisShape -> - if (index[axis] !in 0 until axisShape) throw IndexOutOfShapeException(index, shape) - } -} diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndexer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndexer.kt deleted file mode 100644 index 2dce407ca..000000000 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndexer.kt +++ /dev/null @@ -1,127 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.nd - -import kotlin.native.concurrent.ThreadLocal - -/** - * A converter from linear index to multivariate index - */ -public interface ShapeIndexer : Iterable { - public val shape: Shape - - /** - * Get linear index from multidimensional index - */ - public fun offset(index: IntArray): Int - - /** - * Get multidimensional from linear - */ - public fun index(offset: Int): IntArray - - /** - * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides - */ - public val linearSize: Int - - // TODO introduce a fast way to calculate index of the next element? - - /** - * Iterate over ND indices in a natural order - */ - public fun asSequence(): Sequence - - override fun iterator(): Iterator = asSequence().iterator() - - override fun equals(other: Any?): Boolean - override fun hashCode(): Int -} - -/** - * Linear transformation of indexes - */ -public abstract class Strides : ShapeIndexer { - /** - * Array strides - */ - public abstract val strides: IntArray - - public override fun offset(index: IntArray): Int = index.mapIndexed { i, value -> - if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})") - value * strides[i] - }.sum() - - // TODO introduce a fast way to calculate index of the next element? - - /** - * Iterate over ND indices in a natural order - */ - public override fun asSequence(): Sequence = (0 until linearSize).asSequence().map(::index) -} - -/** - * Simple implementation of [Strides]. - */ -public class DefaultStrides(override val shape: IntArray) : Strides() { - override val linearSize: Int get() = strides[shape.size] - - /** - * Strides for memory access - */ - override val strides: IntArray by lazy { - sequence { - var current = 1 - yield(1) - - shape.forEach { - current *= it - yield(current) - } - }.toList().toIntArray() - } - - override fun index(offset: Int): IntArray { - val res = IntArray(shape.size) - var current = offset - var strideIndex = strides.size - 2 - - while (strideIndex >= 0) { - res[strideIndex] = (current / strides[strideIndex]) - current %= strides[strideIndex] - strideIndex-- - } - - return res - } - - override fun equals(other: Any?): Boolean { - if (this === other) return true - if (other !is DefaultStrides) return false - if (!shape.contentEquals(other.shape)) return false - return true - } - - override fun hashCode(): Int = shape.contentHashCode() - - - public companion object { - /** - * Cached builder for default strides - */ - @Deprecated("Replace by Strides(shape)") - public operator fun invoke(shape: IntArray): Strides = - defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) } - } -} - -@ThreadLocal -private val defaultStridesCache = HashMap() - -/** - * Cached builder for default strides - */ -public fun Strides(shape: IntArray): Strides = defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) } \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndices.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndices.kt new file mode 100644 index 000000000..3a27614c5 --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndices.kt @@ -0,0 +1,174 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.nd + +import kotlin.math.max +import kotlin.native.concurrent.ThreadLocal + +/** + * A converter from linear index to multivariate index + */ +public interface ShapeIndexer : Iterable { + public val shape: ShapeND + + /** + * Get linear index from multidimensional index + */ + public fun offset(index: IntArray): Int + + /** + * Get multidimensional from linear + */ + public fun index(offset: Int): IntArray + + /** + * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides + */ + public val linearSize: Int + + // TODO introduce a fast way to calculate index of the next element? + + /** + * Iterate over ND indices in a natural order + */ + public fun asSequence(): Sequence + + override fun iterator(): Iterator = asSequence().iterator() + + override fun equals(other: Any?): Boolean + override fun hashCode(): Int +} + +/** + * Linear transformation of indexes + */ +public abstract class Strides : ShapeIndexer { + /** + * Array strides + */ + internal abstract val strides: IntArray + + public override fun offset(index: IntArray): Int { + var res = 0 + index.forEachIndexed { i, value -> + if (value !in 0 until shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0, ${this.shape[i]})") + res += value * strides[i] + + } + return res + } + + // TODO introduce a fast way to calculate index of the next element? + + /** + * Iterate over ND indices in a natural order + */ + public override fun asSequence(): Sequence = (0 until linearSize).asSequence().map(::index) + +} + +/** + * Column-first [Strides]. Columns are represented as continuous arrays + */ +public class ColumnStrides(override val shape: ShapeND) : Strides() { + override val linearSize: Int get() = strides[shape.size] + + /** + * Strides for memory access + */ + override val strides: IntArray = sequence { + var current = 1 + yield(1) + + shape.forEach { + current *= it + yield(current) + } + }.toList().toIntArray() + + override fun index(offset: Int): IntArray { + val res = IntArray(shape.size) + var current = offset + var strideIndex = strides.size - 2 + + while (strideIndex >= 0) { + res[strideIndex] = (current / strides[strideIndex]) + current %= strides[strideIndex] + strideIndex-- + } + + return res + } + + override fun equals(other: Any?): Boolean { + if (this === other) return true + if (other !is ColumnStrides) return false + return shape.contentEquals(other.shape) + } + + override fun hashCode(): Int = shape.contentHashCode() + + + public companion object +} + +/** + * This [Strides] implementation follows the last dimension first convention + * For more information: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.strides.html + * + * @param shape the shape of the tensor. + */ +public class RowStrides(override val shape: ShapeND) : Strides() { + + override val strides: IntArray = run { + val nDim = shape.size + val res = IntArray(nDim) + if (nDim == 0) return@run res + + var current = nDim - 1 + res[current] = 1 + + while (current > 0) { + res[current - 1] = max(1, shape[current]) * res[current] + current-- + } + res + } + + override fun index(offset: Int): IntArray { + val res = IntArray(shape.size) + var current = offset + var strideIndex = 0 + + while (strideIndex < shape.size) { + res[strideIndex] = (current / strides[strideIndex]) + current %= strides[strideIndex] + strideIndex++ + } + return res + } + + override val linearSize: Int get() = shape.linearSize + + override fun equals(other: Any?): Boolean { + if (this === other) return true + if (other !is RowStrides) return false + return shape.contentEquals(other.shape) + } + + override fun hashCode(): Int = shape.contentHashCode() + + public companion object + +} + +@ThreadLocal +private val defaultStridesCache = HashMap() + +/** + * Cached builder for default strides + */ +public fun Strides(shape: ShapeND): Strides = defaultStridesCache.getOrPut(shape) { RowStrides(shape) } \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeND.kt new file mode 100644 index 000000000..63728e94f --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeND.kt @@ -0,0 +1,102 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.nd + +import space.kscience.kmath.misc.UnsafeKMathAPI +import kotlin.jvm.JvmInline + +/** + * A read-only ND shape + */ +@JvmInline +public value class ShapeND(@PublishedApi internal val array: IntArray) { + public val size: Int get() = array.size + public operator fun get(index: Int): Int = array[index] + override fun toString(): String = array.contentToString() +} + +public inline fun ShapeND.forEach(block: (value: Int) -> Unit): Unit = array.forEach(block) + +public inline fun ShapeND.forEachIndexed(block: (index: Int, value: Int) -> Unit): Unit = array.forEachIndexed(block) + +public infix fun ShapeND.contentEquals(other: ShapeND): Boolean = array.contentEquals(other.array) + +public fun ShapeND.contentHashCode(): Int = array.contentHashCode() + +public val ShapeND.indices: IntRange get() = array.indices +public val ShapeND.linearSize: Int get() = array.reduce(Int::times) + +public fun ShapeND.slice(range: IntRange): ShapeND = ShapeND(array.sliceArray(range)) + +public fun ShapeND.last(): Int = array.last() + +/** + * A shape including last [n] dimensions of this shape + */ +public fun ShapeND.last(n: Int): ShapeND = ShapeND(array.copyOfRange(size - n, size)) + +public fun ShapeND.first(): Int = array.first() + +/** + * A shape including first [n] dimensions of this shape + */ +public fun ShapeND.first(n: Int): ShapeND = ShapeND(array.copyOfRange(0, n)) + +public operator fun ShapeND.plus(add: IntArray): ShapeND = ShapeND(array + add) + +public operator fun ShapeND.plus(add: ShapeND): ShapeND = ShapeND(array + add.array) + +public fun ShapeND.isEmpty(): Boolean = size == 0 +public fun ShapeND.isNotEmpty(): Boolean = size > 0 + +public fun ShapeND.transposed(i: Int, j: Int): ShapeND = ShapeND(array.copyOf().apply { + val ith = get(i) + val jth = get(j) + set(i, jth) + set(j, ith) +}) + +public operator fun ShapeND.component1(): Int = get(0) +public operator fun ShapeND.component2(): Int = get(1) +public operator fun ShapeND.component3(): Int = get(2) + +/** + * Convert to array with protective copy + */ +public fun ShapeND.toArray(): IntArray = array.copyOf() + +@UnsafeKMathAPI +public fun ShapeND.asArray(): IntArray = array + +public fun ShapeND.asList(): List = array.asList() + + +/** + * An exception is thrown when the expected and actual shape of NDArray differ. + * + * @property expected the expected shape. + * @property actual the actual shape. + */ +public class ShapeMismatchException(public val expected: ShapeND, public val actual: ShapeND) : + RuntimeException("Shape $actual doesn't fit in expected shape ${expected}.") + +public class IndexOutOfShapeException(public val shape: ShapeND, public val index: IntArray) : + RuntimeException("Index ${index.contentToString()} is out of shape ${shape}") + +public fun ShapeND(shapeFirst: Int, vararg shapeRest: Int): ShapeND = ShapeND(intArrayOf(shapeFirst, *shapeRest)) + +public interface WithShape { + public val shape: ShapeND + + public val indices: ShapeIndexer get() = ColumnStrides(shape) +} + +internal fun requireIndexInShape(index: IntArray, shape: ShapeND) { + if (index.size != shape.size) throw IndexOutOfShapeException(shape, index) + shape.forEachIndexed { axis, axisShape -> + if (index[axis] !in 0 until axisShape) throw IndexOutOfShapeException(shape, index) + } +} diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt index 249b6801d..34d748b3f 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt @@ -18,7 +18,7 @@ public sealed class ShortRingOpsND : BufferedRingOpsND(ShortRi @OptIn(UnstableKMathAPI::class) public class ShortRingND( - override val shape: Shape + override val shape: ShapeND ) : ShortRingOpsND(), RingND, NumbersAddOps> { override fun number(value: Number): BufferND { @@ -30,5 +30,5 @@ public class ShortRingND( public inline fun ShortRing.withNdAlgebra(vararg shape: Int, action: ShortRingND.() -> R): R { contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) } - return ShortRingND(shape).run(action) + return ShortRingND(ShapeND(shape)).run(action) } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt index 2a258a7f4..ba48e25ce 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt @@ -18,6 +18,7 @@ import kotlin.jvm.JvmInline public interface Structure1D : StructureND, Buffer { override val dimension: Int get() = 1 + @PerformancePitfall override operator fun get(index: IntArray): T { require(index.size == 1) { "Index dimension mismatch. Expected 1 but found ${index.size}" } return get(index[0]) @@ -32,6 +33,8 @@ public interface Structure1D : StructureND, Buffer { * A mutable structure that is guaranteed to be one-dimensional */ public interface MutableStructure1D : Structure1D, MutableStructureND, MutableBuffer { + + @PerformancePitfall override operator fun set(index: IntArray, value: T) { require(index.size == 1) { "Index dimension mismatch. Expected 1 but found ${index.size}" } set(index[0], value) @@ -43,9 +46,10 @@ public interface MutableStructure1D : Structure1D, MutableStructureND, */ @JvmInline private value class Structure1DWrapper(val structure: StructureND) : Structure1D { - override val shape: IntArray get() = structure.shape + override val shape: ShapeND get() = structure.shape override val size: Int get() = structure.shape[0] + @PerformancePitfall override operator fun get(index: Int): T = structure[index] @PerformancePitfall @@ -56,13 +60,16 @@ private value class Structure1DWrapper(val structure: StructureND) : S * A 1D wrapper for a mutable nd-structure */ private class MutableStructure1DWrapper(val structure: MutableStructureND) : MutableStructure1D { - override val shape: IntArray get() = structure.shape + override val shape: ShapeND get() = structure.shape override val size: Int get() = structure.shape[0] @PerformancePitfall override fun elements(): Sequence> = structure.elements() + @PerformancePitfall override fun get(index: Int): T = structure[index] + + @PerformancePitfall override fun set(index: Int, value: T) { structure[intArrayOf(index)] = value } @@ -83,7 +90,7 @@ private class MutableStructure1DWrapper(val structure: MutableStructureND) */ @JvmInline private value class Buffer1DWrapper(val buffer: Buffer) : Structure1D { - override val shape: IntArray get() = intArrayOf(buffer.size) + override val shape: ShapeND get() = ShapeND(buffer.size) override val size: Int get() = buffer.size @PerformancePitfall @@ -95,7 +102,7 @@ private value class Buffer1DWrapper(val buffer: Buffer) : Structure1D< } internal class MutableBuffer1DWrapper(val buffer: MutableBuffer) : MutableStructure1D { - override val shape: IntArray get() = intArrayOf(buffer.size) + override val shape: ShapeND get() = ShapeND(buffer.size) override val size: Int get() = buffer.size @PerformancePitfall diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt index d8fd2031c..a9c6c2748 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt @@ -7,6 +7,7 @@ package space.kscience.kmath.nd import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.structures.Buffer +import space.kscience.kmath.structures.MutableBuffer import space.kscience.kmath.structures.MutableListBuffer import space.kscience.kmath.structures.VirtualBuffer import kotlin.jvm.JvmInline @@ -28,7 +29,7 @@ public interface Structure2D : StructureND { */ public val colNum: Int - override val shape: IntArray get() = intArrayOf(rowNum, colNum) + override val shape: ShapeND get() = ShapeND(rowNum, colNum) /** * The buffer of rows of this structure. It gets elements from the structure dynamically. @@ -53,6 +54,7 @@ public interface Structure2D : StructureND { */ public operator fun get(i: Int, j: Int): T + @PerformancePitfall override operator fun get(index: IntArray): T { require(index.size == 2) { "Index dimension mismatch. Expected 2 but found ${index.size}" } return get(index[0], index[1]) @@ -84,15 +86,15 @@ public interface MutableStructure2D : Structure2D, MutableStructureND { * The buffer of rows of this structure. It gets elements from the structure dynamically. */ @PerformancePitfall - override val rows: List> - get() = List(rowNum) { i -> MutableBuffer1DWrapper(MutableListBuffer(colNum) { j -> get(i, j) }) } + override val rows: List> + get() = List(rowNum) { i -> MutableListBuffer(colNum) { j -> get(i, j) } } /** * The buffer of columns of this structure. It gets elements from the structure dynamically. */ @PerformancePitfall - override val columns: List> - get() = List(colNum) { j -> MutableBuffer1DWrapper(MutableListBuffer(rowNum) { i -> get(i, j) }) } + override val columns: List> + get() = List(colNum) { j -> MutableListBuffer(rowNum) { i -> get(i, j) } } } /** @@ -100,11 +102,12 @@ public interface MutableStructure2D : Structure2D, MutableStructureND { */ @JvmInline private value class Structure2DWrapper(val structure: StructureND) : Structure2D { - override val shape: Shape get() = structure.shape + override val shape: ShapeND get() = structure.shape override val rowNum: Int get() = shape[0] override val colNum: Int get() = shape[1] + @PerformancePitfall override operator fun get(i: Int, j: Int): T = structure[i, j] override fun getFeature(type: KClass): F? = structure.getFeature(type) @@ -117,17 +120,20 @@ private value class Structure2DWrapper(val structure: StructureND) : S * A 2D wrapper for a mutable nd-structure */ private class MutableStructure2DWrapper(val structure: MutableStructureND) : MutableStructure2D { - override val shape: Shape get() = structure.shape + override val shape: ShapeND get() = structure.shape override val rowNum: Int get() = shape[0] override val colNum: Int get() = shape[1] + @PerformancePitfall override operator fun get(i: Int, j: Int): T = structure[i, j] + @PerformancePitfall override fun set(index: IntArray, value: T) { structure[index] = value } + @PerformancePitfall override operator fun set(i: Int, j: Int, value: T) { structure[intArrayOf(i, j)] = value } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt index b2da083bb..c96843651 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt @@ -33,7 +33,7 @@ public interface StructureND : Featured, WithShape { * The shape of structure i.e., non-empty sequence of non-negative integers that specify sizes of dimensions of * this structure. */ - override val shape: Shape + override val shape: ShapeND /** * The count of dimensions in this structure. It should be equal to size of [shape]. @@ -46,6 +46,7 @@ public interface StructureND : Featured, WithShape { * @param index the indices. * @return the value. */ + @PerformancePitfall public operator fun get(index: IntArray): T /** @@ -97,6 +98,7 @@ public interface StructureND : Featured, WithShape { /** * Debug output to string */ + @OptIn(PerformancePitfall::class) public fun toString(structure: StructureND<*>): String { val bufferRepr: String = when (structure.shape.size) { 1 -> (0 until structure.shape[0]).map { structure[it] } @@ -116,7 +118,7 @@ public interface StructureND : Featured, WithShape { } val className = structure::class.simpleName ?: "StructureND" - return "$className(shape=${structure.shape.contentToString()}, buffer=$bufferRepr)" + return "$className(shape=${structure.shape}, buffer=$bufferRepr)" } /** @@ -145,28 +147,28 @@ public interface StructureND : Featured, WithShape { ): BufferND = BufferND(strides, Buffer.auto(type, strides.linearSize) { i -> initializer(strides.index(i)) }) public fun buffered( - shape: IntArray, + shape: ShapeND, bufferFactory: BufferFactory = BufferFactory.boxing(), initializer: (IntArray) -> T, - ): BufferND = buffered(DefaultStrides(shape), bufferFactory, initializer) + ): BufferND = buffered(ColumnStrides(shape), bufferFactory, initializer) public inline fun auto( - shape: IntArray, + shape: ShapeND, crossinline initializer: (IntArray) -> T, - ): BufferND = auto(DefaultStrides(shape), initializer) + ): BufferND = auto(ColumnStrides(shape), initializer) @JvmName("autoVarArg") public inline fun auto( vararg shape: Int, crossinline initializer: (IntArray) -> T, ): BufferND = - auto(DefaultStrides(shape), initializer) + auto(ColumnStrides(ShapeND(shape)), initializer) public inline fun auto( type: KClass, vararg shape: Int, crossinline initializer: (IntArray) -> T, - ): BufferND = auto(type, DefaultStrides(shape), initializer) + ): BufferND = auto(type, ColumnStrides(ShapeND(shape)), initializer) } } @@ -214,8 +216,13 @@ public fun > LinearSpace>.contentEquals( * @param index the indices. * @return the value. */ +@PerformancePitfall public operator fun StructureND.get(vararg index: Int): T = get(index) +public operator fun StructureND.get(vararg index: Int): Double = getDouble(index) + +public operator fun StructureND.get(vararg index: Int): Int = getInt(index) + //@UnstableKMathAPI //public inline fun StructureND<*>.getFeature(): T? = getFeature(T::class) @@ -229,12 +236,14 @@ public interface MutableStructureND : StructureND { * @param index the indices. * @param value the value. */ + @PerformancePitfall public operator fun set(index: IntArray, value: T) } /** * Set value at specified indices */ +@PerformancePitfall public operator fun MutableStructureND.set(vararg index: Int, value: T) { set(index, value) } \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/VirtualStructureND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/VirtualStructureND.kt index 579a0d7c8..4932dca41 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/VirtualStructureND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/VirtualStructureND.kt @@ -5,12 +5,15 @@ package space.kscience.kmath.nd +import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI public open class VirtualStructureND( - override val shape: Shape, + override val shape: ShapeND, public val producer: (IntArray) -> T, ) : StructureND { + + @PerformancePitfall override fun get(index: IntArray): T { requireIndexInShape(index, shape) return producer(index) @@ -19,12 +22,12 @@ public open class VirtualStructureND( @UnstableKMathAPI public class VirtualDoubleStructureND( - shape: Shape, + shape: ShapeND, producer: (IntArray) -> Double, ) : VirtualStructureND(shape, producer) @UnstableKMathAPI public class VirtualIntStructureND( - shape: Shape, + shape: ShapeND, producer: (IntArray) -> Int, ) : VirtualStructureND(shape, producer) \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt index 1b7bd20db..f0d4bd7f5 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt @@ -15,9 +15,9 @@ public fun > AlgebraND.structureND( shapeFirst: Int, vararg shapeRest: Int, initializer: A.(IntArray) -> T -): StructureND = structureND(Shape(shapeFirst, *shapeRest), initializer) +): StructureND = structureND(ShapeND(shapeFirst, *shapeRest), initializer) -public fun > AlgebraND.zero(shape: Shape): StructureND = structureND(shape) { zero } +public fun > AlgebraND.zero(shape: ShapeND): StructureND = structureND(shape) { zero } @JvmName("zeroVarArg") public fun > AlgebraND.zero( @@ -25,7 +25,7 @@ public fun > AlgebraND.zero( vararg shapeRest: Int, ): StructureND = structureND(shapeFirst, *shapeRest) { zero } -public fun > AlgebraND.one(shape: Shape): StructureND = structureND(shape) { one } +public fun > AlgebraND.one(shape: ShapeND): StructureND = structureND(shape) { one } @JvmName("oneVarArg") public fun > AlgebraND.one( diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/operationsND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/operationsND.kt index 5814e2f9c..424081738 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/operationsND.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/operationsND.kt @@ -5,6 +5,9 @@ package space.kscience.kmath.nd +import space.kscience.kmath.misc.PerformancePitfall + +@OptIn(PerformancePitfall::class) public fun StructureND.roll(axis: Int, step: Int = 1): StructureND { require(axis in shape.indices) { "Axis $axis is outside of shape dimensions: [0, ${shape.size})" } return VirtualStructureND(shape) { index -> @@ -19,6 +22,7 @@ public fun StructureND.roll(axis: Int, step: Int = 1): StructureND { } } +@OptIn(PerformancePitfall::class) public fun StructureND.roll(pair: Pair, vararg others: Pair): StructureND { val axisMap: Map = mapOf(pair, *others) require(axisMap.keys.all { it in shape.indices }) { "Some of axes ${axisMap.keys} is outside of shape dimensions: [0, ${shape.size})" } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/primitiveStructureND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/primitiveStructureND.kt new file mode 100644 index 000000000..f50233ecc --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/primitiveStructureND.kt @@ -0,0 +1,45 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.nd + +import space.kscience.kmath.misc.PerformancePitfall + +public interface StructureNDOfDouble : StructureND { + /** + * Guaranteed non-blocking access to content + */ + public fun getDouble(index: IntArray): Double +} + +/** + * Optimized method to access primitive without boxing if possible + */ +@OptIn(PerformancePitfall::class) +public fun StructureND.getDouble(index: IntArray): Double = + if (this is StructureNDOfDouble) getDouble(index) else get(index) + +public interface MutableStructureNDOfDouble : StructureNDOfDouble, MutableStructureND { + /** + * Guaranteed non-blocking access to content + */ + public fun setDouble(index: IntArray, value: Double) +} + +@OptIn(PerformancePitfall::class) +public fun MutableStructureND.getDouble(index: IntArray): Double = + if (this is StructureNDOfDouble) getDouble(index) else get(index) + + +public interface StructureNDOfInt : StructureND { + /** + * Guaranteed non-blocking access to content + */ + public fun getInt(index: IntArray): Int +} + +@OptIn(PerformancePitfall::class) +public fun StructureND.getInt(index: IntArray): Int = + if (this is StructureNDOfInt) getInt(index) else get(index) diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt index 449730e7a..2e6b63a92 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt @@ -5,8 +5,6 @@ package space.kscience.kmath.operations -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.DoubleField.pow import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.DoubleBuffer @@ -32,9 +30,9 @@ public class DoubleBufferField(public val size: Int) : ExtendedField): DoubleBuffer = super.atanh(arg) override fun power(arg: Buffer, pow: Number): DoubleBuffer = if (pow.isInteger()) { - arg.mapInline { it.pow(pow.toInt()) } + arg.map { it.pow(pow.toInt()) } } else { - arg.mapInline { + arg.map { if(it<0) throw IllegalArgumentException("Negative argument $it could not be raised to the fractional power") it.pow(pow.toDouble()) } @@ -42,103 +40,4 @@ public class DoubleBufferField(public val size: Int) : ExtendedField) -> Buffer = super.unaryOperationFunction(operation) - - // override fun number(value: Number): Buffer = DoubleBuffer(size) { value.toDouble() } -// -// override fun Buffer.unaryMinus(): Buffer = DoubleBufferOperations.run { -// -this@unaryMinus -// } -// -// override fun add(a: Buffer, b: Buffer): DoubleBuffer { -// require(a.size == size) { "The buffer size ${a.size} does not match context size $size" } -// return DoubleBufferOperations.add(a, b) -// } -// - -// -// override fun multiply(a: Buffer, b: Buffer): DoubleBuffer { -// require(a.size == size) { "The buffer size ${a.size} does not match context size $size" } -// return DoubleBufferOperations.multiply(a, b) -// } -// -// override fun divide(a: Buffer, b: Buffer): DoubleBuffer { -// require(a.size == size) { "The buffer size ${a.size} does not match context size $size" } -// return DoubleBufferOperations.divide(a, b) -// } -// -// override fun sin(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.sin(arg) -// } -// -// override fun cos(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.cos(arg) -// } -// -// override fun tan(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.tan(arg) -// } -// -// override fun asin(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.asin(arg) -// } -// -// override fun acos(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.acos(arg) -// } -// -// override fun atan(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.atan(arg) -// } -// -// override fun sinh(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.sinh(arg) -// } -// -// override fun cosh(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.cosh(arg) -// } -// -// override fun tanh(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.tanh(arg) -// } -// -// override fun asinh(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.asinh(arg) -// } -// -// override fun acosh(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.acosh(arg) -// } -// -// override fun atanh(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.atanh(arg) -// } -// -// override fun power(arg: Buffer, pow: Number): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.power(arg, pow) -// } -// -// override fun exp(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.exp(arg) -// } -// -// override fun ln(arg: Buffer): DoubleBuffer { -// require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" } -// return DoubleBufferOperations.ln(arg) -// } - } \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt index ded8753a3..7ba1a7066 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt @@ -6,10 +6,8 @@ package space.kscience.kmath.operations import space.kscience.kmath.linear.Point -import space.kscience.kmath.structures.Buffer -import space.kscience.kmath.structures.DoubleBuffer -import space.kscience.kmath.structures.MutableBufferFactory -import space.kscience.kmath.structures.asBuffer +import space.kscience.kmath.misc.UnstableKMathAPI +import space.kscience.kmath.structures.* import kotlin.math.* /** @@ -19,10 +17,29 @@ public abstract class DoubleBufferOps : BufferAlgebra, Exte Norm, Double> { override val elementAlgebra: DoubleField get() = DoubleField + override val elementBufferFactory: MutableBufferFactory get() = elementAlgebra.bufferFactory - override fun Buffer.map(block: DoubleField.(Double) -> Double): DoubleBuffer = - mapInline { DoubleField.block(it) } + @Suppress("OVERRIDE_BY_INLINE") + @OptIn(UnstableKMathAPI::class) + final override inline fun Buffer.map(block: DoubleField.(Double) -> Double): DoubleBuffer = + DoubleArray(size) { DoubleField.block(getDouble(it)) }.asBuffer() + + + @OptIn(UnstableKMathAPI::class) + @Suppress("OVERRIDE_BY_INLINE") + final override inline fun Buffer.mapIndexed(block: DoubleField.(index: Int, arg: Double) -> Double): DoubleBuffer = + DoubleBuffer(size) { DoubleField.block(it, getDouble(it)) } + + @OptIn(UnstableKMathAPI::class) + @Suppress("OVERRIDE_BY_INLINE") + final override inline fun Buffer.zip( + other: Buffer, + block: DoubleField.(left: Double, right: Double) -> Double, + ): DoubleBuffer { + require(size == other.size) { "Incompatible buffer sizes. left: ${size}, right: ${other.size}" } + return DoubleBuffer(size) { DoubleField.block(getDouble(it), other.getDouble(it)) } + } override fun unaryOperationFunction(operation: String): (arg: Buffer) -> Buffer = super.unaryOperationFunction(operation) @@ -30,7 +47,7 @@ public abstract class DoubleBufferOps : BufferAlgebra, Exte override fun binaryOperationFunction(operation: String): (left: Buffer, right: Buffer) -> Buffer = super.binaryOperationFunction(operation) - override fun Buffer.unaryMinus(): DoubleBuffer = mapInline { -it } + override fun Buffer.unaryMinus(): DoubleBuffer = map { -it } override fun add(left: Buffer, right: Buffer): DoubleBuffer { require(right.size == left.size) { @@ -77,6 +94,7 @@ public abstract class DoubleBufferOps : BufferAlgebra, Exte // } else RealBuffer(DoubleArray(a.size) { a[it] / kValue }) // } + @UnstableKMathAPI override fun multiply(left: Buffer, right: Buffer): DoubleBuffer { require(right.size == left.size) { "The size of the first buffer ${left.size} should be the same as for second one: ${right.size} " @@ -101,55 +119,83 @@ public abstract class DoubleBufferOps : BufferAlgebra, Exte } else DoubleBuffer(DoubleArray(left.size) { left[it] / right[it] }) } - override fun sin(arg: Buffer): DoubleBuffer = arg.mapInline(::sin) + override fun sin(arg: Buffer): DoubleBuffer = arg.map { sin(it) } - override fun cos(arg: Buffer): DoubleBuffer = arg.mapInline(::cos) + override fun cos(arg: Buffer): DoubleBuffer = arg.map { cos(it) } - override fun tan(arg: Buffer): DoubleBuffer = arg.mapInline(::tan) + override fun tan(arg: Buffer): DoubleBuffer = arg.map { tan(it) } - override fun asin(arg: Buffer): DoubleBuffer = arg.mapInline(::asin) + override fun asin(arg: Buffer): DoubleBuffer = arg.map { asin(it) } - override fun acos(arg: Buffer): DoubleBuffer = arg.mapInline(::acos) + override fun acos(arg: Buffer): DoubleBuffer = arg.map { acos(it) } - override fun atan(arg: Buffer): DoubleBuffer = arg.mapInline(::atan) + override fun atan(arg: Buffer): DoubleBuffer = arg.map { atan(it) } - override fun sinh(arg: Buffer): DoubleBuffer = arg.mapInline(::sinh) + override fun sinh(arg: Buffer): DoubleBuffer = arg.map { sinh(it) } - override fun cosh(arg: Buffer): DoubleBuffer = arg.mapInline(::cosh) + override fun cosh(arg: Buffer): DoubleBuffer = arg.map { cosh(it) } - override fun tanh(arg: Buffer): DoubleBuffer = arg.mapInline(::tanh) + override fun tanh(arg: Buffer): DoubleBuffer = arg.map { tanh(it) } - override fun asinh(arg: Buffer): DoubleBuffer = arg.mapInline(::asinh) + override fun asinh(arg: Buffer): DoubleBuffer = arg.map { asinh(it) } - override fun acosh(arg: Buffer): DoubleBuffer = arg.mapInline(::acosh) + override fun acosh(arg: Buffer): DoubleBuffer = arg.map { acosh(it) } - override fun atanh(arg: Buffer): DoubleBuffer = arg.mapInline(::atanh) + override fun atanh(arg: Buffer): DoubleBuffer = arg.map { atanh(it) } - override fun exp(arg: Buffer): DoubleBuffer = arg.mapInline(::exp) + override fun exp(arg: Buffer): DoubleBuffer = arg.map { exp(it) } - override fun ln(arg: Buffer): DoubleBuffer = arg.mapInline(::ln) + override fun ln(arg: Buffer): DoubleBuffer = arg.map { ln(it) } override fun norm(arg: Buffer): Double = DoubleL2Norm.norm(arg) - override fun scale(a: Buffer, value: Double): DoubleBuffer = a.mapInline { it * value } + override fun scale(a: Buffer, value: Double): DoubleBuffer = a.map { it * value } override fun power(arg: Buffer, pow: Number): Buffer = if (pow is Int) { - arg.mapInline { it.pow(pow) } + arg.map { it.pow(pow) } } else { - arg.mapInline { it.pow(pow.toDouble()) } + arg.map { it.pow(pow.toDouble()) } } - public companion object : DoubleBufferOps() { - public inline fun Buffer.mapInline(block: (Double) -> Double): DoubleBuffer = - if (this is DoubleBuffer) { - DoubleArray(size) { block(array[it]) }.asBuffer() - } else { - DoubleArray(size) { block(get(it)) }.asBuffer() - } - } + public companion object : DoubleBufferOps() } public object DoubleL2Norm : Norm, Double> { override fun norm(arg: Point): Double = sqrt(arg.fold(0.0) { acc: Double, d: Double -> acc + d.pow(2) }) } +public fun DoubleBufferOps.sum(buffer: Buffer): Double = buffer.reduce(Double::plus) + +/** + * Sum of elements using given [conversion] + */ +public inline fun DoubleBufferOps.sumOf(buffer: Buffer, conversion: (T) -> Double): Double = + buffer.fold(0.0) { acc, value -> acc + conversion(value) } + +public fun DoubleBufferOps.average(buffer: Buffer): Double = sum(buffer) / buffer.size + +/** + * Average of elements using given [conversion] + */ +public inline fun DoubleBufferOps.averageOf(buffer: Buffer, conversion: (T) -> Double): Double = + sumOf(buffer, conversion) / buffer.size + +public fun DoubleBufferOps.dispersion(buffer: Buffer): Double { + val av = average(buffer) + return buffer.fold(0.0) { acc, value -> acc + (value - av).pow(2) } / buffer.size +} + +public fun DoubleBufferOps.std(buffer: Buffer): Double = sqrt(dispersion(buffer)) + +public fun DoubleBufferOps.covariance(x: Buffer, y: Buffer): Double { + require(x.size == y.size) { "Expected buffers of the same size, but x.size == ${x.size} and y.size == ${y.size}" } + val xMean = average(x) + val yMean = average(y) + var sum = 0.0 + x.indices.forEach { + sum += (x[it] - xMean) * (y[it] - yMean) + } + return sum / (x.size - 1) +} + + diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt index efadfb3cc..f05ddafb8 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt @@ -5,6 +5,21 @@ package space.kscience.kmath.operations +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.structures.Buffer + +/** + * Returns the sum of all elements in the iterable in this [Group]. + * + * @receiver the algebra that provides addition. + * @param data the iterable to sum up. + * @return the sum. + */ +@PerformancePitfall("Potential boxing access to buffer elements") +public fun Group.sum(data: Buffer): T = data.fold(zero) { left, right -> + add(left, right) +} + /** * Returns the sum of all elements in the iterable in this [Group]. * @@ -29,6 +44,18 @@ public fun Group.sum(data: Sequence): T = data.fold(zero) { left, righ add(left, right) } +/** + * Returns an average value of elements in the iterable in this [Group]. + * + * @receiver the algebra that provides addition and division. + * @param data the iterable to find average. + * @return the average value. + * @author Iaroslav Postovalov + */ +@PerformancePitfall("Potential boxing access to buffer elements") +public fun S.average(data: Buffer): T where S : Group, S : ScaleOperations = + sum(data) / data.size + /** * Returns an average value of elements in the iterable in this [Group]. * @@ -95,4 +122,3 @@ public fun Iterable.averageWith(space: S): T where S : Group, S : S */ public fun Sequence.averageWith(space: S): T where S : Group, S : ScaleOperations = space.average(this) - diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt index 5cfafe5a5..cef8d1d4d 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt @@ -5,6 +5,7 @@ package space.kscience.kmath.structures +import space.kscience.kmath.operations.WithSize import space.kscience.kmath.operations.asSequence import kotlin.jvm.JvmInline import kotlin.reflect.KClass @@ -50,11 +51,11 @@ public fun interface MutableBufferFactory : BufferFactory { * * @param T the type of elements contained in the buffer. */ -public interface Buffer { +public interface Buffer : WithSize { /** * The size of this buffer. */ - public val size: Int + override val size: Int /** * Gets element at given index. @@ -64,7 +65,7 @@ public interface Buffer { /** * Iterates over all elements. */ - public operator fun iterator(): Iterator + public operator fun iterator(): Iterator = indices.asSequence().map(::get).iterator() override fun toString(): String @@ -122,7 +123,14 @@ public interface Buffer { /** * Returns an [IntRange] of the valid indices for this [Buffer]. */ -public val Buffer<*>.indices: IntRange get() = 0 until size +public val Buffer.indices: IntRange get() = 0 until size + +public operator fun Buffer.get(index: UInt): T = get(index.toInt()) + +/** + * if index is in range of buffer, return the value. Otherwise, return null. + */ +public fun Buffer.getOrNull(index: Int): T? = if (index in indices) get(index) else null public fun Buffer.first(): T { require(size > 0) { "Can't get the first element of empty buffer" } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt index 07355d396..48f3e919b 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt @@ -5,10 +5,7 @@ package space.kscience.kmath.structures -import space.kscience.kmath.nd.DefaultStrides -import space.kscience.kmath.nd.Structure2D -import space.kscience.kmath.nd.StructureND -import space.kscience.kmath.nd.as2D +import space.kscience.kmath.nd.* /** * A context that allows to operate on a [MutableBuffer] as on 2d array @@ -31,7 +28,7 @@ internal class BufferAccessor2D( //TODO optimize wrapper fun MutableBuffer.collect(): Structure2D = StructureND.buffered( - DefaultStrides(intArrayOf(rowNum, colNum)), + ColumnStrides(ShapeND(rowNum, colNum)), factory ) { (i, j) -> get(i, j) diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferView.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferView.kt new file mode 100644 index 000000000..697939bdf --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferView.kt @@ -0,0 +1,192 @@ +package space.kscience.kmath.structures + +import space.kscience.kmath.misc.UnstableKMathAPI + +/** + * A buffer that wraps an original buffer + */ +public interface BufferView : Buffer { + public val origin: Buffer + + /** + * Get the index in [origin] buffer from index in this buffer. + * Return -1 if element not present in the original buffer + * This method should be used internally to optimize non-boxing access. + */ + @UnstableKMathAPI + public fun originIndex(index: Int): Int + + @OptIn(UnstableKMathAPI::class) + override fun get(index: Int): T = origin[originIndex(index)] +} + +/** + * A zero-copy buffer that "sees" only part of original buffer. Slice can't go beyond original buffer borders. + */ +public class BufferSlice( + override val origin: Buffer, + public val offset: Int = 0, + override val size: Int, +) : BufferView { + + init { + require(size > 0) { "Size must be positive" } + require(offset + size <= origin.size) { + "End of buffer ${offset + size} is beyond the end of origin buffer size ${origin.size}" + } + } + + override fun get(index: Int): T = if (index >= size) { + throw IndexOutOfBoundsException("$index is out of ${0 until size} rage") + } else { + origin[index + offset] + } + + override fun iterator(): Iterator = + (offset until (offset + size)).asSequence().map { origin[it] }.iterator() + + @UnstableKMathAPI + override fun originIndex(index: Int): Int = if (index >= size) -1 else index - offset + + override fun toString(): String = "$origin[$offset..${offset + size}" +} + +/** + * An expanded buffer that could include the whole initial buffer or its part and fills all space beyond it borders with [defaultValue]. + * + * The [offset] parameter shows the shift of expanded buffer start relative to origin start and could be both positive and negative. + */ +public class BufferExpanded( + override val origin: Buffer, + private val defaultValue: T, + public val offset: Int = 0, + override val size: Int = origin.size, +) : BufferView { + + init { + require(size > 0) { "Size must be positive" } + } + + override fun get(index: Int): T = when (index) { + !in 0 until size -> throw IndexOutOfBoundsException("Index $index is not in $indices") + in -offset until origin.size - offset -> origin[index + offset] + else -> defaultValue + } + + @UnstableKMathAPI + override fun originIndex(index: Int): Int = if (index in -offset until origin.size - offset) index + offset else -1 + + override fun toString(): String = "$origin[$offset..${offset + size}]" +} + +/** + * Zero-copy select a slice inside the original buffer + */ +public fun Buffer.slice(range: IntRange): BufferView = if (this is BufferSlice) { + BufferSlice( + origin, + this.offset + range.first, + (range.last - range.first) + 1 + ) +} else { + BufferSlice( + this, + range.first, + (range.last - range.first) + 1 + ) +} + +/** + * Resize original buffer to a given range using given [range], filling additional segments with [defaultValue]. + * Range left border could be negative to designate adding new blank segment to the beginning of the buffer + */ +public fun Buffer.expand( + range: IntRange, + defaultValue: T, +): BufferView = if (range.first >= 0 && range.last < size) { + BufferSlice( + this, + range.first, + (range.last - range.first) + 1 + ) +} else { + BufferExpanded( + this, + defaultValue, + range.first, + (range.last - range.first) + 1 + ) +} + +/** + * A [BufferView] that overrides indexing of the original buffer + */ +public class PermutedBuffer( + override val origin: Buffer, + private val permutations: IntArray, +) : BufferView { + init { + permutations.forEach { index -> + if (index !in origin.indices) { + throw IndexOutOfBoundsException("Index $index is not in ${origin.indices}") + } + } + } + + override val size: Int get() = permutations.size + + override fun get(index: Int): T = origin[permutations[index]] + + override fun iterator(): Iterator = permutations.asSequence().map { origin[it] }.iterator() + + @UnstableKMathAPI + override fun originIndex(index: Int): Int = if (index in permutations.indices) permutations[index] else -1 + + override fun toString(): String = Buffer.toString(this) +} + +/** + * Created a permuted view of given buffer using provided [indices] + */ +public fun Buffer.permute(indices: IntArray): PermutedBuffer = + PermutedBuffer(this, indices) + +/** + * A [BufferView] that overrides indexing of the original buffer + */ +public class PermutedMutableBuffer( + override val origin: MutableBuffer, + private val permutations: IntArray, +) : BufferView, MutableBuffer { + init { + permutations.forEach { index -> + if (index !in origin.indices) { + throw IndexOutOfBoundsException("Index $index is not in ${origin.indices}") + } + } + } + + override val size: Int get() = permutations.size + + override fun get(index: Int): T = origin[permutations[index]] + + override fun set(index: Int, value: T) { + origin[permutations[index]] = value + } + + override fun copy(): MutableBuffer = PermutedMutableBuffer(origin.copy(), permutations) + //TODO Probably could be optimized + + override fun iterator(): Iterator = permutations.asSequence().map { origin[it] }.iterator() + + @UnstableKMathAPI + override fun originIndex(index: Int): Int = if (index in permutations.indices) permutations[index] else -1 + + override fun toString(): String = Buffer.toString(this) +} + +/** + * Created a permuted mutable view of given buffer using provided [indices] + */ +public fun MutableBuffer.permute(indices: IntArray): PermutedMutableBuffer = + PermutedMutableBuffer(this, indices) \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/DoubleBuffer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/DoubleBuffer.kt index 4dd9003f3..1696d5055 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/DoubleBuffer.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/DoubleBuffer.kt @@ -5,6 +5,7 @@ package space.kscience.kmath.structures +import space.kscience.kmath.operations.BufferTransform import kotlin.jvm.JvmInline /** @@ -13,7 +14,7 @@ import kotlin.jvm.JvmInline * @property array the underlying array. */ @JvmInline -public value class DoubleBuffer(public val array: DoubleArray) : MutableBuffer { +public value class DoubleBuffer(public val array: DoubleArray) : PrimitiveBuffer { override val size: Int get() = array.size override operator fun get(index: Int): Double = array[index] @@ -28,7 +29,7 @@ public value class DoubleBuffer(public val array: DoubleArray) : MutableBuffer Double): DoubleBuffer = DoubleBuffer(DoubleArray(size) { init(it) }) +public inline fun DoubleBuffer(size: Int, init: (Int) -> Double): DoubleBuffer = + DoubleBuffer(DoubleArray(size) { init(it) }) /** * Returns a new [DoubleBuffer] of given elements. @@ -51,10 +53,18 @@ public fun DoubleBuffer(vararg doubles: Double): DoubleBuffer = DoubleBuffer(dou * Returns a new [DoubleArray] containing all the elements of this [Buffer]. */ public fun Buffer.toDoubleArray(): DoubleArray = when (this) { - is DoubleBuffer -> array.copyOf() + is DoubleBuffer -> array else -> DoubleArray(size, ::get) } +/** + * Represent this buffer as [DoubleBuffer]. Does not guarantee that changes in the original buffer are reflected on this buffer. + */ +public fun Buffer.toDoubleBuffer(): DoubleBuffer = when (this) { + is DoubleBuffer -> this + else -> DoubleArray(size, ::get).asBuffer() +} + /** * Returns [DoubleBuffer] over this array. * @@ -62,3 +72,10 @@ public fun Buffer.toDoubleArray(): DoubleArray = when (this) { * @return the new buffer. */ public fun DoubleArray.asBuffer(): DoubleBuffer = DoubleBuffer(this) + + +public fun interface DoubleBufferTransform : BufferTransform { + public fun transform(arg: DoubleBuffer): DoubleBuffer + + override fun transform(arg: Buffer): DoubleBuffer = arg.toDoubleBuffer() +} diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/FloatBuffer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/FloatBuffer.kt index 8666ca675..f1533ee3a 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/FloatBuffer.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/FloatBuffer.kt @@ -14,7 +14,7 @@ import kotlin.jvm.JvmInline * @author Iaroslav Postovalov */ @JvmInline -public value class FloatBuffer(public val array: FloatArray) : MutableBuffer { +public value class FloatBuffer(public val array: FloatArray) : PrimitiveBuffer { override val size: Int get() = array.size override operator fun get(index: Int): Float = array[index] diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/IntBuffer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/IntBuffer.kt index f80ad0ff7..0de7119b1 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/IntBuffer.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/IntBuffer.kt @@ -13,7 +13,7 @@ import kotlin.jvm.JvmInline * @property array the underlying array. */ @JvmInline -public value class IntBuffer(public val array: IntArray) : MutableBuffer { +public value class IntBuffer(public val array: IntArray) : PrimitiveBuffer { override val size: Int get() = array.size override operator fun get(index: Int): Int = array[index] diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/LongBuffer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/LongBuffer.kt index 9d6f1b2a7..9f77fc9d8 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/LongBuffer.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/LongBuffer.kt @@ -13,7 +13,7 @@ import kotlin.jvm.JvmInline * @property array the underlying array. */ @JvmInline -public value class LongBuffer(public val array: LongArray) : MutableBuffer { +public value class LongBuffer(public val array: LongArray) : PrimitiveBuffer { override val size: Int get() = array.size override operator fun get(index: Int): Long = array[index] diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/MutableBuffer.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/MutableBuffer.kt index 709ebd680..c0bfc6ecc 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/MutableBuffer.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/MutableBuffer.kt @@ -94,4 +94,7 @@ public interface MutableBuffer : Buffer { public inline fun auto(size: Int, initializer: (Int) -> T): MutableBuffer = auto(T::class, size, initializer) } -} \ No newline at end of file +} + + +public sealed interface PrimitiveBuffer: MutableBuffer \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/bufferOperation.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferExtensions.kt similarity index 67% rename from kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/bufferOperation.kt rename to kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferExtensions.kt index 3d25d8750..0a475187f 100644 --- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/bufferOperation.kt +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferExtensions.kt @@ -9,14 +9,18 @@ import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.structures.* /** - * Typealias for buffer transformations. + * Type alias for buffer transformations. */ -public typealias BufferTransform = (Buffer) -> Buffer +public fun interface BufferTransform { + public fun transform(arg: Buffer): Buffer +} -/** - * Typealias for buffer transformations with suspend function. - */ -public typealias SuspendBufferTransform = suspend (Buffer) -> Buffer +///** +// * Type alias for buffer transformations with suspend function. +// */ +//public fun interface SuspendBufferTransform{ +// public suspend fun transform(arg: Buffer): Buffer +//} /** @@ -57,18 +61,18 @@ public fun Buffer.toMutableList(): MutableList = when (this) { */ @UnstableKMathAPI public inline fun Buffer.toTypedArray(): Array = Array(size, ::get) - -/** - * Create a new buffer from this one with the given mapping function and using [Buffer.Companion.auto] buffer factory. - */ -public inline fun Buffer.map(block: (T) -> R): Buffer = - Buffer.auto(size) { block(get(it)) } +// +///** +// * Create a new buffer from this one with the given mapping function and using [Buffer.Companion.auto] buffer factory. +// */ +//public inline fun Buffer.map(block: (T) -> R): Buffer = +// Buffer.auto(size) { block(get(it)) } /** * Create a new buffer from this one with the given mapping function. * Provided [bufferFactory] is used to construct the new buffer. */ -public inline fun Buffer.map( +public inline fun Buffer.mapToBuffer( bufferFactory: BufferFactory, crossinline block: (T) -> R, ): Buffer = bufferFactory(size) { block(get(it)) } @@ -77,23 +81,24 @@ public inline fun Buffer.map( * Create a new buffer from this one with the given mapping (indexed) function. * Provided [bufferFactory] is used to construct the new buffer. */ -public inline fun Buffer.mapIndexed( +public inline fun Buffer.mapIndexedToBuffer( bufferFactory: BufferFactory, crossinline block: (index: Int, value: T) -> R, ): Buffer = bufferFactory(size) { block(it, get(it)) } - -/** - * Create a new buffer from this one with the given indexed mapping function. - * Provided [BufferFactory] is used to construct the new buffer. - */ -public inline fun Buffer.mapIndexed( - crossinline block: (index: Int, value: T) -> R, -): Buffer = Buffer.auto(size) { block(it, get(it)) } +// +///** +// * Create a new buffer from this one with the given indexed mapping function. +// * Provided [BufferFactory] is used to construct the new buffer. +// */ +//public inline fun Buffer.mapIndexed( +// crossinline block: (index: Int, value: T) -> R, +//): Buffer = Buffer.auto(size) { block(it, get(it)) } /** * Fold given buffer according to [operation] */ public inline fun Buffer.fold(initial: R, operation: (acc: R, T) -> R): R { + if (size == 0) return initial var accumulator = initial for (index in this.indices) accumulator = operation(accumulator, get(index)) return accumulator @@ -103,18 +108,31 @@ public inline fun Buffer.fold(initial: R, operation: (acc: R, T) -> R) * Fold given buffer according to indexed [operation] */ public inline fun Buffer.foldIndexed(initial: R, operation: (index: Int, acc: R, T) -> R): R { + if (size == 0) return initial var accumulator = initial for (index in this.indices) accumulator = operation(index, accumulator, get(index)) return accumulator } +/** + * Reduce a buffer from left to right according to [operation] + */ +public inline fun Buffer.reduce(operation: (left: T, value: T) -> T): T { + require(size > 0) { "Buffer must have elements" } + var current = get(0) + for (i in 1 until size) { + current = operation(current, get(i)) + } + return current +} + /** * Zip two buffers using given [transform]. */ @UnstableKMathAPI -public inline fun Buffer.zip( +public inline fun Buffer.combineToBuffer( other: Buffer, - bufferFactory: BufferFactory = BufferFactory.auto(), + bufferFactory: BufferFactory, crossinline transform: (T1, T2) -> R, ): Buffer { require(size == other.size) { "Buffer size mismatch in zip: expected $size but found ${other.size}" } diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferPrimitiveAccess.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferPrimitiveAccess.kt new file mode 100644 index 000000000..2f2cc80b3 --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferPrimitiveAccess.kt @@ -0,0 +1,38 @@ +package space.kscience.kmath.structures + +import space.kscience.kmath.misc.UnstableKMathAPI + +/** + * Non-boxing access to primitive [Double] + */ + +@UnstableKMathAPI +public fun Buffer.getDouble(index: Int): Double = if (this is BufferView) { + val originIndex = originIndex(index) + if (originIndex >= 0) { + origin.getDouble(originIndex) + } else { + get(index) + } +} else if (this is DoubleBuffer) { + array[index] +} else { + get(index) +} + +/** + * Non-boxing access to primitive [Int] + */ +@UnstableKMathAPI +public fun Buffer.getInt(index: Int): Int = if (this is BufferView) { + val originIndex = originIndex(index) + if (originIndex >= 0) { + origin.getInt(originIndex) + } else { + get(index) + } +} else if (this is IntBuffer) { + array[index] +} else { + get(index) +} \ No newline at end of file diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/types.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/types.kt new file mode 100644 index 000000000..4ace17538 --- /dev/null +++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/types.kt @@ -0,0 +1,20 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.structures + + +public typealias Float32 = Float +public typealias Float64 = Double + +public typealias Int8 = Byte +public typealias Int16 = Short +public typealias Int32 = Int +public typealias Int64 = Long + +public typealias UInt8 = UByte +public typealias UInt16 = UShort +public typealias UInt32 = UInt +public typealias UInt64 = ULong \ No newline at end of file diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/nd/StridesTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/nd/StridesTest.kt new file mode 100644 index 000000000..e6335f652 --- /dev/null +++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/nd/StridesTest.kt @@ -0,0 +1,38 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.nd + +import kotlin.test.Test + +class StridesTest { + @Test + fun checkRowBasedStrides() { + val strides = RowStrides(ShapeND(3, 3)) + var counter = 0 + for(i in 0..2){ + for(j in 0..2){ +// print(strides.offset(intArrayOf(i,j)).toString() + "\t") + require(strides.offset(intArrayOf(i,j)) == counter) + counter++ + } + println() + } + } + + @Test + fun checkColumnBasedStrides() { + val strides = ColumnStrides(ShapeND(3, 3)) + var counter = 0 + for(i in 0..2){ + for(j in 0..2){ +// print(strides.offset(intArrayOf(i,j)).toString() + "\t") + require(strides.offset(intArrayOf(j,i)) == counter) + counter++ + } + println() + } + } +} \ No newline at end of file diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/BufferExpandedTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/BufferExpandedTest.kt new file mode 100644 index 000000000..04671e040 --- /dev/null +++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/BufferExpandedTest.kt @@ -0,0 +1,27 @@ +package space.kscience.kmath.structures + +import kotlin.test.Test +import kotlin.test.assertEquals +import kotlin.test.assertFails + +internal class BufferExpandedTest { + private val buffer = (0..100).toList().asBuffer() + + @Test + fun shrink(){ + val view = buffer.slice(20..30) + assertEquals(20, view[0]) + assertEquals(30, view[10]) + assertFails { view[11] } + } + + @Test + fun expandNegative(){ + val view: BufferView = buffer.expand(-20..113,0) + assertEquals(0,view[4]) + assertEquals(0,view[123]) + assertEquals(100, view[120]) + assertFails { view[-2] } + assertFails { view[134] } + } +} \ No newline at end of file diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt index a54af571e..147488273 100644 --- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt +++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt @@ -88,7 +88,7 @@ class NumberNDFieldTest { @Test fun testInternalContext() { algebra { - (DoubleField.ndAlgebra(*array1.shape)) { with(L2Norm) { 1 + norm(array1) + exp(array2) } } + (DoubleField.ndAlgebra(array1.shape)) { with(L2Norm) { 1 + norm(array1) + exp(array2) } } } } } diff --git a/kmath-core/src/jvmTest/kotlin/space/kscience/kmath/misc/JBigTest.kt b/kmath-core/src/jvmTest/kotlin/space/kscience/kmath/misc/JBigTest.kt new file mode 100644 index 000000000..f7f8027e6 --- /dev/null +++ b/kmath-core/src/jvmTest/kotlin/space/kscience/kmath/misc/JBigTest.kt @@ -0,0 +1,20 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.misc + +import org.junit.jupiter.api.Test +import space.kscience.kmath.operations.JBigDecimalField +import kotlin.test.assertEquals +import kotlin.test.assertNotEquals + +class JBigTest { + + @Test + fun testExact() = with(JBigDecimalField) { + assertNotEquals(0.3, 0.1 + 0.2) + assertEquals(one * 0.3, one * 0.1 + one * 0.2) + } +} \ No newline at end of file diff --git a/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/coroutines/coroutinesExtra.kt b/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/coroutines/coroutinesExtra.kt index 3f06693b0..7bae388a8 100644 --- a/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/coroutines/coroutinesExtra.kt +++ b/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/coroutines/coroutinesExtra.kt @@ -81,9 +81,7 @@ public suspend fun AsyncFlow.collect(concurrency: Int, collector: FlowCol public suspend inline fun AsyncFlow.collect( concurrency: Int, crossinline action: suspend (value: T) -> Unit, -): Unit = collect(concurrency, object : FlowCollector { - override suspend fun emit(value: T): Unit = action(value) -}) +): Unit = collect(concurrency, FlowCollector { value -> action(value) }) public inline fun Flow.mapParallel( dispatcher: CoroutineDispatcher = Dispatchers.Default, diff --git a/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/streaming/BufferFlow.kt b/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/streaming/BufferFlow.kt index 00c874751..8aa5a937c 100644 --- a/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/streaming/BufferFlow.kt +++ b/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/streaming/BufferFlow.kt @@ -5,8 +5,10 @@ package space.kscience.kmath.streaming -import kotlinx.coroutines.FlowPreview -import kotlinx.coroutines.flow.* +import kotlinx.coroutines.flow.Flow +import kotlinx.coroutines.flow.asFlow +import kotlinx.coroutines.flow.flatMapConcat +import kotlinx.coroutines.flow.flow import space.kscience.kmath.chains.BlockingDoubleChain import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.BufferFactory @@ -20,7 +22,6 @@ public fun Buffer.asFlow(): Flow = iterator().asFlow() /** * Flat map a [Flow] of [Buffer] into continuous [Flow] of elements */ -@FlowPreview public fun Flow>.spread(): Flow = flatMapConcat { it.asFlow() } /** diff --git a/kmath-coroutines/src/jvmMain/kotlin/space/kscience/kmath/structures/LazyStructureND.kt b/kmath-coroutines/src/jvmMain/kotlin/space/kscience/kmath/structures/LazyStructureND.kt index 786d32190..1f717658e 100644 --- a/kmath-coroutines/src/jvmMain/kotlin/space/kscience/kmath/structures/LazyStructureND.kt +++ b/kmath-coroutines/src/jvmMain/kotlin/space/kscience/kmath/structures/LazyStructureND.kt @@ -8,12 +8,13 @@ package space.kscience.kmath.structures import kotlinx.coroutines.* import space.kscience.kmath.coroutines.Math import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.DefaultStrides +import space.kscience.kmath.nd.ColumnStrides +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND public class LazyStructureND( public val scope: CoroutineScope, - override val shape: IntArray, + override val shape: ShapeND, public val function: suspend (IntArray) -> T, ) : StructureND { private val cache: MutableMap> = HashMap() @@ -23,30 +24,35 @@ public class LazyStructureND( } public suspend fun await(index: IntArray): T = async(index).await() + @PerformancePitfall override operator fun get(index: IntArray): T = runBlocking { async(index).await() } @OptIn(PerformancePitfall::class) override fun elements(): Sequence> { - val strides = DefaultStrides(shape) + val strides = ColumnStrides(shape) val res = runBlocking { strides.asSequence().toList().map { index -> index to await(index) } } return res.asSequence() } } +@OptIn(PerformancePitfall::class) public fun StructureND.async(index: IntArray): Deferred = if (this is LazyStructureND) this@async.async(index) else CompletableDeferred(get(index)) +@OptIn(PerformancePitfall::class) public suspend fun StructureND.await(index: IntArray): T = if (this is LazyStructureND) await(index) else get(index) /** * PENDING would benefit from KEEP-176 */ +@OptIn(PerformancePitfall::class) public inline fun StructureND.mapAsyncIndexed( scope: CoroutineScope, crossinline function: suspend (T, index: IntArray) -> R, ): LazyStructureND = LazyStructureND(scope, shape) { index -> function(get(index), index) } +@OptIn(PerformancePitfall::class) public inline fun StructureND.mapAsync( scope: CoroutineScope, crossinline function: suspend (T) -> R, diff --git a/kmath-dimensions/src/commonMain/kotlin/space/kscience/kmath/dimensions/Wrappers.kt b/kmath-dimensions/src/commonMain/kotlin/space/kscience/kmath/dimensions/Wrappers.kt index b93114804..dde2d4fcf 100644 --- a/kmath-dimensions/src/commonMain/kotlin/space/kscience/kmath/dimensions/Wrappers.kt +++ b/kmath-dimensions/src/commonMain/kotlin/space/kscience/kmath/dimensions/Wrappers.kt @@ -6,6 +6,7 @@ package space.kscience.kmath.dimensions import space.kscience.kmath.linear.* +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.Structure2D import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.operations.Ring @@ -47,7 +48,7 @@ public interface DMatrix : Structure2D { public value class DMatrixWrapper( private val structure: Structure2D, ) : DMatrix { - override val shape: IntArray get() = structure.shape + override val shape: ShapeND get() = structure.shape override val rowNum: Int get() = shape[0] override val colNum: Int get() = shape[1] override operator fun get(i: Int, j: Int): T = structure[i, j] diff --git a/kmath-ejml/src/test/kotlin/space/kscience/kmath/ejml/EjmlMatrixTest.kt b/kmath-ejml/src/test/kotlin/space/kscience/kmath/ejml/EjmlMatrixTest.kt index e3bff8987..d1ae80ef9 100644 --- a/kmath-ejml/src/test/kotlin/space/kscience/kmath/ejml/EjmlMatrixTest.kt +++ b/kmath-ejml/src/test/kotlin/space/kscience/kmath/ejml/EjmlMatrixTest.kt @@ -15,6 +15,7 @@ import space.kscience.kmath.linear.* import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.nd.StructureND +import space.kscience.kmath.nd.toArray import space.kscience.kmath.operations.algebra import kotlin.random.Random import kotlin.random.asJavaRandom @@ -52,7 +53,7 @@ internal class EjmlMatrixTest { fun shape() { val m = randomMatrix val w = EjmlDoubleMatrix(m) - assertContentEquals(intArrayOf(m.numRows, m.numCols), w.shape) + assertContentEquals(intArrayOf(m.numRows, m.numCols), w.shape.toArray()) } @OptIn(UnstableKMathAPI::class) diff --git a/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/RealMatrix.kt b/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/RealMatrix.kt index c44b1dff0..cfa59bf32 100644 --- a/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/RealMatrix.kt +++ b/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/RealMatrix.kt @@ -131,7 +131,7 @@ public fun RealMatrix.extractColumn(columnIndex: Int): RealMatrix = extractColumns(columnIndex..columnIndex) public fun RealMatrix.sumByColumn(): DoubleBuffer = DoubleBuffer(colNum) { j -> - columns[j].asIterable().sum() + columns[j].sum() } public fun RealMatrix.minByColumn(): DoubleBuffer = DoubleBuffer(colNum) { j -> diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt index 4cfed8efe..fc76ea819 100644 --- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt +++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt @@ -5,7 +5,7 @@ package space.kscience.kmath.integration -import space.kscience.kmath.operations.map +import space.kscience.kmath.operations.mapToBuffer import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.DoubleBuffer import space.kscience.kmath.structures.asBuffer @@ -30,14 +30,14 @@ public fun GaussIntegratorRuleFactory.build( numPoints: Int, range: ClosedRange, ): Pair, Buffer> { - val normalized = build(numPoints) + val normalized: Pair, Buffer> = build(numPoints) val length = range.endInclusive - range.start - val points = normalized.first.map(::DoubleBuffer) { + val points = normalized.first.mapToBuffer(::DoubleBuffer) { range.start + length / 2 + length / 2 * it } - val weights = normalized.second.map(::DoubleBuffer) { + val weights = normalized.second.mapToBuffer(::DoubleBuffer) { it * length / 2 } diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt index 9a8f475c8..c66674fbb 100644 --- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt +++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt @@ -65,9 +65,9 @@ public class SplineIntegrator>( DoubleBuffer(numPoints) { i -> range.start + i * step } } - val values = nodes.map(bufferFactory) { integrand.function(it) } + val values = nodes.mapToBuffer(bufferFactory) { integrand.function(it) } val polynomials = interpolator.interpolatePolynomials( - nodes.map(bufferFactory) { number(it) }, + nodes.mapToBuffer(bufferFactory) { number(it) }, values ) val res = polynomials.integrate(algebra, number(range.start)..number(range.endInclusive)) @@ -93,7 +93,7 @@ public object DoubleSplineIntegrator : UnivariateIntegrator { DoubleBuffer(numPoints) { i -> range.start + i * step } } - val values = nodes.map { integrand.function(it) } + val values = nodes.mapToBuffer(::DoubleBuffer) { integrand.function(it) } val polynomials = interpolator.interpolatePolynomials(nodes, values) val res = polynomials.integrate(DoubleField, range) return integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + nodes.size) diff --git a/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Vector2DTest.kt b/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Vector2DTest.kt index c33567f11..0db06f4c8 100644 --- a/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Vector2DTest.kt +++ b/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Vector2DTest.kt @@ -5,6 +5,7 @@ package space.kscience.kmath.geometry + import space.kscience.kmath.operations.toList import kotlin.test.Test import kotlin.test.assertEquals diff --git a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/HistogramND.kt b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/HistogramND.kt index 2cefb33a5..623452422 100644 --- a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/HistogramND.kt +++ b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/HistogramND.kt @@ -7,9 +7,10 @@ package space.kscience.kmath.histogram import space.kscience.kmath.domains.Domain import space.kscience.kmath.linear.Point -import space.kscience.kmath.nd.DefaultStrides +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.ColumnStrides import space.kscience.kmath.nd.FieldOpsND -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND import space.kscience.kmath.operations.Group import space.kscience.kmath.operations.ScaleOperations @@ -24,6 +25,7 @@ public class HistogramND, D : Domain, V : Any>( internal val values: StructureND, ) : Histogram> { + @OptIn(PerformancePitfall::class) override fun get(point: Point): DomainBin? { val index = group.getIndexOrNull(point) ?: return null return group.produceBin(index, values[index]) @@ -31,8 +33,9 @@ public class HistogramND, D : Domain, V : Any>( override val dimension: Int get() = group.shape.size + @OptIn(PerformancePitfall::class) override val bins: Iterable> - get() = DefaultStrides(group.shape).asSequence().map { + get() = ColumnStrides(group.shape).asSequence().map { group.produceBin(it, values[it]) }.asIterable() } @@ -42,7 +45,7 @@ public class HistogramND, D : Domain, V : Any>( */ public interface HistogramGroupND, D : Domain, V : Any> : Group>, ScaleOperations> { - public val shape: Shape + public val shape: ShapeND public val valueAlgebraND: FieldOpsND //= NDAlgebra.space(valueSpace, Buffer.Companion::boxing, *shape), /** diff --git a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/UniformHistogramGroupND.kt b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/UniformHistogramGroupND.kt index 36e994bcf..b62780ed5 100644 --- a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/UniformHistogramGroupND.kt +++ b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/UniformHistogramGroupND.kt @@ -9,11 +9,10 @@ package space.kscience.kmath.histogram import space.kscience.kmath.domains.HyperSquareDomain import space.kscience.kmath.linear.Point +import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.nd.* -import space.kscience.kmath.operations.DoubleField -import space.kscience.kmath.operations.Field -import space.kscience.kmath.operations.invoke +import space.kscience.kmath.operations.* import space.kscience.kmath.structures.* import kotlin.math.floor @@ -40,7 +39,7 @@ public class UniformHistogramGroupND>( public val dimension: Int get() = lower.size - override val shape: IntArray = IntArray(binNums.size) { binNums[it] + 2 } + override val shape: ShapeND = ShapeND(IntArray(binNums.size) { binNums[it] + 2 }) private val binSize = DoubleBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] } @@ -83,8 +82,12 @@ public class UniformHistogramGroupND>( } - override fun produce(builder: HistogramBuilder.() -> Unit): HistogramND { - val ndCounter = StructureND.buffered(shape) { Counter.of(valueAlgebraND.elementAlgebra) } + @OptIn(PerformancePitfall::class) + override fun produce( + builder: HistogramBuilder.() -> Unit, + ): HistogramND { + val ndCounter: BufferND> = + StructureND.buffered(shape) { Counter.of(valueAlgebraND.elementAlgebra) } val hBuilder = object : HistogramBuilder { override val defaultValue: V get() = valueAlgebraND.elementAlgebra.one @@ -94,7 +97,8 @@ public class UniformHistogramGroupND>( } } hBuilder.apply(builder) - val values: BufferND = ndCounter.mapToBuffer(valueBufferFactory) { it.value } + val values: BufferND = BufferND(ndCounter.indices, ndCounter.buffer.mapToBuffer(valueBufferFactory) { it.value }) + return HistogramND(this, values) } diff --git a/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt b/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt index 717f9d7a1..64cc4f203 100644 --- a/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt +++ b/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt @@ -7,8 +7,9 @@ package space.kscience.kmath.histogram +import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.nd.DefaultStrides +import space.kscience.kmath.nd.ColumnStrides import space.kscience.kmath.operations.invoke import space.kscience.kmath.real.DoubleVector import kotlin.random.Random @@ -50,6 +51,7 @@ internal class MultivariateHistogramTest { assertEquals(n, histogram.bins.sumOf { it.binValue.toInt() }) } + @OptIn(PerformancePitfall::class) @Test fun testHistogramAlgebra() { Histogram.uniformDoubleNDFromRanges( @@ -73,7 +75,7 @@ internal class MultivariateHistogramTest { } val res = histogram1 - histogram2 assertTrue { - DefaultStrides(shape).asSequence().all { index -> + ColumnStrides(shape).asSequence().all { index -> res.values[index] <= histogram1.values[index] } } diff --git a/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/UniformHistogram1DTest.kt b/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/UniformHistogram1DTest.kt index fd107f5e8..c4554b575 100644 --- a/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/UniformHistogram1DTest.kt +++ b/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/UniformHistogram1DTest.kt @@ -10,7 +10,7 @@ import kotlinx.coroutines.test.runTest import space.kscience.kmath.distributions.NormalDistribution import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.operations.DoubleField -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.stat.nextBuffer import kotlin.native.concurrent.ThreadLocal import kotlin.test.Test @@ -36,7 +36,7 @@ internal class UniformHistogram1DTest { @Test fun rebinDown() = runTest { val h1 = Histogram.uniform1D(DoubleField, 0.01).produce(generator.nextDoubleBuffer(10000)) - val h2 = Histogram.uniform1D(DoubleField,0.03).produceFrom(h1) + val h2 = Histogram.uniform1D(DoubleField, 0.03).produceFrom(h1) assertEquals(10000, h2.bins.sumOf { it.binValue }.toInt()) } @@ -44,13 +44,13 @@ internal class UniformHistogram1DTest { @Test fun rebinUp() = runTest { val h1 = Histogram.uniform1D(DoubleField, 0.03).produce(generator.nextDoubleBuffer(10000)) - val h2 = Histogram.uniform1D(DoubleField,0.01).produceFrom(h1) + val h2 = Histogram.uniform1D(DoubleField, 0.01).produceFrom(h1) assertEquals(10000, h2.bins.sumOf { it.binValue }.toInt()) } @ThreadLocal - companion object{ + companion object { private val generator = RandomGenerator.default(123) } } \ No newline at end of file diff --git a/kmath-jupyter/src/main/kotlin/space/kscience/kmath/jupyter/KMathJupyter.kt b/kmath-jupyter/src/main/kotlin/space/kscience/kmath/jupyter/KMathJupyter.kt index 85797134f..1fe9fe92f 100644 --- a/kmath-jupyter/src/main/kotlin/space/kscience/kmath/jupyter/KMathJupyter.kt +++ b/kmath-jupyter/src/main/kotlin/space/kscience/kmath/jupyter/KMathJupyter.kt @@ -47,11 +47,13 @@ internal class KMathJupyter : JupyterIntegration() { syntaxRender.renderPart(mathRender.render(MST.Numeric(it)), s) +s.toString() } + is MST -> { val s = StringBuilder() syntaxRender.renderPart(mathRender.render(it), s) +s.toString() } + else -> { +"" +it.toString() diff --git a/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensor.kt b/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensor.kt index 38d61e982..ae526873d 100644 --- a/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensor.kt +++ b/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensor.kt @@ -7,20 +7,22 @@ package space.kscience.kmath.multik import org.jetbrains.kotlinx.multik.ndarray.data.* import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.tensors.api.Tensor import kotlin.jvm.JvmInline @JvmInline public value class MultikTensor(public val array: MutableMultiArray) : Tensor { - override val shape: Shape get() = array.shape + override val shape: ShapeND get() = ShapeND(array.shape) + @PerformancePitfall override fun get(index: IntArray): T = array[index] @PerformancePitfall override fun elements(): Sequence> = array.multiIndices.iterator().asSequence().map { it to get(it) } + @PerformancePitfall override fun set(index: IntArray, value: T) { array[index] = value } diff --git a/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt b/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt index 194c5fcee..1736b48e3 100644 --- a/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt +++ b/kmath-multik/src/commonMain/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt @@ -14,6 +14,7 @@ import org.jetbrains.kotlinx.multik.api.stat.Statistics import org.jetbrains.kotlinx.multik.ndarray.data.* import org.jetbrains.kotlinx.multik.ndarray.operations.* import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.misc.UnsafeKMathAPI import space.kscience.kmath.nd.* import space.kscience.kmath.operations.* import space.kscience.kmath.tensors.api.Tensor @@ -30,21 +31,22 @@ public abstract class MultikTensorAlgebra>( protected val multikLinAl: LinAlg = multikEngine.getLinAlg() protected val multikStat: Statistics = multikEngine.getStatistics() - override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor { - val strides = DefaultStrides(shape) + @OptIn(UnsafeKMathAPI::class) + override fun structureND(shape: ShapeND, initializer: A.(IntArray) -> T): MultikTensor { + val strides = ColumnStrides(shape) val memoryView = initMemoryView(strides.linearSize, type) strides.asSequence().forEachIndexed { linearIndex, tensorIndex -> memoryView[linearIndex] = elementAlgebra.initializer(tensorIndex) } - return MultikTensor(NDArray(memoryView, shape = shape, dim = DN(shape.size))) + return MultikTensor(NDArray(memoryView, shape = shape.asArray(), dim = DN(shape.size))) } - @OptIn(PerformancePitfall::class) + @OptIn(PerformancePitfall::class, UnsafeKMathAPI::class) override fun StructureND.map(transform: A.(T) -> T): MultikTensor = if (this is MultikTensor) { val data = initMemoryView(array.size, type) var count = 0 for (el in array) data[count++] = elementAlgebra.transform(el) - NDArray(data, shape = shape, dim = array.dim).wrap() + NDArray(data, shape = shape.asArray(), dim = array.dim).wrap() } else { structureND(shape) { index -> transform(get(index)) @@ -75,6 +77,7 @@ public abstract class MultikTensorAlgebra>( /** * Transform a structure element-by element in place. */ + @OptIn(PerformancePitfall::class) public inline fun MutableStructureND.mapIndexedInPlace(operation: (index: IntArray, t: T) -> T): Unit { if (this is MultikTensor) { array.multiIndices.iterator().forEach { @@ -106,10 +109,11 @@ public abstract class MultikTensorAlgebra>( * Convert a tensor to [MultikTensor] if necessary. If tensor is converted, changes on the resulting tensor * are not reflected back onto the source */ + @OptIn(UnsafeKMathAPI::class, PerformancePitfall::class) public fun StructureND.asMultik(): MultikTensor = if (this is MultikTensor) { this } else { - val res = mk.zeros(shape, type).asDNArray() + val res = mk.zeros(shape.asArray(), type).asDNArray() for (index in res.multiIndices) { res[index] = this[index] } @@ -118,7 +122,8 @@ public abstract class MultikTensorAlgebra>( public fun MutableMultiArray.wrap(): MultikTensor = MultikTensor(this.asDNArray()) - override fun StructureND.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) { + @OptIn(PerformancePitfall::class) + override fun StructureND.valueOrNull(): T? = if (shape contentEquals ShapeND(1)) { get(intArrayOf(0)) } else null @@ -139,6 +144,7 @@ public abstract class MultikTensorAlgebra>( } } + @OptIn(PerformancePitfall::class) override fun Tensor.plusAssign(arg: StructureND) { if (this is MultikTensor) { array.plusAssign(arg.asMultik().array) @@ -163,6 +169,7 @@ public abstract class MultikTensorAlgebra>( } } + @OptIn(PerformancePitfall::class) override fun Tensor.minusAssign(arg: StructureND) { if (this is MultikTensor) { array.minusAssign(arg.asMultik().array) @@ -188,6 +195,7 @@ public abstract class MultikTensorAlgebra>( } } + @OptIn(PerformancePitfall::class) override fun Tensor.timesAssign(arg: StructureND) { if (this is MultikTensor) { array.timesAssign(arg.asMultik().array) @@ -201,13 +209,13 @@ public abstract class MultikTensorAlgebra>( override fun Tensor.getTensor(i: Int): MultikTensor = asMultik().array.mutableView(i).wrap() - override fun Tensor.transposed(i: Int, j: Int): MultikTensor = asMultik().array.transpose(i, j).wrap() + override fun StructureND.transposed(i: Int, j: Int): MultikTensor = asMultik().array.transpose(i, j).wrap() - override fun Tensor.view(shape: IntArray): MultikTensor { - require(shape.all { it > 0 }) - require(shape.fold(1, Int::times) == this.shape.size) { + override fun Tensor.view(shape: ShapeND): MultikTensor { + require(shape.asList().all { it > 0 }) + require(shape.linearSize == this.shape.size) { "Cannot reshape array of size ${this.shape.size} into a new shape ${ - shape.joinToString( + shape.asList().joinToString( prefix = "(", postfix = ")" ) @@ -215,10 +223,11 @@ public abstract class MultikTensorAlgebra>( } val mt = asMultik().array - return if (mt.shape.contentEquals(shape)) { + return if (ShapeND(mt.shape).contentEquals(shape)) { mt } else { - NDArray(mt.data, mt.offset, shape, dim = DN(shape.size), base = mt.base ?: mt) + @OptIn(UnsafeKMathAPI::class) + NDArray(mt.data, mt.offset, shape.asArray(), dim = DN(shape.size), base = mt.base ?: mt) }.wrap() } @@ -241,7 +250,7 @@ public abstract class MultikTensorAlgebra>( TODO("Not implemented for broadcasting") } - override fun diagonalEmbedding(diagonalEntries: Tensor, offset: Int, dim1: Int, dim2: Int): MultikTensor { + override fun diagonalEmbedding(diagonalEntries: StructureND, offset: Int, dim1: Int, dim2: Int): MultikTensor { TODO("Diagonal embedding not implemented") } @@ -284,8 +293,9 @@ public abstract class MultikDivisionTensorAlgebra>( multikEngine: Engine, ) : MultikTensorAlgebra(multikEngine), TensorPartialDivisionAlgebra where T : Number, T : Comparable { + @OptIn(UnsafeKMathAPI::class) override fun T.div(arg: StructureND): MultikTensor = - Multik.ones(arg.shape, type).apply { divAssign(arg.asMultik().array) }.wrap() + Multik.ones(arg.shape.asArray(), type).apply { divAssign(arg.asMultik().array) }.wrap() override fun StructureND.div(arg: T): MultikTensor = asMultik().array.div(arg).wrap() @@ -301,6 +311,7 @@ public abstract class MultikDivisionTensorAlgebra>( } } + @OptIn(PerformancePitfall::class) override fun Tensor.divAssign(arg: StructureND) { if (this is MultikTensor) { array.divAssign(arg.asMultik().array) diff --git a/kmath-multik/src/commonTest/kotlin/space/kscience/kmath/multik/MultikNDTest.kt b/kmath-multik/src/commonTest/kotlin/space/kscience/kmath/multik/MultikNDTest.kt index 392532d8e..d52420fc6 100644 --- a/kmath-multik/src/commonTest/kotlin/space/kscience/kmath/multik/MultikNDTest.kt +++ b/kmath-multik/src/commonTest/kotlin/space/kscience/kmath/multik/MultikNDTest.kt @@ -7,10 +7,12 @@ package space.kscience.kmath.multik import org.jetbrains.kotlinx.multik.default.DefaultEngine import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND import space.kscience.kmath.nd.one import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.tensors.core.DoubleTensorAlgebra +import space.kscience.kmath.tensors.core.randomNormal import space.kscience.kmath.tensors.core.tensorAlgebra import kotlin.test.Test import kotlin.test.assertTrue @@ -28,8 +30,8 @@ internal class MultikNDTest { fun dotResult() { val dim = 100 - val tensor1 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12224) - val tensor2 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12225) + val tensor1 = DoubleTensorAlgebra.randomNormal(shape = ShapeND(dim, dim), 12224) + val tensor2 = DoubleTensorAlgebra.randomNormal(shape = ShapeND(dim, dim), 12225) val multikResult = with(multikAlgebra) { tensor1 dot tensor2 diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt index 859773211..6f01233d7 100644 --- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt +++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt @@ -11,6 +11,7 @@ import org.nd4j.linalg.api.ops.impl.transforms.strict.ASinh import org.nd4j.linalg.factory.Nd4j import org.nd4j.linalg.ops.transforms.Transforms import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.misc.UnsafeKMathAPI import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.nd.* import space.kscience.kmath.operations.* @@ -32,8 +33,10 @@ public sealed interface Nd4jArrayAlgebra> : AlgebraND.ndArray: INDArray - override fun structureND(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure { - val struct = Nd4j.create(*shape)!!.wrap() + @OptIn(PerformancePitfall::class) + override fun structureND(shape: ShapeND, initializer: C.(IntArray) -> T): Nd4jArrayStructure { + @OptIn(UnsafeKMathAPI::class) + val struct: Nd4jArrayStructure = Nd4j.create(*shape.asArray())!!.wrap() struct.indicesIterator().forEach { struct[it] = elementAlgebra.initializer(it) } return struct } @@ -45,23 +48,23 @@ public sealed interface Nd4jArrayAlgebra> : AlgebraND.mapIndexed( transform: C.(index: IntArray, T) -> T, ): Nd4jArrayStructure { - val new = Nd4j.create(*shape).wrap() + val new = Nd4j.create(*shape.asArray()).wrap() new.indicesIterator().forEach { idx -> new[idx] = elementAlgebra.transform(idx, this[idx]) } return new } - @OptIn(PerformancePitfall::class) + @OptIn(PerformancePitfall::class, UnsafeKMathAPI::class) override fun zip( left: StructureND, right: StructureND, transform: C.(T, T) -> T, ): Nd4jArrayStructure { require(left.shape.contentEquals(right.shape)) { "Can't zip tow structures of shape ${left.shape} and ${right.shape}" } - val new = Nd4j.create(*left.shape).wrap() + val new = Nd4j.create(*left.shape.asArray()).wrap() new.indicesIterator().forEach { idx -> new[idx] = elementAlgebra.transform(left[idx], right[idx]) } return new } @@ -192,11 +195,11 @@ public open class DoubleNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps = asDoubleStructure() - @OptIn(PerformancePitfall::class) + @OptIn(PerformancePitfall::class, UnsafeKMathAPI::class) override val StructureND.ndArray: INDArray get() = when (this) { is Nd4jArrayStructure -> ndArray - else -> Nd4j.zeros(*shape).also { + else -> Nd4j.zeros(*shape.asArray()).also { elements().forEach { (idx, value) -> it.putScalar(idx, value) } } } @@ -222,10 +225,10 @@ public open class DoubleNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps +public class DoubleNd4jArrayField(override val shape: ShapeND) : DoubleNd4jArrayFieldOps(), FieldND public fun DoubleField.nd4j(shapeFirst: Int, vararg shapeRest: Int): DoubleNd4jArrayField = - DoubleNd4jArrayField(intArrayOf(shapeFirst, * shapeRest)) + DoubleNd4jArrayField(ShapeND(shapeFirst, * shapeRest)) /** @@ -236,11 +239,11 @@ public open class FloatNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps = asFloatStructure() - @OptIn(PerformancePitfall::class) + @OptIn(PerformancePitfall::class, UnsafeKMathAPI::class) override val StructureND.ndArray: INDArray get() = when (this) { is Nd4jArrayStructure -> ndArray - else -> Nd4j.zeros(*shape).also { + else -> Nd4j.zeros(*shape.asArray()).also { elements().forEach { (idx, value) -> it.putScalar(idx, value) } } } @@ -269,12 +272,12 @@ public open class FloatNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps +public class FloatNd4jArrayField(override val shape: ShapeND) : FloatNd4jArrayFieldOps(), RingND public val FloatField.nd4j: FloatNd4jArrayFieldOps get() = FloatNd4jArrayFieldOps public fun FloatField.nd4j(shapeFirst: Int, vararg shapeRest: Int): FloatNd4jArrayField = - FloatNd4jArrayField(intArrayOf(shapeFirst, * shapeRest)) + FloatNd4jArrayField(ShapeND(shapeFirst, * shapeRest)) /** * Represents [RingND] over [Nd4jArrayIntStructure]. @@ -284,11 +287,11 @@ public open class IntNd4jArrayRingOps : Nd4jArrayRingOps { override fun INDArray.wrap(): Nd4jArrayStructure = asIntStructure() - @OptIn(PerformancePitfall::class) + @OptIn(PerformancePitfall::class, UnsafeKMathAPI::class) override val StructureND.ndArray: INDArray get() = when (this) { is Nd4jArrayStructure -> ndArray - else -> Nd4j.zeros(*shape).also { + else -> Nd4j.zeros(*shape.asArray()).also { elements().forEach { (idx, value) -> it.putScalar(idx, value) } } } @@ -310,7 +313,7 @@ public open class IntNd4jArrayRingOps : Nd4jArrayRingOps { public val IntRing.nd4j: IntNd4jArrayRingOps get() = IntNd4jArrayRingOps -public class IntNd4jArrayRing(override val shape: Shape) : IntNd4jArrayRingOps(), RingND +public class IntNd4jArrayRing(override val shape: ShapeND) : IntNd4jArrayRingOps(), RingND public fun IntRing.nd4j(shapeFirst: Int, vararg shapeRest: Int): IntNd4jArrayRing = - IntNd4jArrayRing(intArrayOf(shapeFirst, * shapeRest)) \ No newline at end of file + IntNd4jArrayRing(ShapeND(shapeFirst, * shapeRest)) \ No newline at end of file diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructure.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructure.kt index 0a7d15e20..a1405ccfb 100644 --- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructure.kt +++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructure.kt @@ -7,8 +7,7 @@ package space.kscience.kmath.nd4j import org.nd4j.linalg.api.ndarray.INDArray import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.MutableStructureND -import space.kscience.kmath.nd.StructureND +import space.kscience.kmath.nd.* /** * Represents a [StructureND] wrapping an [INDArray] object. @@ -22,7 +21,7 @@ public sealed class Nd4jArrayStructure : MutableStructureND { */ public abstract val ndArray: INDArray - override val shape: IntArray get() = ndArray.shape().toIntArray() + override val shape: ShapeND get() = ShapeND(ndArray.shape().toIntArray()) internal abstract fun elementsIterator(): Iterator> internal fun indicesIterator(): Iterator = ndArray.indicesIterator() @@ -31,20 +30,31 @@ public sealed class Nd4jArrayStructure : MutableStructureND { override fun elements(): Sequence> = Sequence(::elementsIterator) } -private data class Nd4jArrayIntStructure(override val ndArray: INDArray) : Nd4jArrayStructure() { +public data class Nd4jArrayIntStructure(override val ndArray: INDArray) : Nd4jArrayStructure(), StructureNDOfInt { override fun elementsIterator(): Iterator> = ndArray.intIterator() + + @OptIn(PerformancePitfall::class) override fun get(index: IntArray): Int = ndArray.getInt(*index) + + override fun getInt(index: IntArray): Int = ndArray.getInt(*index) + + @OptIn(PerformancePitfall::class) override fun set(index: IntArray, value: Int): Unit = run { ndArray.putScalar(index, value) } } /** * Wraps this [INDArray] to [Nd4jArrayStructure]. */ -public fun INDArray.asIntStructure(): Nd4jArrayStructure = Nd4jArrayIntStructure(this) +public fun INDArray.asIntStructure(): Nd4jArrayIntStructure = Nd4jArrayIntStructure(this) -private data class Nd4jArrayDoubleStructure(override val ndArray: INDArray) : Nd4jArrayStructure() { +public data class Nd4jArrayDoubleStructure(override val ndArray: INDArray) : Nd4jArrayStructure(), StructureNDOfDouble { override fun elementsIterator(): Iterator> = ndArray.realIterator() + @OptIn(PerformancePitfall::class) override fun get(index: IntArray): Double = ndArray.getDouble(*index) + + override fun getDouble(index: IntArray): Double = ndArray.getDouble(*index) + + @OptIn(PerformancePitfall::class) override fun set(index: IntArray, value: Double): Unit = run { ndArray.putScalar(index, value) } } @@ -53,9 +63,12 @@ private data class Nd4jArrayDoubleStructure(override val ndArray: INDArray) : Nd */ public fun INDArray.asDoubleStructure(): Nd4jArrayStructure = Nd4jArrayDoubleStructure(this) -private data class Nd4jArrayFloatStructure(override val ndArray: INDArray) : Nd4jArrayStructure() { +public data class Nd4jArrayFloatStructure(override val ndArray: INDArray) : Nd4jArrayStructure() { override fun elementsIterator(): Iterator> = ndArray.floatIterator() + @PerformancePitfall override fun get(index: IntArray): Float = ndArray.getFloat(*index) + + @PerformancePitfall override fun set(index: IntArray, value: Float): Unit = run { ndArray.putScalar(index, value) } } diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jTensorAlgebra.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jTensorAlgebra.kt index c1772683f..ef7b7f257 100644 --- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jTensorAlgebra.kt +++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jTensorAlgebra.kt @@ -13,9 +13,8 @@ import org.nd4j.linalg.factory.Nd4j import org.nd4j.linalg.factory.ops.NDBase import org.nd4j.linalg.ops.transforms.Transforms import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.DefaultStrides -import space.kscience.kmath.nd.Shape -import space.kscience.kmath.nd.StructureND +import space.kscience.kmath.misc.UnsafeKMathAPI +import space.kscience.kmath.nd.* import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.operations.Field import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra @@ -38,7 +37,7 @@ public sealed interface Nd4jTensorAlgebra> : AnalyticTe */ public val StructureND.ndArray: INDArray - override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): Nd4jArrayStructure + override fun structureND(shape: ShapeND, initializer: A.(IntArray) -> T): Nd4jArrayStructure @OptIn(PerformancePitfall::class) override fun StructureND.map(transform: A.(T) -> T): Nd4jArrayStructure = @@ -96,7 +95,7 @@ public sealed interface Nd4jTensorAlgebra> : AnalyticTe override fun StructureND.unaryMinus(): Nd4jArrayStructure = ndArray.neg().wrap() override fun Tensor.getTensor(i: Int): Nd4jArrayStructure = ndArray.slice(i.toLong()).wrap() - override fun Tensor.transposed(i: Int, j: Int): Nd4jArrayStructure = ndArray.swapAxes(i, j).wrap() + override fun StructureND.transposed(i: Int, j: Int): Nd4jArrayStructure = ndArray.swapAxes(i, j).wrap() override fun StructureND.dot(other: StructureND): Nd4jArrayStructure = ndArray.mmul(other.ndArray).wrap() override fun StructureND.min(dim: Int, keepDim: Boolean): Nd4jArrayStructure = @@ -108,7 +107,9 @@ public sealed interface Nd4jTensorAlgebra> : AnalyticTe override fun StructureND.max(dim: Int, keepDim: Boolean): Nd4jArrayStructure = ndArray.max(keepDim, dim).wrap() - override fun Tensor.view(shape: IntArray): Nd4jArrayStructure = ndArray.reshape(shape).wrap() + @OptIn(UnsafeKMathAPI::class) + override fun Tensor.view(shape: ShapeND): Nd4jArrayStructure = ndArray.reshape(shape.asArray()).wrap() + override fun Tensor.viewAs(other: StructureND): Nd4jArrayStructure = view(other.shape) override fun StructureND.argMin(dim: Int, keepDim: Boolean): Tensor = @@ -117,35 +118,35 @@ public sealed interface Nd4jTensorAlgebra> : AnalyticTe override fun StructureND.argMax(dim: Int, keepDim: Boolean): Tensor = ndBase.get().argmax(ndArray, keepDim, dim).asIntStructure() - override fun StructureND.mean(dim: Int, keepDim: Boolean): Nd4jArrayStructure = - ndArray.mean(keepDim, dim).wrap() + override fun mean(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor = + structureND.ndArray.mean(keepDim, dim).wrap() - override fun StructureND.exp(): Nd4jArrayStructure = Transforms.exp(ndArray).wrap() - override fun StructureND.ln(): Nd4jArrayStructure = Transforms.log(ndArray).wrap() - override fun StructureND.sqrt(): Nd4jArrayStructure = Transforms.sqrt(ndArray).wrap() - override fun StructureND.cos(): Nd4jArrayStructure = Transforms.cos(ndArray).wrap() - override fun StructureND.acos(): Nd4jArrayStructure = Transforms.acos(ndArray).wrap() - override fun StructureND.cosh(): Nd4jArrayStructure = Transforms.cosh(ndArray).wrap() + override fun exp(arg: StructureND): Nd4jArrayStructure = Transforms.exp(arg.ndArray).wrap() + override fun ln(arg: StructureND): Nd4jArrayStructure = Transforms.log(arg.ndArray).wrap() + override fun sqrt(arg: StructureND): Nd4jArrayStructure = Transforms.sqrt(arg.ndArray).wrap() + override fun cos(arg: StructureND): Nd4jArrayStructure = Transforms.cos(arg.ndArray).wrap() + override fun acos(arg: StructureND): Nd4jArrayStructure = Transforms.acos(arg.ndArray).wrap() + override fun cosh(arg: StructureND): Nd4jArrayStructure = Transforms.cosh(arg.ndArray).wrap() - override fun StructureND.acosh(): Nd4jArrayStructure = - Nd4j.getExecutioner().exec(ACosh(ndArray, ndArray.ulike())).wrap() + override fun acosh(arg: StructureND): Nd4jArrayStructure = + Nd4j.getExecutioner().exec(ACosh(arg.ndArray, arg.ndArray.ulike())).wrap() - override fun StructureND.sin(): Nd4jArrayStructure = Transforms.sin(ndArray).wrap() - override fun StructureND.asin(): Nd4jArrayStructure = Transforms.asin(ndArray).wrap() - override fun StructureND.sinh(): Tensor = Transforms.sinh(ndArray).wrap() + override fun sin(arg: StructureND): Nd4jArrayStructure = Transforms.sin(arg.ndArray).wrap() + override fun asin(arg: StructureND): Nd4jArrayStructure = Transforms.asin(arg.ndArray).wrap() + override fun sinh(arg: StructureND): Tensor = Transforms.sinh(arg.ndArray).wrap() - override fun StructureND.asinh(): Nd4jArrayStructure = - Nd4j.getExecutioner().exec(ASinh(ndArray, ndArray.ulike())).wrap() + override fun asinh(arg: StructureND): Nd4jArrayStructure = + Nd4j.getExecutioner().exec(ASinh(arg.ndArray, arg.ndArray.ulike())).wrap() - override fun StructureND.tan(): Nd4jArrayStructure = Transforms.tan(ndArray).wrap() - override fun StructureND.atan(): Nd4jArrayStructure = Transforms.atan(ndArray).wrap() - override fun StructureND.tanh(): Nd4jArrayStructure = Transforms.tanh(ndArray).wrap() - override fun StructureND.atanh(): Nd4jArrayStructure = Transforms.atanh(ndArray).wrap() + override fun tan(arg: StructureND): Nd4jArrayStructure = Transforms.tan(arg.ndArray).wrap() + override fun atan(arg: StructureND): Nd4jArrayStructure = Transforms.atan(arg.ndArray).wrap() + override fun tanh(arg: StructureND): Nd4jArrayStructure = Transforms.tanh(arg.ndArray).wrap() + override fun atanh(arg: StructureND): Nd4jArrayStructure = Transforms.atanh(arg.ndArray).wrap() override fun power(arg: StructureND, pow: Number): StructureND = Transforms.pow(arg.ndArray, pow).wrap() - override fun StructureND.ceil(): Nd4jArrayStructure = Transforms.ceil(ndArray).wrap() - override fun StructureND.floor(): Nd4jArrayStructure = Transforms.floor(ndArray).wrap() - override fun StructureND.std(dim: Int, keepDim: Boolean): Nd4jArrayStructure = - ndArray.std(true, keepDim, dim).wrap() + override fun ceil(arg: StructureND): Nd4jArrayStructure = Transforms.ceil(arg.ndArray).wrap() + override fun floor(structureND: StructureND): Nd4jArrayStructure = Transforms.floor(structureND.ndArray).wrap() + override fun std(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor = + structureND.ndArray.std(true, keepDim, dim).wrap() override fun T.div(arg: StructureND): Nd4jArrayStructure = arg.ndArray.rdiv(this).wrap() override fun StructureND.div(arg: T): Nd4jArrayStructure = ndArray.div(arg).wrap() @@ -159,8 +160,8 @@ public sealed interface Nd4jTensorAlgebra> : AnalyticTe ndArray.divi(arg.ndArray) } - override fun StructureND.variance(dim: Int, keepDim: Boolean): Nd4jArrayStructure = - Nd4j.getExecutioner().exec(Variance(ndArray, true, true, dim)).wrap() + override fun variance(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor = + Nd4j.getExecutioner().exec(Variance(structureND.ndArray, true, true, dim)).wrap() private companion object { private val ndBase: ThreadLocal = ThreadLocal.withInitial(::NDBase) @@ -176,9 +177,10 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra { override fun INDArray.wrap(): Nd4jArrayStructure = asDoubleStructure() - override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): Nd4jArrayStructure { - val array: INDArray = Nd4j.zeros(*shape) - val indices = DefaultStrides(shape) + @OptIn(UnsafeKMathAPI::class) + override fun structureND(shape: ShapeND, initializer: DoubleField.(IntArray) -> Double): Nd4jArrayStructure { + val array: INDArray = Nd4j.zeros(*shape.asArray()) + val indices = ColumnStrides(shape) indices.asSequence().forEach { index -> array.putScalar(index, elementAlgebra.initializer(index)) } @@ -186,21 +188,21 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra { } - @OptIn(PerformancePitfall::class) + @OptIn(PerformancePitfall::class, UnsafeKMathAPI::class) override val StructureND.ndArray: INDArray get() = when (this) { is Nd4jArrayStructure -> ndArray - else -> Nd4j.zeros(*shape).also { + else -> Nd4j.zeros(*shape.asArray()).also { elements().forEach { (idx, value) -> it.putScalar(idx, value) } } } override fun StructureND.valueOrNull(): Double? = - if (shape contentEquals intArrayOf(1)) ndArray.getDouble(0) else null + if (shape contentEquals ShapeND(1)) ndArray.getDouble(0) else null // TODO rewrite override fun diagonalEmbedding( - diagonalEntries: Tensor, + diagonalEntries: StructureND, offset: Int, dim1: Int, dim2: Int, @@ -209,7 +211,7 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra { override fun StructureND.sum(): Double = ndArray.sumNumber().toDouble() override fun StructureND.min(): Double = ndArray.minNumber().toDouble() override fun StructureND.max(): Double = ndArray.maxNumber().toDouble() - override fun StructureND.mean(): Double = ndArray.meanNumber().toDouble() - override fun StructureND.std(): Double = ndArray.stdNumber().toDouble() - override fun StructureND.variance(): Double = ndArray.varNumber().toDouble() + override fun mean(structureND: StructureND): Double = structureND.ndArray.meanNumber().toDouble() + override fun std(structureND: StructureND): Double = structureND.ndArray.stdNumber().toDouble() + override fun variance(structureND: StructureND): Double = structureND.ndArray.varNumber().toDouble() } diff --git a/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructureTest.kt b/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructureTest.kt index d1ad746fe..25c3fe23f 100644 --- a/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructureTest.kt +++ b/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayStructureTest.kt @@ -7,6 +7,7 @@ package space.kscience.kmath.nd4j import org.nd4j.linalg.factory.Nd4j import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.asList import space.kscience.kmath.nd.get import kotlin.test.Test import kotlin.test.assertEquals @@ -27,7 +28,7 @@ internal class Nd4jArrayStructureTest { fun testShape() { val nd = Nd4j.rand(10, 2, 3, 6) ?: fail() val struct = nd.asDoubleStructure() - assertEquals(intArrayOf(10, 2, 3, 6).toList(), struct.shape.toList()) + assertEquals(intArrayOf(10, 2, 3, 6).toList(), struct.shape.asList()) } @Test diff --git a/kmath-optimization/src/commonMain/tmp/minuit/HessianGradientCalculator.kt b/kmath-optimization/src/commonMain/tmp/minuit/HessianGradientCalculator.kt index 150d192f9..4ef743955 100644 --- a/kmath-optimization/src/commonMain/tmp/minuit/HessianGradientCalculator.kt +++ b/kmath-optimization/src/commonMain/tmp/minuit/HessianGradientCalculator.kt @@ -33,7 +33,7 @@ internal class HessianGradientCalculator(fcn: MnFcn, par: MnUserTransformation, val g2: RealVector = gradient.getGradientDerivative() val gstep: RealVector = gradient.getStep() val fcnmin: Double = par.fval() - // std::cout<<"fval: "< prec.eps()) { return e } - // std::cout<<"MnPosDef init matrix= "< -@PublishedApi -internal constructor( - /** - * Map that contains coefficients of the polynomial. - * - * Every monomial \(a x_1^{d_1} ... x_n^{d_n}\) is stored as a pair "key-value" in the map, where the value is the - * coefficient \(a\) and the key is a map that associates variables in the monomial with their degree in the monomial. - * For example, coefficients of a polynomial \(5 a^2 c^3 - 6 b\) can be represented as - * ``` - * mapOf( - * mapOf( - * a to 2, - * c to 3 - * ) to 5, - * mapOf( - * b to 1 - * ) to (-6) - * ) - * ``` - * and also as - * ``` - * mapOf( - * mapOf( - * a to 2, - * c to 3 - * ) to 5, - * mapOf( - * b to 1 - * ) to (-6), - * mapOf( - * b to 1, - * c to 1 - * ) to 0 - * ) - * ``` - * where \(a\), \(b\) and \(c\) are corresponding [Symbol] objects. - * - * It is not prohibited to put extra zero monomials into the map (as for \(0 b c\) in the example). But the - * bigger the coefficients map the worse performance of arithmetical operations performed on it. Thus, it is - * recommended not to put (or even to remove) extra (or useless) monomials in the coefficients map. - * @usesMathJax - */ - public val coefficients: Map, C> -) { - override fun toString(): String = "LabeledPolynomial$coefficients" -} - -/** - * Arithmetic context for multivariate polynomials with coefficients stored as a [Map] and terms' signatures stored as a - * [Map] constructed with the provided [ring] of constants. - * - * @param C the type of constants. Polynomials have them a coefficients in their terms. - * @param A type of provided underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public class LabeledPolynomialSpace>( - public override val ring: A, -) : MultivariatePolynomialSpace>, PolynomialSpaceOverRing, A> { - /** - * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - public override operator fun Symbol.plus(other: Int): LabeledPolynomial = - if (other == 0) LabeledPolynomialAsIs( - mapOf(this@plus to 1U) to constantOne, - ) - else LabeledPolynomialAsIs( - mapOf(this@plus to 1U) to constantOne, - emptyMap() to other.asConstant(), - ) - /** - * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - public override operator fun Symbol.minus(other: Int): LabeledPolynomial = - if (other == 0) LabeledPolynomialAsIs( - mapOf(this@minus to 1U) to constantOne, - ) - else LabeledPolynomialAsIs( - mapOf(this@minus to 1U) to constantOne, - emptyMap() to (-other).asConstant(), - ) - /** - * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - public override operator fun Symbol.times(other: Int): LabeledPolynomial = - if (other == 0) zero - else LabeledPolynomialAsIs( - mapOf(this to 1U) to other.asConstant(), - ) - - /** - * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - public override operator fun Int.plus(other: Symbol): LabeledPolynomial = - if (this == 0) LabeledPolynomialAsIs( - mapOf(other to 1U) to constantOne, - ) - else LabeledPolynomialAsIs( - mapOf(other to 1U) to constantOne, - emptyMap() to this@plus.asConstant(), - ) - /** - * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - public override operator fun Int.minus(other: Symbol): LabeledPolynomial = - if (this == 0) LabeledPolynomialAsIs( - mapOf(other to 1U) to -constantOne, - ) - else LabeledPolynomialAsIs( - mapOf(other to 1U) to -constantOne, - emptyMap() to constantOne * this@minus, - ) - /** - * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - public override operator fun Int.times(other: Symbol): LabeledPolynomial = - if (this == 0) zero - else LabeledPolynomialAsIs( - mapOf(other to 1U) to this@times.asConstant(), - ) - - /** - * Returns sum of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - public override operator fun LabeledPolynomial.plus(other: Int): LabeledPolynomial = - when { - other == 0 -> this - coefficients.isEmpty() -> other.asPolynomial() - else -> LabeledPolynomialAsIs( - coefficients.withPutOrChanged(emptyMap(), other.asConstant()) { it -> it + other } - ) - } - /** - * Returns difference between the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - public override operator fun LabeledPolynomial.minus(other: Int): LabeledPolynomial = - when { - other == 0 -> this - coefficients.isEmpty() -> other.asPolynomial() - else -> LabeledPolynomialAsIs( - coefficients.withPutOrChanged(emptyMap(), (-other).asConstant()) { it -> it - other } - ) - } - /** - * Returns product of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - public override operator fun LabeledPolynomial.times(other: Int): LabeledPolynomial = - when(other) { - 0 -> zero - 1 -> this - else -> LabeledPolynomialAsIs( - coefficients.mapValues { (_, value) -> value * other } - ) - } - - /** - * Returns sum of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - public override operator fun Int.plus(other: LabeledPolynomial): LabeledPolynomial = - when { - this == 0 -> other - other.coefficients.isEmpty() -> this@plus.asPolynomial() - else -> LabeledPolynomialAsIs( - other.coefficients.withPutOrChanged(emptyMap(), this@plus.asConstant()) { it -> this@plus + it } - ) - } - /** - * Returns difference between the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - public override operator fun Int.minus(other: LabeledPolynomial): LabeledPolynomial = - when { - this == 0 -> -other - other.coefficients.isEmpty() -> this@minus.asPolynomial() - else -> LabeledPolynomialAsIs( - buildMap(other.coefficients.size + 1) { - put(emptyMap(), asConstant()) - other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC }) - } - ) - } - /** - * Returns product of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - public override operator fun Int.times(other: LabeledPolynomial): LabeledPolynomial = - when(this) { - 0 -> zero - 1 -> other - else -> LabeledPolynomialAsIs( - other.coefficients.mapValues { (_, value) -> this@times * value } - ) - } - - /** - * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - public override operator fun Symbol.plus(other: C): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(this@plus to 1U) to constantOne, - emptyMap() to other, - ) - /** - * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - public override operator fun Symbol.minus(other: C): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(this@minus to 1U) to constantOne, - emptyMap() to -other, - ) - /** - * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - public override operator fun Symbol.times(other: C): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(this@times to 1U) to other, - ) - - /** - * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - public override operator fun C.plus(other: Symbol): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(other to 1U) to constantOne, - emptyMap() to this@plus, - ) - /** - * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - public override operator fun C.minus(other: Symbol): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(other to 1U) to -constantOne, - emptyMap() to this@minus, - ) - /** - * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - public override operator fun C.times(other: Symbol): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(other to 1U) to this@times, - ) - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - override operator fun C.plus(other: LabeledPolynomial): LabeledPolynomial = - if (other.coefficients.isEmpty()) this@plus.asLabeledPolynomial() - else LabeledPolynomialAsIs( - other.coefficients.withPutOrChanged(emptyMap(), this@plus) { it -> this@plus + it } - ) - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - override operator fun C.minus(other: LabeledPolynomial): LabeledPolynomial = - if (other.coefficients.isEmpty()) this@minus.asPolynomial() - else LabeledPolynomialAsIs( - buildMap(other.coefficients.size + 1) { - put(emptyMap(), this@minus) - other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC }) - } - ) - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - override operator fun C.times(other: LabeledPolynomial): LabeledPolynomial = - LabeledPolynomialAsIs( - other.coefficients.mapValues { this@times * it.value } - ) - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - override operator fun LabeledPolynomial.plus(other: C): LabeledPolynomial = - if (coefficients.isEmpty()) other.asLabeledPolynomial() - else LabeledPolynomialAsIs( - coefficients.withPutOrChanged(emptyMap(), other) { it -> it + other } - ) - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - override operator fun LabeledPolynomial.minus(other: C): LabeledPolynomial = - if (coefficients.isEmpty()) other.asLabeledPolynomial() - else LabeledPolynomialAsIs( - coefficients.withPutOrChanged(emptyMap(), -other) { it -> it - other } - ) - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - override operator fun LabeledPolynomial.times(other: C): LabeledPolynomial = - LabeledPolynomialAsIs( - coefficients.mapValues { it.value * other } - ) - - /** - * Converts the constant [value] to polynomial. - */ - public override fun number(value: C): LabeledPolynomial = value.asLabeledPolynomial() - - /** - * Represents the variable as a monic monomial. - */ - public override operator fun Symbol.unaryPlus(): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(this to 1U) to constantOne, - ) - /** - * Returns negation of representation of the variable as a monic monomial. - */ - public override operator fun Symbol.unaryMinus(): LabeledPolynomial = - LabeledPolynomialAsIs( - mapOf(this to 1U) to -constantOne, - ) - /** - * Returns sum of the variables represented as monic monomials. - */ - public override operator fun Symbol.plus(other: Symbol): LabeledPolynomial = - if (this == other) LabeledPolynomialAsIs( - mapOf(this to 1U) to constantOne * 2 - ) - else LabeledPolynomialAsIs( - mapOf(this to 1U) to constantOne, - mapOf(other to 1U) to constantOne, - ) - /** - * Returns difference between the variables represented as monic monomials. - */ - public override operator fun Symbol.minus(other: Symbol): LabeledPolynomial = - if (this == other) zero - else LabeledPolynomialAsIs( - mapOf(this to 1U) to constantOne, - mapOf(other to 1U) to -constantOne, - ) - /** - * Returns product of the variables represented as monic monomials. - */ - public override operator fun Symbol.times(other: Symbol): LabeledPolynomial = - if (this == other) LabeledPolynomialAsIs( - mapOf(this to 2U) to constantOne - ) - else LabeledPolynomialAsIs( - mapOf(this to 1U, other to 1U) to constantOne, - ) - - /** - * Returns sum of the variable represented as a monic monomial and the polynomial. - */ - public override operator fun Symbol.plus(other: LabeledPolynomial): LabeledPolynomial = - if (other.coefficients.isEmpty()) this@plus.asPolynomial() - else LabeledPolynomialAsIs( - other.coefficients.withPutOrChanged(mapOf(this@plus to 1U), constantOne) { it -> constantOne + it } - ) - /** - * Returns difference between the variable represented as a monic monomial and the polynomial. - */ - public override operator fun Symbol.minus(other: LabeledPolynomial): LabeledPolynomial = - if (other.coefficients.isEmpty()) this@minus.asPolynomial() - else LabeledPolynomialAsIs( - buildMap(other.coefficients.size + 1) { - put(mapOf(this@minus to 1U), constantOne) - other.coefficients.copyMapToBy(this, { _, c -> -c }) { currentC, newC -> currentC - newC } - } - ) - /** - * Returns product of the variable represented as a monic monomial and the polynomial. - */ - public override operator fun Symbol.times(other: LabeledPolynomial): LabeledPolynomial = - LabeledPolynomialAsIs( - other.coefficients - .mapKeys { (degs, _) -> degs.withPutOrChanged(this, 1u) { it -> it + 1u } } - ) - - /** - * Returns sum of the polynomial and the variable represented as a monic monomial. - */ - public override operator fun LabeledPolynomial.plus(other: Symbol): LabeledPolynomial = - if (coefficients.isEmpty()) other.asPolynomial() - else LabeledPolynomialAsIs( - coefficients.withPutOrChanged(mapOf(other to 1U), constantOne) { it -> it + constantOne } - ) - /** - * Returns difference between the polynomial and the variable represented as a monic monomial. - */ - public override operator fun LabeledPolynomial.minus(other: Symbol): LabeledPolynomial = - if (coefficients.isEmpty()) other.asPolynomial() - else LabeledPolynomialAsIs( - coefficients.withPutOrChanged(mapOf(other to 1U), -constantOne) { it -> it - constantOne } - ) - /** - * Returns product of the polynomial and the variable represented as a monic monomial. - */ - public override operator fun LabeledPolynomial.times(other: Symbol): LabeledPolynomial = - LabeledPolynomialAsIs( - coefficients - .mapKeys { (degs, _) -> degs.withPutOrChanged(other, 1u) { it -> it + 1u } } - ) - - /** - * Returns negation of the polynomial. - */ - override fun LabeledPolynomial.unaryMinus(): LabeledPolynomial = - LabeledPolynomialAsIs( - coefficients.mapValues { -it.value } - ) - /** - * Returns sum of the polynomials. - */ - override operator fun LabeledPolynomial.plus(other: LabeledPolynomial): LabeledPolynomial = - LabeledPolynomialAsIs( - mergeBy(coefficients, other.coefficients) { c1, c2 -> c1 + c2 } - ) - /** - * Returns difference of the polynomials. - */ - override operator fun LabeledPolynomial.minus(other: LabeledPolynomial): LabeledPolynomial = - LabeledPolynomialAsIs( - buildMap(coefficients.size + other.coefficients.size) { - coefficients.copyTo(this) - other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC }) - } - ) - /** - * Returns product of the polynomials. - */ - override operator fun LabeledPolynomial.times(other: LabeledPolynomial): LabeledPolynomial = - LabeledPolynomialAsIs( - buildMap(coefficients.size * other.coefficients.size) { - for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) { - val degs = mergeBy(degs1, degs2) { deg1, deg2 -> deg1 + deg2 } - val c = c1 * c2 - this.putOrChange(degs, c) { it -> it + c } - } - } - ) - - /** - * Instance of zero polynomial (zero of the polynomial ring). - */ - override val zero: LabeledPolynomial = LabeledPolynomialAsIs() - /** - * Instance of unit polynomial (unit of the polynomial ring). - */ - override val one: LabeledPolynomial = constantOne.asLabeledPolynomial() - - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - override val LabeledPolynomial.degree: Int - get() = coefficients.entries.maxOfOrNull { (degs, _) -> degs.values.sum().toInt() } ?: -1 - /** - * Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents - * in which they are appeared in the polynomial. - * - * As consequence all values in the map are positive integers. Also, if the polynomial is constant, the map is empty. - * And keys of the map is the same as in [variables]. - */ - public override val LabeledPolynomial.degrees: Map - get() = - buildMap { - coefficients.keys.forEach { degs -> - degs.copyToBy(this, ::max) - } - } - /** - * Counts degree of the polynomial by the specified [variable]. - */ - public override fun LabeledPolynomial.degreeBy(variable: Symbol): UInt = - coefficients.entries.maxOfOrNull { (degs, _) -> degs.getOrElse(variable) { 0u } } ?: 0u - /** - * Counts degree of the polynomial by the specified [variables]. - */ - public override fun LabeledPolynomial.degreeBy(variables: Collection): UInt = - coefficients.entries.maxOfOrNull { (degs, _) -> degs.filterKeys { it in variables }.values.sum() } ?: 0u - /** - * Set of all variables that appear in the polynomial in positive exponents. - */ - public override val LabeledPolynomial.variables: Set - get() = - buildSet { - coefficients.entries.forEach { (degs, _) -> addAll(degs.keys) } - } - /** - * Count of all variables that appear in the polynomial in positive exponents. - */ - public override val LabeledPolynomial.countOfVariables: Int get() = variables.size - - // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with - // [ListPolynomialSpace] as a context receiver - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - public inline fun LabeledPolynomial.substitute(arguments: Map): LabeledPolynomial = substitute(ring, arguments) - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - @JvmName("substitutePolynomial") - public inline fun LabeledPolynomial.substitute(arguments: Map>) : LabeledPolynomial = substitute(ring, arguments) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledRationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledRationalFunction.kt deleted file mode 100644 index 185782f22..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledRationalFunction.kt +++ /dev/null @@ -1,92 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.operations.Ring -import kotlin.jvm.JvmName - - -/** - * Represents multivariate rational function that stores its numerator and denominator as [LabeledPolynomial]s. - */ -public data class LabeledRationalFunction( - public override val numerator: LabeledPolynomial, - public override val denominator: LabeledPolynomial -) : RationalFunction> { - override fun toString(): String = "LabeledRationalFunction${numerator.coefficients}/${denominator.coefficients}" -} - -/** - * Arithmetic context for univariate rational functions with numerator and denominator represented as [LabeledPolynomial]s. - * - * @param C the type of constants. Polynomials have them a coefficients in their terms. - * @param A type of provided underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public class LabeledRationalFunctionSpace>( - public val ring: A, -) : - MultivariateRationalFunctionSpaceOverMultivariatePolynomialSpace< - C, - Symbol, - LabeledPolynomial, - LabeledRationalFunction, - LabeledPolynomialSpace, - >, - MultivariatePolynomialSpaceOfFractions< - C, - Symbol, - LabeledPolynomial, - LabeledRationalFunction, - >() { - - /** - * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations. - */ - override val polynomialRing : LabeledPolynomialSpace = LabeledPolynomialSpace(ring) - /** - * Constructor of rational functions (of type [LabeledRationalFunction]) from numerator and denominator (of type [LabeledPolynomial]). - */ - override fun constructRationalFunction( - numerator: LabeledPolynomial, - denominator: LabeledPolynomial - ): LabeledRationalFunction = - LabeledRationalFunction(numerator, denominator) - - // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with - // [ListPolynomialSpace] as a context receiver - /** - * Substitutes provided constant [argument] into [this] polynomial. - */ - public inline fun LabeledPolynomial.substitute(argument: Map): LabeledPolynomial = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] polynomial. - */ - @JvmName("substitutePolynomial") - public inline fun LabeledPolynomial.substitute(argument: Map>): LabeledPolynomial = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] polynomial. - */ - @JvmName("substituteRationalFunction") - public inline fun LabeledPolynomial.substitute(argument: Map>): LabeledRationalFunction = substitute(ring, argument) - /** - * Substitutes provided constant [argument] into [this] rational function. - */ - public inline fun LabeledRationalFunction.substitute(argument: Map): LabeledRationalFunction = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] rational function. - */ - @JvmName("substitutePolynomial") - public inline fun LabeledRationalFunction.substitute(argument: Map>): LabeledRationalFunction = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] rational function. - */ - @JvmName("substituteRationalFunction") - public inline fun LabeledRationalFunction.substitute(argument: Map>): LabeledRationalFunction = substitute(ring, argument) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/ListPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/ListPolynomial.kt deleted file mode 100644 index 3753a93c4..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/ListPolynomial.kt +++ /dev/null @@ -1,374 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.operations.ScaleOperations -import space.kscience.kmath.operations.invoke -import kotlin.math.max -import kotlin.math.min - - -/** - * Represents univariate polynomial that stores its coefficients in a [List]. - * - * @param C the type of constants. - */ -public data class ListPolynomial( - /** - * List that contains coefficients of the polynomial. - * - * Every monomial \(a x^d\) is stored as a coefficient \(a\) placed - * into the list at index \(d\). For example, coefficients of a polynomial \(5 x^2 - 6\) can be represented as - * ``` - * listOf( - * -6, // -6 + - * 0, // 0 x + - * 5, // 5 x^2 - * ) - * ``` - * and also as - * ``` - * listOf( - * -6, // -6 + - * 0, // 0 x + - * 5, // 5 x^2 - * 0, // 0 x^3 - * 0, // 0 x^4 - * ) - * ``` - * It is not prohibited to put extra zeros at end of the list (as for \(0x^3\) and \(0x^4\) in the example). But the - * longer the coefficients list the worse performance of arithmetical operations performed on it. Thus, it is - * recommended not to put (or even to remove) extra (or useless) coefficients at the end of the coefficients list. - * @usesMathJax - */ - public val coefficients: List -) { - override fun toString(): String = "ListPolynomial$coefficients" -} - -/** - * Arithmetic context for univariate polynomials with coefficients stored as a [List] constructed with the provided - * [ring] of constants. - * - * @param C the type of constants. Polynomials have them a coefficients in their terms. - * @param A type of provided underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public open class ListPolynomialSpace>( - public override val ring: A, -) : PolynomialSpaceOverRing, A> { - /** - * Returns sum of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - public override operator fun ListPolynomial.plus(other: Int): ListPolynomial = - if (other == 0) this - else - ListPolynomial( - coefficients - .toMutableList() - .apply { - val result = getOrElse(0) { constantZero } + other - - if(size == 0) add(result) - else this[0] = result - } - ) - /** - * Returns difference between the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - public override operator fun ListPolynomial.minus(other: Int): ListPolynomial = - if (other == 0) this - else - ListPolynomial( - coefficients - .toMutableList() - .apply { - val result = getOrElse(0) { constantZero } - other - - if(size == 0) add(result) - else this[0] = result - } - ) - /** - * Returns product of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - public override operator fun ListPolynomial.times(other: Int): ListPolynomial = - when (other) { - 0 -> zero - 1 -> this - else -> ListPolynomial( - coefficients.map { it * other } - ) - } - - /** - * Returns sum of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - public override operator fun Int.plus(other: ListPolynomial): ListPolynomial = - if (this == 0) other - else - ListPolynomial( - other.coefficients - .toMutableList() - .apply { - val result = this@plus + getOrElse(0) { constantZero } - - if(size == 0) add(result) - else this[0] = result - } - ) - /** - * Returns difference between the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - public override operator fun Int.minus(other: ListPolynomial): ListPolynomial = - ListPolynomial( - other.coefficients - .toMutableList() - .apply { - if (this@minus == 0) { - indices.forEach { this[it] = -this[it] } - } else { - (1..lastIndex).forEach { this[it] = -this[it] } - - val result = this@minus - getOrElse(0) { constantZero } - - if (size == 0) add(result) - else this[0] = result - } - } - ) - /** - * Returns product of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - public override operator fun Int.times(other: ListPolynomial): ListPolynomial = - when (this) { - 0 -> zero - 1 -> other - else -> ListPolynomial( - other.coefficients.map { this@times * it } - ) - } - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - public override operator fun C.plus(other: ListPolynomial): ListPolynomial = - with(other.coefficients) { - if (isEmpty()) ListPolynomial(listOf(this@plus)) - else ListPolynomial( - toMutableList() - .apply { - val result = if (size == 0) this@plus else this@plus + get(0) - - if(size == 0) add(result) - else this[0] = result - } - ) - } - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - public override operator fun C.minus(other: ListPolynomial): ListPolynomial = - with(other.coefficients) { - if (isEmpty()) ListPolynomial(listOf(this@minus)) - else ListPolynomial( - toMutableList() - .apply { - (1 .. lastIndex).forEach { this[it] = -this[it] } - - val result = if (size == 0) this@minus else this@minus - get(0) - - if(size == 0) add(result) - else this[0] = result - } - ) - } - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - public override operator fun C.times(other: ListPolynomial): ListPolynomial = - ListPolynomial( - other.coefficients.map { this@times * it } - ) - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - public override operator fun ListPolynomial.plus(other: C): ListPolynomial = - with(coefficients) { - if (isEmpty()) ListPolynomial(listOf(other)) - else ListPolynomial( - toMutableList() - .apply { - val result = if (size == 0) other else get(0) + other - - if(size == 0) add(result) - else this[0] = result - } - ) - } - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - public override operator fun ListPolynomial.minus(other: C): ListPolynomial = - with(coefficients) { - if (isEmpty()) ListPolynomial(listOf(-other)) - else ListPolynomial( - toMutableList() - .apply { - val result = if (size == 0) other else get(0) - other - - if(size == 0) add(result) - else this[0] = result - } - ) - } - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - public override operator fun ListPolynomial.times(other: C): ListPolynomial = - ListPolynomial( - coefficients.map { it * other } - ) - - /** - * Converts the constant [value] to polynomial. - */ - public override fun number(value: C): ListPolynomial = ListPolynomial(listOf(value)) - - /** - * Returns negation of the polynomial. - */ - public override operator fun ListPolynomial.unaryMinus(): ListPolynomial = - ListPolynomial(coefficients.map { -it }) - /** - * Returns sum of the polynomials. - */ - public override operator fun ListPolynomial.plus(other: ListPolynomial): ListPolynomial { - val thisDegree = degree - val otherDegree = other.degree - return ListPolynomial( - List(max(thisDegree, otherDegree) + 1) { - when { - it > thisDegree -> other.coefficients[it] - it > otherDegree -> coefficients[it] - else -> coefficients[it] + other.coefficients[it] - } - } - ) - } - /** - * Returns difference of the polynomials. - */ - public override operator fun ListPolynomial.minus(other: ListPolynomial): ListPolynomial { - val thisDegree = degree - val otherDegree = other.degree - return ListPolynomial( - List(max(thisDegree, otherDegree) + 1) { - when { - it > thisDegree -> -other.coefficients[it] - it > otherDegree -> coefficients[it] - else -> coefficients[it] - other.coefficients[it] - } - } - ) - } - /** - * Returns product of the polynomials. - */ - public override operator fun ListPolynomial.times(other: ListPolynomial): ListPolynomial { - val thisDegree = degree - val otherDegree = other.degree - return ListPolynomial( - List(thisDegree + otherDegree + 1) { d -> - (max(0, d - otherDegree)..min(thisDegree, d)) - .map { coefficients[it] * other.coefficients[d - it] } - .reduce { acc, rational -> acc + rational } - } - ) - } - /** - * Raises [arg] to the integer power [exponent]. - */ // TODO: To optimize boxing - override fun power(arg: ListPolynomial, exponent: UInt): ListPolynomial = super.power(arg, exponent) - - /** - * Instance of zero polynomial (zero of the polynomial ring). - */ - override val zero: ListPolynomial = ListPolynomial(emptyList()) - /** - * Instance of unit polynomial (unit of the polynomial ring). - */ - override val one: ListPolynomial by lazy { ListPolynomial(listOf(constantOne)) } - - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - public override val ListPolynomial.degree: Int get() = coefficients.lastIndex - - // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with - // [ListPolynomialSpace] as a context receiver - /** - * Evaluates value of [this] polynomial on provided [argument]. - */ - public inline fun ListPolynomial.substitute(argument: C): C = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] polynomial. - */ - public inline fun ListPolynomial.substitute(argument: ListPolynomial): ListPolynomial = substitute(ring, argument) - - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunction(): (C) -> C = asFunctionOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunctionOfConstant(): (C) -> C = asFunctionOfConstantOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunctionOfPolynomial(): (ListPolynomial) -> ListPolynomial = asFunctionOfPolynomialOver(ring) - - /** - * Evaluates value of [this] polynomial on provided [argument]. - */ - public inline operator fun ListPolynomial.invoke(argument: C): C = substitute(ring, argument) - /** - * Evaluates value of [this] polynomial on provided [argument]. - */ - public inline operator fun ListPolynomial.invoke(argument: ListPolynomial): ListPolynomial = substitute(ring, argument) -} - -/** - * Space of polynomials constructed over ring. - * - * @param C the type of constants. Polynomials have them as a coefficients in their terms. - * @param A type of underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public class ScalableListPolynomialSpace( - ring: A, -) : ListPolynomialSpace(ring), ScaleOperations> where A : Ring, A : ScaleOperations { - override fun scale(a: ListPolynomial, value: Double): ListPolynomial = - ring { ListPolynomial(a.coefficients.map { scale(it, value) }) } -} diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt deleted file mode 100644 index c2fa6b2ec..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt +++ /dev/null @@ -1,123 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring - - -/** - * Represents univariate rational function that stores its numerator and denominator as [ListPolynomial]s. - */ -public data class ListRationalFunction( - public override val numerator: ListPolynomial, - public override val denominator: ListPolynomial -) : RationalFunction> { - override fun toString(): String = "ListRationalFunction${numerator.coefficients}/${denominator.coefficients}" -} - -/** - * Arithmetic context for univariate rational functions with numerator and denominator represented as [ListPolynomial]s. - * - * @param C the type of constants. Polynomials have them a coefficients in their terms. - * @param A type of provided underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public class ListRationalFunctionSpace> ( - public val ring: A, -) : - RationalFunctionSpaceOverPolynomialSpace< - C, - ListPolynomial, - ListRationalFunction, - ListPolynomialSpace, - >, - PolynomialSpaceOfFractions< - C, - ListPolynomial, - ListRationalFunction, - >() { - - /** - * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations. - */ - override val polynomialRing : ListPolynomialSpace = ListPolynomialSpace(ring) - /** - * Constructor of [ListRationalFunction] from numerator and denominator [ListPolynomial]. - */ - override fun constructRationalFunction(numerator: ListPolynomial, denominator: ListPolynomial): ListRationalFunction = - ListRationalFunction(numerator, denominator) - - // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with - // [ListPolynomialSpace] as a context receiver - /** - * Evaluates value of [this] polynomial on provided argument. - */ - public inline fun ListPolynomial.substitute(argument: C): C = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] polynomial. - */ - public inline fun ListPolynomial.substitute(argument: ListPolynomial): ListPolynomial = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] polynomial. - */ - public inline fun ListPolynomial.substitute(argument: ListRationalFunction): ListRationalFunction = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] rational function. - */ - public inline fun ListRationalFunction.substitute(argument: ListPolynomial): ListRationalFunction = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] rational function. - */ - public inline fun ListRationalFunction.substitute(argument: ListRationalFunction): ListRationalFunction = substitute(ring, argument) - - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunction(): (C) -> C = { substitute(ring, it) } - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunctionOfConstant(): (C) -> C = { substitute(ring, it) } - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunctionOfPolynomial(): (ListPolynomial) -> ListPolynomial = { substitute(ring, it) } - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun ListPolynomial.asFunctionOfRationalFunction(): (ListRationalFunction) -> ListRationalFunction = { substitute(ring, it) } - /** - * Represent [this] rational function as a regular context-less function. - */ - public inline fun ListRationalFunction.asFunctionOfPolynomial(): (ListPolynomial) -> ListRationalFunction = { substitute(ring, it) } - /** - * Represent [this] rational function as a regular context-less function. - */ - public inline fun ListRationalFunction.asFunctionOfRationalFunction(): (ListRationalFunction) -> ListRationalFunction = { substitute(ring, it) } - - /** - * Evaluates value of [this] polynomial on provided argument. - */ - public inline operator fun ListPolynomial.invoke(argument: C): C = substitute(ring, argument) - /** - * Evaluates value of [this] polynomial on provided argument. - */ - public inline operator fun ListPolynomial.invoke(argument: ListPolynomial): ListPolynomial = substitute(ring, argument) - /** - * Evaluates value of [this] polynomial on provided argument. - */ - public inline operator fun ListPolynomial.invoke(argument: ListRationalFunction): ListRationalFunction = substitute(ring, argument) - /** - * Evaluates value of [this] rational function on provided argument. - */ - public inline operator fun ListRationalFunction.invoke(argument: ListPolynomial): ListRationalFunction = substitute(ring, argument) - /** - * Evaluates value of [this] rational function on provided argument. - */ - public inline operator fun ListRationalFunction.invoke(argument: ListRationalFunction): ListRationalFunction = substitute(ring, argument) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt deleted file mode 100644 index eaf5befb1..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt +++ /dev/null @@ -1,350 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.structures.Buffer -import kotlin.jvm.JvmName -import kotlin.math.max - - -/** - * Represents multivariate polynomial that stores its coefficients in a [Map] and terms' signatures in a [List]. - * - * @param C the type of constants. - */ -public data class NumberedPolynomial -@PublishedApi -internal constructor( - /** - * Map that contains coefficients of the polynomial. - * - * Every monomial \(a x_1^{d_1} ... x_n^{d_n}\) is stored as a pair "key-value" in the map, where the value is the - * coefficient \(a\) and the key is a list that associates index of every variable in the monomial with their degree - * in the monomial. For example, coefficients of a polynomial \(5 x_1^2 x_3^3 - 6 x_2\) can be represented as - * ``` - * mapOf( - * listOf(2, 0, 3) to 5, // 5 x_1^2 x_3^3 + - * listOf(0, 1) to (-6), // (-6) x_2^1 - * ) - * ``` - * and also as - * ``` - * mapOf( - * listOf(2, 0, 3) to 5, // 5 x_1^2 x_3^3 + - * listOf(0, 1) to (-6), // (-6) x_2^1 - * listOf(0, 1, 1) to 0, // 0 x_2^1 x_3^1 - * ) - * ``` - * It is not prohibited to put extra zero monomials into the map (as for \(0 x_2 x_3\) in the example). But the - * bigger the coefficients map the worse performance of arithmetical operations performed on it. Thus, it is - * recommended not to put (or even to remove) extra (or useless) monomials in the coefficients map. - * @usesMathJax - */ - public val coefficients: Map, C> -) { - override fun toString(): String = "NumberedPolynomial$coefficients" -} - -/** - * Arithmetic context for multivariate polynomials with coefficients stored as a [Map] and terms' signatures stored as a - * [List] constructed with the provided [ring] of constants. - * - * @param C the type of constants. Polynomials have them a coefficients in their terms. - * @param A type of provided underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public class NumberedPolynomialSpace>( - public override val ring: A, -) : PolynomialSpaceOverRing, A> { - /** - * Returns sum of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - public override operator fun NumberedPolynomial.plus(other: Int): NumberedPolynomial = - if (other == 0) this - else NumberedPolynomialAsIs( - coefficients.withPutOrChanged(emptyList(), other.asConstant()) { it -> it + other } - ) - /** - * Returns difference between the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - public override operator fun NumberedPolynomial.minus(other: Int): NumberedPolynomial = - if (other == 0) this - else NumberedPolynomialAsIs( - coefficients.withPutOrChanged(emptyList(), (-other).asConstant()) { it -> it - other } - ) - /** - * Returns product of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - public override operator fun NumberedPolynomial.times(other: Int): NumberedPolynomial = - when (other) { - 0 -> zero - 1 -> this - else -> NumberedPolynomialAsIs( - coefficients.mapValues { it.value * other } - ) - } - - /** - * Returns sum of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - public override operator fun Int.plus(other: NumberedPolynomial): NumberedPolynomial = - if (this == 0) other - else NumberedPolynomialAsIs( - other.coefficients.withPutOrChanged(emptyList(), this@plus.asConstant()) { it -> this@plus + it } - ) - /** - * Returns difference between the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - public override operator fun Int.minus(other: NumberedPolynomial): NumberedPolynomial = - when { - this == 0 -> -other - other.coefficients.isEmpty() -> this.asPolynomial() - else -> NumberedPolynomialAsIs( - buildMap(other.coefficients.size + 1) { - put(emptyList(), other.coefficients.computeOnOrElse(emptyList(), { this@minus.asConstant() }, { it -> this@minus - it})) - other.coefficients.copyMapToBy(this, { _, c -> -c }) { currentC, _ -> currentC } - } - ) - } - /** - * Returns product of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - public override operator fun Int.times(other: NumberedPolynomial): NumberedPolynomial = - when (this) { - 0 -> zero - 1 -> other - else -> NumberedPolynomialAsIs( - other.coefficients.mapValues { this@times * it.value } - ) - } - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - override operator fun C.plus(other: NumberedPolynomial): NumberedPolynomial = - if (other.coefficients.isEmpty()) this@plus.asPolynomial() - else NumberedPolynomialAsIs( - other.coefficients.withPutOrChanged(emptyList(), this@plus) { it -> this@plus + it } - ) - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - override operator fun C.minus(other: NumberedPolynomial): NumberedPolynomial = - if (other.coefficients.isEmpty()) this@minus.asPolynomial() - else NumberedPolynomialAsIs( - buildMap(other.coefficients.size) { - put(emptyList(), other.coefficients.computeOnOrElse(emptyList(), this@minus) { it -> this@minus - it }) - other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, _ -> currentC }) - } - ) - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - override operator fun C.times(other: NumberedPolynomial): NumberedPolynomial = - NumberedPolynomialAsIs( - other.coefficients.mapValues { this@times * it.value } - ) - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - override operator fun NumberedPolynomial.plus(other: C): NumberedPolynomial = - if (coefficients.isEmpty()) other.asPolynomial() - else NumberedPolynomialAsIs( - coefficients.withPutOrChanged(emptyList(), other) { it -> it + other } - ) - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - override operator fun NumberedPolynomial.minus(other: C): NumberedPolynomial = - if (coefficients.isEmpty()) other.asPolynomial() - else NumberedPolynomialAsIs( - coefficients.withPutOrChanged(emptyList(), -other) { it -> it - other } - ) - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - override operator fun NumberedPolynomial.times(other: C): NumberedPolynomial = - NumberedPolynomialAsIs( - coefficients.mapValues { it.value * other } - ) - - /** - * Converts the constant [value] to polynomial. - */ - public override fun number(value: C): NumberedPolynomial = - NumberedPolynomialAsIs(mapOf(emptyList() to value)) - - /** - * Returns negation of the polynomial. - */ - override fun NumberedPolynomial.unaryMinus(): NumberedPolynomial = - NumberedPolynomialAsIs( - coefficients.mapValues { -it.value } - ) - /** - * Returns sum of the polynomials. - */ - override operator fun NumberedPolynomial.plus(other: NumberedPolynomial): NumberedPolynomial = - NumberedPolynomialAsIs( - mergeBy(coefficients, other.coefficients) { c1, c2 -> c1 + c2 } - ) - /** - * Returns difference of the polynomials. - */ - override operator fun NumberedPolynomial.minus(other: NumberedPolynomial): NumberedPolynomial = - NumberedPolynomialAsIs( - buildMap(coefficients.size + other.coefficients.size) { - coefficients.copyTo(this) - other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC }) - } - ) - /** - * Returns product of the polynomials. - */ - override operator fun NumberedPolynomial.times(other: NumberedPolynomial): NumberedPolynomial = - NumberedPolynomialAsIs( - buildMap(coefficients.size * other.coefficients.size) { - for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) { - val degs = - (0..max(degs1.lastIndex, degs2.lastIndex)) - .map { degs1.getOrElse(it) { 0U } + degs2.getOrElse(it) { 0U } } - val c = c1 * c2 - putOrChange(degs, c) { it -> it + c } - } - } - ) - /** - * Raises [arg] to the integer power [exponent]. - */ // TODO: To optimize boxing - override fun power(arg: NumberedPolynomial, exponent: UInt): NumberedPolynomial = super.power(arg, exponent) - - /** - * Instance of zero polynomial (zero of the polynomial ring). - */ - override val zero: NumberedPolynomial = NumberedPolynomialAsIs(emptyMap()) - /** - * Instance of unit polynomial (unit of the polynomial ring). - */ - override val one: NumberedPolynomial by lazy { NumberedPolynomialAsIs(mapOf(emptyList() to constantOne)) } - - /** - * Maximal index (ID) of variable occurring in the polynomial with positive power. If there is no such variable, - * the result is -1. - */ - public val NumberedPolynomial.lastVariable: Int - get() = coefficients.keys.maxOfOrNull { degs -> degs.lastIndex } ?: -1 - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - override val NumberedPolynomial.degree: Int - get() = coefficients.keys.maxOfOrNull { degs -> degs.sum().toInt() } ?: -1 - /** - * List that associates indices of variables (that appear in the polynomial in positive exponents) with their most - * exponents in which the variables are appeared in the polynomial. - * - * As consequence all values in the list are non-negative integers. Also, if the polynomial is constant, the list is empty. - * And last index of the list is [lastVariable]. - */ - public val NumberedPolynomial.degrees: List - get() = - MutableList(lastVariable + 1) { 0u }.apply { - coefficients.keys.forEach { degs -> - degs.forEachIndexed { index, deg -> - this[index] = max(this[index], deg) - } - } - } - /** - * Counts degree of the polynomial by the specified [variable]. - */ - public fun NumberedPolynomial.degreeBy(variable: Int): UInt = - coefficients.keys.maxOfOrNull { degs -> degs.getOrElse(variable) { 0u } } ?: 0u - /** - * Counts degree of the polynomial by the specified [variables]. - */ - public fun NumberedPolynomial.degreeBy(variables: Collection): UInt = - coefficients.keys.maxOfOrNull { degs -> - degs.withIndex().fold(0u) { acc, (index, value) -> if (index in variables) acc + value else acc } - } ?: 0u - /** - * Count of variables occurring in the polynomial with positive power. If there is no such variable, - * the result is 0. - */ - public val NumberedPolynomial.countOfVariables: Int - get() = - MutableList(lastVariable + 1) { false }.apply { - coefficients.entries.forEach { (degs, _) -> - degs.forEachIndexed { index, deg -> - if (deg != 0u) this[index] = true - } - } - }.count { it } - - // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with - // [ListPolynomialSpace] as a context receiver - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - public inline fun NumberedPolynomial.substitute(arguments: Map): NumberedPolynomial = substitute(ring, arguments) - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - @JvmName("substitutePolynomial") - public inline fun NumberedPolynomial.substitute(arguments: Map>) : NumberedPolynomial = substitute(ring, arguments) - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - public inline fun NumberedPolynomial.substitute(arguments: Buffer): NumberedPolynomial = substitute(ring, arguments) - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - @JvmName("substitutePolynomial") - public inline fun NumberedPolynomial.substitute(arguments: Buffer>) : NumberedPolynomial = substitute(ring, arguments) - /** - * Substitutes provided arguments [arguments] into [this] polynomial. - */ - public inline fun NumberedPolynomial.substituteFully(arguments: Buffer): C = this.substituteFully(ring, arguments) - - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunction(): (Buffer) -> C = asFunctionOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunctionOfConstant(): (Buffer) -> C = asFunctionOfConstantOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunctionOfPolynomial(): (Buffer>) -> NumberedPolynomial = asFunctionOfPolynomialOver(ring) - - /** - * Evaluates value of [this] polynomial on provided [arguments]. - */ - public inline operator fun NumberedPolynomial.invoke(arguments: Buffer): C = substituteFully(ring, arguments) - /** - * Substitutes provided [arguments] into [this] polynomial. - */ - @JvmName("invokePolynomial") - public inline operator fun NumberedPolynomial.invoke(arguments: Buffer>): NumberedPolynomial = substitute(ring, arguments) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedRationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedRationalFunction.kt deleted file mode 100644 index 4109338fd..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedRationalFunction.kt +++ /dev/null @@ -1,225 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.operations.invoke -import space.kscience.kmath.structures.Buffer -import kotlin.jvm.JvmName -import kotlin.math.max - - -/** - * Represents multivariate rational function that stores its numerator and denominator as [NumberedPolynomial]s. - */ -public data class NumberedRationalFunction( - public override val numerator: NumberedPolynomial, - public override val denominator: NumberedPolynomial -) : RationalFunction> { - override fun toString(): String = "NumberedRationalFunction${numerator.coefficients}/${denominator.coefficients}" -} - -/** - * Arithmetic context for univariate rational functions with numerator and denominator represented as [NumberedPolynomial]s. - * - * @param C the type of constants. Polynomials have them a coefficients in their terms. - * @param A type of provided underlying ring of constants. It's [Ring] of [C]. - * @param ring underlying ring of constants of type [A]. - */ -public class NumberedRationalFunctionSpace> ( - public val ring: A, -) : - RationalFunctionSpaceOverPolynomialSpace< - C, - NumberedPolynomial, - NumberedRationalFunction, - NumberedPolynomialSpace, - >, - PolynomialSpaceOfFractions< - C, - NumberedPolynomial, - NumberedRationalFunction, - >() { - - /** - * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations. - */ - public override val polynomialRing : NumberedPolynomialSpace = NumberedPolynomialSpace(ring) - /** - * Constructor of rational functions (of type [NumberedRationalFunction]) from numerator and denominator (of type [NumberedPolynomial]). - */ - protected override fun constructRationalFunction( - numerator: NumberedPolynomial, - denominator: NumberedPolynomial - ): NumberedRationalFunction = - NumberedRationalFunction(numerator, denominator) - - /** - * Maximal index (ID) of variable occurring in the polynomial with positive power. If there is no such variable, - * the result is `-1`. - */ - public val NumberedPolynomial.lastVariable: Int get() = polynomialRing { lastVariable } - /** - * List that associates indices of variables (that appear in the polynomial in positive exponents) with their most - * exponents in which the variables are appeared in the polynomial. - * - * As consequence all values in the list are non-negative integers. Also, if the polynomial is constant, the list is empty. - * And last index of the list is [lastVariable]. - */ - public val NumberedPolynomial.degrees: List get() = polynomialRing { degrees } - /** - * Counts degree of the polynomial by the specified [variable]. - */ - public fun NumberedPolynomial.degreeBy(variable: Int): UInt = polynomialRing { degreeBy(variable) } - /** - * Counts degree of the polynomial by the specified [variables]. - */ - public fun NumberedPolynomial.degreeBy(variables: Collection): UInt = polynomialRing { degreeBy(variables) } - /** - * Count of variables occurring in the polynomial with positive power. If there is no such variable, - * the result is `0`. - */ - public val NumberedPolynomial.countOfVariables: Int get() = polynomialRing { countOfVariables } - - /** - * Count of all variables that appear in the polynomial in positive exponents. - */ - public val NumberedRationalFunction.lastVariable: Int - get() = polynomialRing { max(numerator.lastVariable, denominator.lastVariable) } - /** - * Count of variables occurring in the rational function with positive power. If there is no such variable, - * the result is `0`. - */ - public val NumberedRationalFunction.countOfVariables: Int - get() = - MutableList(lastVariable + 1) { false }.apply { - numerator.coefficients.entries.forEach { (degs, _) -> - degs.forEachIndexed { index, deg -> - if (deg != 0u) this[index] = true - } - } - denominator.coefficients.entries.forEach { (degs, _) -> - degs.forEachIndexed { index, deg -> - if (deg != 0u) this[index] = true - } - } - }.count { it } - - // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with - // [ListPolynomialSpace] as a context receiver - /** - * Substitutes provided constant [argument] into [this] polynomial. - */ - public inline fun NumberedPolynomial.substitute(argument: Map): NumberedPolynomial = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] polynomial. - */ - @JvmName("substitutePolynomial") - public inline fun NumberedPolynomial.substitute(argument: Map>): NumberedPolynomial = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] polynomial. - */ - @JvmName("substituteRationalFunction") - public inline fun NumberedPolynomial.substitute(argument: Map>): NumberedRationalFunction = substitute(ring, argument) - /** - * Substitutes provided constant [argument] into [this] rational function. - */ - public inline fun NumberedRationalFunction.substitute(argument: Map): NumberedRationalFunction = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] rational function. - */ - @JvmName("substitutePolynomial") - public inline fun NumberedRationalFunction.substitute(argument: Map>): NumberedRationalFunction = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] rational function. - */ - @JvmName("substituteRationalFunction") - public inline fun NumberedRationalFunction.substitute(argument: Map>): NumberedRationalFunction = substitute(ring, argument) - /** - * Substitutes provided constant [argument] into [this] polynomial. - */ - public inline fun NumberedPolynomial.substitute(argument: Buffer): NumberedPolynomial = substitute(ring, argument) - /** - * Substitutes provided polynomial [argument] into [this] polynomial. - */ - @JvmName("substitutePolynomial") - public inline fun NumberedPolynomial.substitute(argument: Buffer>): NumberedPolynomial = substitute(ring, argument) - /** - * Substitutes provided rational function [argument] into [this] polynomial. - */ - @JvmName("substituteRationalFunction") - public inline fun NumberedPolynomial.substitute(argument: Buffer>): NumberedRationalFunction = substitute(ring, argument) - /** - * Substitutes provided constant [argument] into [this] rational function. - */ - public inline fun NumberedRationalFunction.substitute(argument: Buffer): NumberedRationalFunction = substitute(ring, argument) - /** - * Substitutes provided polynomial [arguments] into [this] rational function. - */ - @JvmName("substitutePolynomial") - public inline fun NumberedRationalFunction.substitute(arguments: Buffer>): NumberedRationalFunction = substitute(ring, arguments) - /** - * Substitutes provided rational function [arguments] into [this] rational function. - */ - @JvmName("substituteRationalFunction") - public inline fun NumberedRationalFunction.substitute(arguments: Buffer>): NumberedRationalFunction = substitute(ring, arguments) - /** - * Substitutes provided constant [arguments] into [this] polynomial. - */ - public inline fun NumberedPolynomial.substituteFully(arguments: Buffer): C = substituteFully(ring, arguments) - - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunction(): (Buffer) -> C = asFunctionOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunctionOfConstant(): (Buffer) -> C = asFunctionOfConstantOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunctionOfPolynomial(): (Buffer>) -> NumberedPolynomial = asFunctionOfPolynomialOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedPolynomial.asFunctionOfRationalFunction(): (Buffer>) -> NumberedRationalFunction = asFunctionOfRationalFunctionOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedRationalFunction.asFunctionOfPolynomial(): (Buffer>) -> NumberedRationalFunction = asFunctionOfPolynomialOver(ring) - /** - * Represent [this] polynomial as a regular context-less function. - */ - public inline fun NumberedRationalFunction.asFunctionOfRationalFunction(): (Buffer>) -> NumberedRationalFunction = asFunctionOfRationalFunctionOver(ring) - - /** - * Evaluates value of [this] polynomial on provided [arguments]. - */ - public inline operator fun NumberedPolynomial.invoke(arguments: Buffer): C = substituteFully(ring, arguments) - /** - * Substitutes provided [arguments] into [this] polynomial. - */ - @JvmName("invokePolynomial") - public inline operator fun NumberedPolynomial.invoke(arguments: Buffer>): NumberedPolynomial = substitute(ring, arguments) - /** - * Substitutes provided [arguments] into [this] polynomial. - */ - @JvmName("invokeRationalFunction") - public inline operator fun NumberedPolynomial.invoke(arguments: Buffer>): NumberedRationalFunction = substitute(ring, arguments) - /** - * Substitutes provided [arguments] into [this] rational function. - */ - @JvmName("invokePolynomial") - public inline operator fun NumberedRationalFunction.invoke(arguments: Buffer>): NumberedRationalFunction = substitute(ring, arguments) - /** - * Substitutes provided [arguments] into [this] rational function. - */ - @JvmName("invokeRationalFunction") - public inline operator fun NumberedRationalFunction.invoke(arguments: Buffer>): NumberedRationalFunction = substitute(ring, arguments) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt deleted file mode 100644 index 7140ba70e..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt +++ /dev/null @@ -1,527 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.operations.invoke -import kotlin.js.JsName -import kotlin.jvm.JvmName - - -/** - * Abstraction of ring of polynomials of type [P] over ring of constants of type [C]. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param P the type of polynomials. - */ -@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE") // FIXME: Waiting for KT-31420 -public interface PolynomialSpace : Ring

{ - /** - * Returns sum of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. - */ - @JvmName("plusConstantInt") - public operator fun C.plus(other: Int): C - /** - * Returns difference between the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. - */ - @JvmName("minusConstantInt") - public operator fun C.minus(other: Int): C - /** - * Returns product of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesConstantInt") - public operator fun C.times(other: Int): C - - /** - * Returns sum of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. - */ - @JvmName("plusIntConstant") - public operator fun Int.plus(other: C): C - /** - * Returns difference between the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. - */ - @JvmName("minusIntConstant") - public operator fun Int.minus(other: C): C - /** - * Returns product of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntConstant") - public operator fun Int.times(other: C): C - - /** - * Converts the integer [value] to constant. - */ - public fun constantNumber(value: Int): C = constantOne * value - /** - * Converts the integer to constant. - */ - public fun Int.asConstant(): C = constantNumber(this) - - /** - * Returns sum of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - public operator fun P.plus(other: Int): P = addMultipliedByDoubling(this, one, other) - /** - * Returns difference between the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - public operator fun P.minus(other: Int): P = addMultipliedByDoubling(this, one, -other) - /** - * Returns product of the polynomial and the integer represented as a polynomial. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - public operator fun P.times(other: Int): P = multiplyByDoubling(this, other) - - /** - * Returns sum of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - public operator fun Int.plus(other: P): P = addMultipliedByDoubling(other, one, this) - /** - * Returns difference between the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - public operator fun Int.minus(other: P): P = addMultipliedByDoubling(-other, one, this) - /** - * Returns product of the integer represented as a polynomial and the polynomial. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - public operator fun Int.times(other: P): P = multiplyByDoubling(other, this) - - /** - * Converts the integer [value] to polynomial. - */ - public fun number(value: Int): P = number(constantNumber(value)) - /** - * Converts the integer to polynomial. - */ - public fun Int.asPolynomial(): P = number(this) - - /** - * Returns the same constant. - */ - @JvmName("unaryPlusConstant") - @JsName("unaryPlusConstant") - public operator fun C.unaryPlus(): C = this - /** - * Returns negation of the constant. - */ - @JvmName("unaryMinusConstant") - @JsName("unaryMinusConstant") - public operator fun C.unaryMinus(): C - /** - * Returns sum of the constants. - */ - @JvmName("plusConstantConstant") - @JsName("plusConstantConstant") - public operator fun C.plus(other: C): C - /** - * Returns difference of the constants. - */ - @JvmName("minusConstantConstant") - @JsName("minusConstantConstant") - public operator fun C.minus(other: C): C - /** - * Returns product of the constants. - */ - @JvmName("timesConstantConstant") - @JsName("timesConstantConstant") - public operator fun C.times(other: C): C - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerConstant") - @JsName("powerConstant") - public fun power(arg: C, exponent: UInt) : C - - /** - * Instance of zero constant (zero of the underlying ring). - */ - public val constantZero: C - /** - * Instance of unit constant (unit of the underlying ring). - */ - public val constantOne: C - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - @JvmName("plusConstantPolynomial") - public operator fun C.plus(other: P): P - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - @JvmName("minusConstantPolynomial") - public operator fun C.minus(other: P): P - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - @JvmName("timesConstantPolynomial") - public operator fun C.times(other: P): P - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - @JvmName("plusPolynomialConstant") - public operator fun P.plus(other: C): P - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - @JvmName("minusPolynomialConstant") - public operator fun P.minus(other: C): P - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - @JvmName("timesPolynomialConstant") - public operator fun P.times(other: C): P - - /** - * Converts the constant [value] to polynomial. - */ - public fun number(value: C): P = one * value - /** - * Converts the constant to polynomial. - */ - public fun C.asPolynomial(): P = number(this) - - /** - * Returns the same polynomial. - */ - public override operator fun P.unaryPlus(): P = this - /** - * Returns negation of the polynomial. - */ - public override operator fun P.unaryMinus(): P - /** - * Returns sum of the polynomials. - */ - public override operator fun P.plus(other: P): P - /** - * Returns difference of the polynomials. - */ - public override operator fun P.minus(other: P): P - /** - * Returns product of the polynomials. - */ - public override operator fun P.times(other: P): P - /** - * Raises [arg] to the integer power [exponent]. - */ - public override fun power(arg: P, exponent: UInt) : P = exponentiateBySquaring(arg, exponent) - - /** - * Instance of zero polynomial (zero of the polynomial ring). - */ - public override val zero: P - /** - * Instance of unit polynomial (unit of the polynomial ring). - */ - public override val one: P - - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - public val P.degree: Int - - override fun add(left: P, right: P): P = left + right - override fun multiply(left: P, right: P): P = left * right -} - -/** - * Abstraction of ring of polynomials of type [P] over ring of constants of type [C]. It also assumes that there is - * provided [ring] (of type [A]), that provides constant-wise operations. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param P the type of polynomials. - * @param A the type of algebraic structure (precisely, of ring) provided for constants. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public interface PolynomialSpaceOverRing> : PolynomialSpace { - - /** - * Underlying ring of constants. Its operations on constants are inherited by local operations on constants. - */ - public val ring: A - - /** - * Returns sum of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. - */ - @JvmName("plusConstantInt") - public override operator fun C.plus(other: Int): C = ring { addMultipliedByDoubling(this@plus, one, other) } - /** - * Returns difference between the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. - */ - @JvmName("minusConstantInt") - public override operator fun C.minus(other: Int): C = ring { addMultipliedByDoubling(this@minus, one, -other) } - /** - * Returns product of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesConstantInt") - public override operator fun C.times(other: Int): C = ring { multiplyByDoubling(this@times, other) } - - /** - * Returns sum of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. - */ - @JvmName("plusIntConstant") - public override operator fun Int.plus(other: C): C = ring { addMultipliedByDoubling(other, one, this@plus) } - /** - * Returns difference between the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. - */ - @JvmName("minusIntConstant") - public override operator fun Int.minus(other: C): C = ring { addMultipliedByDoubling(-other, one, this@minus) } - /** - * Returns product of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntConstant") - public override operator fun Int.times(other: C): C = ring { multiplyByDoubling(other, this@times) } - - /** - * Returns negation of the constant. - */ - @JvmName("unaryMinusConstant") - public override operator fun C.unaryMinus(): C = ring { -this@unaryMinus } - /** - * Returns sum of the constants. - */ - @JvmName("plusConstantConstant") - public override operator fun C.plus(other: C): C = ring { this@plus + other } - /** - * Returns difference of the constants. - */ - @JvmName("minusConstantConstant") - public override operator fun C.minus(other: C): C = ring { this@minus - other } - /** - * Returns product of the constants. - */ - @JvmName("timesConstantConstant") - public override operator fun C.times(other: C): C = ring { this@times * other } - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerConstant") - override fun power(arg: C, exponent: UInt): C = ring { power(arg, exponent) } - - /** - * Instance of zero constant (zero of the underlying ring). - */ - public override val constantZero: C get() = ring.zero - /** - * Instance of unit constant (unit of the underlying ring). - */ - public override val constantOne: C get() = ring.one -} - -/** - * Abstraction of ring of polynomials of type [P] of variables of type [V] and over ring of constants of type [C]. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param V the type of variables. Polynomials have them in representations of terms. - * @param P the type of polynomials. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public interface MultivariatePolynomialSpace: PolynomialSpace { - /** - * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("plusVariableInt") - @JsName("plusVariableInt") - public operator fun V.plus(other: Int): P - /** - * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("minusVariableInt") - @JsName("minusVariableInt") - public operator fun V.minus(other: Int): P - /** - * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("timesVariableInt") - @JsName("timesVariableInt") - public operator fun V.times(other: Int): P - - /** - * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusIntVariable") - @JsName("plusIntVariable") - public operator fun Int.plus(other: V): P - /** - * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusIntVariable") - @JsName("minusIntVariable") - public operator fun Int.minus(other: V): P - /** - * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesIntVariable") - @JsName("timesIntVariable") - public operator fun Int.times(other: V): P - - /** - * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("plusVariableConstant") - @JsName("plusVariableConstant") - public operator fun V.plus(other: C): P - /** - * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("minusVariableConstant") - @JsName("minusVariableConstant") - public operator fun V.minus(other: C): P - /** - * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("timesVariableConstant") - @JsName("timesVariableConstant") - public operator fun V.times(other: C): P - - /** - * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusConstantVariable") - @JsName("plusConstantVariable") - public operator fun C.plus(other: V): P - /** - * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusConstantVariable") - @JsName("minusConstantVariable") - public operator fun C.minus(other: V): P - /** - * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesConstantVariable") - @JsName("timesConstantVariable") - public operator fun C.times(other: V): P - - /** - * Represents the variable as a monic monomial. - */ - @JvmName("unaryPlusVariable") - public operator fun V.unaryPlus(): P - /** - * Returns negation of representation of the variable as a monic monomial. - */ - @JvmName("unaryMinusVariable") - public operator fun V.unaryMinus(): P - /** - * Returns sum of the variables represented as monic monomials. - */ - @JvmName("plusVariableVariable") - public operator fun V.plus(other: V): P - /** - * Returns difference between the variables represented as monic monomials. - */ - @JvmName("minusVariableVariable") - public operator fun V.minus(other: V): P - /** - * Returns product of the variables represented as monic monomials. - */ - @JvmName("timesVariableVariable") - public operator fun V.times(other: V): P - - /** - * Represents the [variable] as a monic monomial. - */ - @JvmName("numberVariable") - public fun number(variable: V): P = +variable - /** - * Represents the variable as a monic monomial. - */ - @JvmName("asPolynomialVariable") - public fun V.asPolynomial(): P = number(this) - - /** - * Returns sum of the variable represented as a monic monomial and the polynomial. - */ - @JvmName("plusVariablePolynomial") - public operator fun V.plus(other: P): P - /** - * Returns difference between the variable represented as a monic monomial and the polynomial. - */ - @JvmName("minusVariablePolynomial") - public operator fun V.minus(other: P): P - /** - * Returns product of the variable represented as a monic monomial and the polynomial. - */ - @JvmName("timesVariablePolynomial") - public operator fun V.times(other: P): P - - /** - * Returns sum of the polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusPolynomialVariable") - public operator fun P.plus(other: V): P - /** - * Returns difference between the polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusPolynomialVariable") - public operator fun P.minus(other: V): P - /** - * Returns product of the polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesPolynomialVariable") - public operator fun P.times(other: V): P - - /** - * Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents - * in which they are appeared in the polynomial. - * - * As consequence all values in the map are positive integers. Also, if the polynomial is constant, the map is empty. - * And keys of the map is the same as in [variables]. - */ - public val P.degrees: Map - /** - * Counts degree of the polynomial by the specified [variable]. - */ - public fun P.degreeBy(variable: V): UInt = degrees.getOrElse(variable) { 0u } - /** - * Counts degree of the polynomial by the specified [variables]. - */ - public fun P.degreeBy(variables: Collection): UInt - /** - * Set of all variables that appear in the polynomial in positive exponents. - */ - public val P.variables: Set get() = degrees.keys - /** - * Count of all variables that appear in the polynomial in positive exponents. - */ - public val P.countOfVariables: Int get() = variables.size -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt deleted file mode 100644 index 766d9ce98..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt +++ /dev/null @@ -1,1689 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.operations.invoke -import kotlin.js.JsName -import kotlin.jvm.JvmName - - -/** - * Abstraction of rational function. - */ -public interface RationalFunction { - public val numerator: P - public val denominator: P - public operator fun component1(): P = numerator - public operator fun component2(): P = denominator -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] and constants of type - * [C]. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators. - * @param R the type of rational functions. - */ -@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE") // FIXME: Waiting for KT-31420 -public interface RationalFunctionSpace> : Ring { - /** - * Returns sum of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. - */ - @JvmName("plusConstantInt") - public operator fun C.plus(other: Int): C - /** - * Returns difference between the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. - */ - @JvmName("minusConstantInt") - public operator fun C.minus(other: Int): C - /** - * Returns product of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesConstantInt") - public operator fun C.times(other: Int): C - - /** - * Returns sum of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. - */ - @JvmName("plusIntConstant") - public operator fun Int.plus(other: C): C - /** - * Returns difference between the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. - */ - @JvmName("minusIntConstant") - public operator fun Int.minus(other: C): C - /** - * Returns product of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntConstant") - public operator fun Int.times(other: C): C - - /** - * Converts the integer [value] to constant. - */ - public fun constantNumber(value: Int): C = constantOne * value - /** - * Converts the integer to constant. - */ - public fun Int.asConstant(): C = constantNumber(this) - - /** - * Returns sum of the constant and the integer represented as a polynomial. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - @JvmName("plusPolynomialInt") - public operator fun P.plus(other: Int): P - /** - * Returns difference between the constant and the integer represented as a polynomial. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - @JvmName("minusPolynomialInt") - public operator fun P.minus(other: Int): P - /** - * Returns product of the constant and the integer represented as a polynomial. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesPolynomialInt") - public operator fun P.times(other: Int): P - - /** - * Returns sum of the integer represented as a polynomial and the constant. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - @JvmName("plusIntPolynomial") - public operator fun Int.plus(other: P): P - /** - * Returns difference between the integer represented as a polynomial and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - @JvmName("minusIntPolynomial") - public operator fun Int.minus(other: P): P - /** - * Returns product of the integer represented as a polynomial and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntPolynomial") - public operator fun Int.times(other: P): P - - /** - * Converts the integer [value] to polynomial. - */ - public fun polynomialNumber(value: Int): P = polynomialOne * value - /** - * Converts the integer to polynomial. - */ - public fun Int.asPolynomial(): P = polynomialNumber(this) - - /** - * Returns sum of the rational function and the integer represented as a rational function. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - public operator fun R.plus(other: Int): R = addMultipliedByDoubling(this, one, other) - /** - * Returns difference between the rational function and the integer represented as a rational function. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - public operator fun R.minus(other: Int): R = addMultipliedByDoubling(this, one, -other) - /** - * Returns product of the rational function and the integer represented as a rational function. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - public operator fun R.times(other: Int): R = multiplyByDoubling(this, other) - /** - * Returns quotient of the rational function and the integer represented as a rational function. - * - * The operation is equivalent to creating a new rational function by preserving numerator of [this] and - * multiplication denominator of [this] to [other]. - */ - public operator fun R.div(other: Int): R = this / multiplyByDoubling(one, other) - - /** - * Returns sum of the integer represented as a rational function and the rational function. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - public operator fun Int.plus(other: R): R = addMultipliedByDoubling(other, one, this) - /** - * Returns difference between the integer represented as a rational function and the rational function. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - public operator fun Int.minus(other: R): R = addMultipliedByDoubling(-other, one, this) - /** - * Returns product of the integer represented as a rational function and the rational function. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - public operator fun Int.times(other: R): R = multiplyByDoubling(other, this) - /** - * Returns quotient of the integer represented as a rational function and the rational function. - * - * The operation is equivalent to creating a new rational function which numerator is [this] times denominator of - * [other] and which denominator is [other]'s numerator. - */ - public operator fun Int.div(other: R): R = multiplyByDoubling(one / other, this) - - /** - * Converts the integer [value] to rational function. - */ - public fun number(value: Int): R = one * value - /** - * Converts the integer to rational function. - */ - public fun Int.asRationalFunction(): R = number(this) - - /** - * Returns the same constant. - */ - @JvmName("unaryPlusConstant") - @JsName("unaryPlusConstant") - public operator fun C.unaryPlus(): C = this - /** - * Returns negation of the constant. - */ - @JvmName("unaryMinusConstant") - @JsName("unaryMinusConstant") - public operator fun C.unaryMinus(): C - /** - * Returns sum of the constants. - */ - @JvmName("plusConstantConstant") - @JsName("plusConstantConstant") - public operator fun C.plus(other: C): C - /** - * Returns difference of the constants. - */ - @JvmName("minusConstantConstant") - @JsName("minusConstantConstant") - public operator fun C.minus(other: C): C - /** - * Returns product of the constants. - */ - @JvmName("timesConstantConstant") - @JsName("timesConstantConstant") - public operator fun C.times(other: C): C - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerConstant") - @JsName("powerConstant") - public fun power(arg: C, exponent: UInt) : C - - /** - * Instance of zero constant (zero of the underlying ring). - */ - public val constantZero: C - /** - * Instance of unit constant (unit of the underlying ring). - */ - public val constantOne: C - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - @JvmName("plusConstantPolynomial") - public operator fun C.plus(other: P): P - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - @JvmName("minusConstantPolynomial") - public operator fun C.minus(other: P): P - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - @JvmName("timesConstantPolynomial") - public operator fun C.times(other: P): P - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - @JvmName("plusPolynomialConstant") - public operator fun P.plus(other: C): P - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - @JvmName("minusPolynomialConstant") - public operator fun P.minus(other: C): P - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - @JvmName("timesPolynomialConstant") - public operator fun P.times(other: C): P - - /** - * Converts the constant [value] to polynomial. - */ - public fun polynomialNumber(value: C): P = polynomialOne * value - /** - * Converts the constant to polynomial. - */ - public fun C.asPolynomial(): P = polynomialNumber(this) - - /** - * Returns the same polynomial. - */ - @JvmName("unaryPlusPolynomial") - public operator fun P.unaryPlus(): P = this - /** - * Returns negation of the polynomial. - */ - @JvmName("unaryMinusPolynomial") - public operator fun P.unaryMinus(): P - /** - * Returns sum of the polynomials. - */ - @JvmName("plusPolynomialPolynomial") - public operator fun P.plus(other: P): P - /** - * Returns difference of the polynomials. - */ - @JvmName("minusPolynomialPolynomial") - public operator fun P.minus(other: P): P - /** - * Returns product of the polynomials. - */ - @JvmName("timesPolynomialPolynomial") - public operator fun P.times(other: P): P - /** - * Returns quotient of the polynomials as rational function. - */ - @JvmName("divPolynomialPolynomial") - public operator fun P.div(other: P): R - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerPolynomial") - public fun power(arg: P, exponent: UInt) : P - - /** - * Instance of zero polynomial (zero of the polynomial ring). - */ - public val polynomialZero: P - /** - * Instance of unit polynomial (unit of the polynomial ring). - */ - public val polynomialOne: P - - /** - * Returns sum of the constant represented as a rational function and the rational function. - */ - @JvmName("plusConstantRational") - public operator fun C.plus(other: R): R - /** - * Returns difference between the constant represented as a polynomial and the rational function. - */ - @JvmName("minusConstantRational") - public operator fun C.minus(other: R): R - /** - * Returns product of the constant represented as a polynomial and the rational function. - */ - @JvmName("timesConstantRational") - public operator fun C.times(other: R): R - /** - * Returns quotient of the constant represented as a polynomial and the rational function. - */ - @JvmName("divConstantRational") - public operator fun C.div(other: R): R - - /** - * Returns sum of the rational function and the constant represented as a rational function. - */ - @JvmName("plusRationalConstant") - public operator fun R.plus(other: C): R - /** - * Returns difference between the rational function and the constant represented as a rational function. - */ - @JvmName("minusRationalConstant") - public operator fun R.minus(other: C): R - /** - * Returns product of the rational function and the constant represented as a rational function. - */ - @JvmName("timesRationalConstant") - public operator fun R.times(other: C): R - /** - * Returns quotient of the rational function and the constant represented as a rational function. - */ - @JvmName("divRationalConstant") - public operator fun R.div(other: C): R - - /** - * Converts the constant [value] to rational function. - */ - @JvmName("numberConstant") - public fun number(value: C): R = one * value - /** - * Converts the constant to rational function. - */ - @JvmName("asRationalFunctionConstant") - public fun C.asRationalFunction(): R = number(this) - - /** - * Returns sum of the polynomial represented as a rational function and the rational function. - */ - @JvmName("plusPolynomialRational") - public operator fun P.plus(other: R): R - /** - * Returns difference between the polynomial represented as a polynomial and the rational function. - */ - @JvmName("minusPolynomialRational") - public operator fun P.minus(other: R): R - /** - * Returns product of the polynomial represented as a polynomial and the rational function. - */ - @JvmName("timesPolynomialRational") - public operator fun P.times(other: R): R - /** - * Returns quotient of the polynomial represented as a polynomial and the rational function. - */ - @JvmName("divPolynomialRational") - public operator fun P.div(other: R): R - - /** - * Returns sum of the rational function and the polynomial represented as a rational function. - */ - @JvmName("plusRationalPolynomial") - public operator fun R.plus(other: P): R - /** - * Returns difference between the rational function and the polynomial represented as a rational function. - */ - @JvmName("minusRationalPolynomial") - public operator fun R.minus(other: P): R - /** - * Returns product of the rational function and the polynomial represented as a rational function. - */ - @JvmName("timesRationalPolynomial") - public operator fun R.times(other: P): R - /** - * Returns quotient of the rational function and the polynomial represented as a rational function. - */ - @JvmName("divRationalPolynomial") - public operator fun R.div(other: P): R - - /** - * Converts the polynomial [value] to rational function. - */ - @JvmName("numberPolynomial") - public fun number(value: P): R = one * value - /** - * Converts the polynomial to rational function. - */ - @JvmName("asRationalFunctionPolynomial") - public fun P.asRationalFunction(): R = number(this) - - /** - * Returns the same rational function. - */ - public override operator fun R.unaryPlus(): R = this - /** - * Returns negation of the rational function. - */ - public override operator fun R.unaryMinus(): R - /** - * Returns sum of the rational functions. - */ - public override operator fun R.plus(other: R): R - /** - * Returns difference of the rational functions. - */ - public override operator fun R.minus(other: R): R - /** - * Returns product of the rational functions. - */ - public override operator fun R.times(other: R): R - /** - * Returns quotient of the rational functions. - */ - public operator fun R.div(other: R): R - /** - * Raises [arg] to the integer power [exponent]. - */ - public override fun power(arg: R, exponent: UInt) : R = exponentiateBySquaring(arg, exponent) - - /** - * Instance of zero rational function (zero of the rational functions ring). - */ - public override val zero: R - /** - * Instance of unit polynomial (unit of the rational functions ring). - */ - public override val one: R - - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - public val P.degree: Int - - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - public val R.numeratorDegree: Int get() = numerator.degree - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - public val R.denominatorDegree: Int get() = denominator.degree - - override fun add(left: R, right: R): R = left + right - override fun multiply(left: R, right: R): R = left * right -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] and constants of type - * [C]. It also assumes that there is provided [ring] (of type [A]), that provides constant-wise operations. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators in them. - * @param R the type of rational functions. - * @param A the type of algebraic structure (precisely, of ring) provided for constants. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public interface RationalFunctionSpaceOverRing< - C, - P, - R: RationalFunction, - out A: Ring - > : RationalFunctionSpace { - - /** - * Underlying ring of constants. Its operations on constants are inherited by local operations on constants. - */ - public val ring: A - - /** - * Returns sum of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. - */ - @JvmName("plusConstantInt") - public override operator fun C.plus(other: Int): C = ring { addMultipliedByDoubling(this@plus, one, other) } - /** - * Returns difference between the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. - */ - @JvmName("minusConstantInt") - public override operator fun C.minus(other: Int): C = ring { addMultipliedByDoubling(this@minus, one, -other) } - /** - * Returns product of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesConstantInt") - public override operator fun C.times(other: Int): C = ring { multiplyByDoubling(this@times, other) } - - /** - * Returns sum of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. - */ - @JvmName("plusIntConstant") - public override operator fun Int.plus(other: C): C = ring { addMultipliedByDoubling(other, one, this@plus) } - /** - * Returns difference between the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. - */ - @JvmName("minusIntConstant") - public override operator fun Int.minus(other: C): C = ring { addMultipliedByDoubling(-other, one, this@minus) } - /** - * Returns product of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntConstant") - public override operator fun Int.times(other: C): C = ring { multiplyByDoubling(other, this@times) } - - /** - * Returns the same constant. - */ - @JvmName("unaryPlusConstant") - public override operator fun C.unaryPlus(): C = ring { +this@unaryPlus } - /** - * Returns negation of the constant. - */ - @JvmName("unaryMinusConstant") - public override operator fun C.unaryMinus(): C = ring { -this@unaryMinus } - /** - * Returns sum of the constants. - */ - @JvmName("plusConstantConstant") - public override operator fun C.plus(other: C): C = ring { this@plus + other } - /** - * Returns difference of the constants. - */ - @JvmName("minusConstantConstant") - public override operator fun C.minus(other: C): C = ring { this@minus - other } - /** - * Returns product of the constants. - */ - @JvmName("timesConstantConstant") - public override operator fun C.times(other: C): C = ring { this@times * other } - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerConstant") - public override fun power(arg: C, exponent: UInt) : C = ring { power(arg, exponent) } - - /** - * Instance of zero constant (zero of the underlying ring). - */ - public override val constantZero: C get() = ring.zero - /** - * Instance of unit constant (unit of the underlying ring). - */ - public override val constantOne: C get() = ring.one -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] and constants of type - * [C]. It also assumes that there is provided [polynomialRing] (of type [AP]), that provides constant- and - * polynomial-wise operations. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators in them. - * @param R the type of rational functions. - * @param AP the type of algebraic structure (precisely, of ring) provided for polynomials. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public interface RationalFunctionSpaceOverPolynomialSpace< - C, - P, - R: RationalFunction, - out AP: PolynomialSpace, - > : RationalFunctionSpace { - - /** - * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations. - */ - public val polynomialRing: AP - - /** - * Returns sum of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. - */ - @JvmName("plusConstantInt") - public override operator fun C.plus(other: Int): C = polynomialRing { this@plus + other } - /** - * Returns difference between the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. - */ - @JvmName("minusConstantInt") - public override operator fun C.minus(other: Int): C = polynomialRing { this@minus - other } - /** - * Returns product of the constant and the integer represented as a constant (member of underlying ring). - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesConstantInt") - public override operator fun C.times(other: Int): C = polynomialRing { this@times * other } - - /** - * Returns sum of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. - */ - @JvmName("plusIntConstant") - public override operator fun Int.plus(other: C): C = polynomialRing { this@plus + other } - /** - * Returns difference between the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. - */ - @JvmName("minusIntConstant") - public override operator fun Int.minus(other: C): C = polynomialRing { this@minus - other } - /** - * Returns product of the integer represented as a constant (member of underlying ring) and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntConstant") - public override operator fun Int.times(other: C): C = polynomialRing { this@times * other } - - /** - * Converts the integer [value] to constant. - */ - public override fun constantNumber(value: Int): C = polynomialRing { constantNumber(value) } - /** - * Converts the integer to constant. - */ - override fun Int.asConstant(): C = polynomialRing { asConstant() } - - /** - * Returns sum of the constant and the integer represented as a polynomial. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - @JvmName("plusPolynomialInt") - public override operator fun P.plus(other: Int): P = polynomialRing { this@plus + other } - /** - * Returns difference between the constant and the integer represented as a polynomial. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - @JvmName("minusPolynomialInt") - public override operator fun P.minus(other: Int): P = polynomialRing { this@minus - other } - /** - * Returns product of the constant and the integer represented as a polynomial. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - @JvmName("timesPolynomialInt") - public override operator fun P.times(other: Int): P = polynomialRing { this@times * other } - - /** - * Returns sum of the integer represented as a polynomial and the constant. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - @JvmName("plusIntPolynomial") - public override operator fun Int.plus(other: P): P = polynomialRing { this@plus + other } - /** - * Returns difference between the integer represented as a polynomial and the constant. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - @JvmName("minusIntPolynomial") - public override operator fun Int.minus(other: P): P = polynomialRing { this@minus - other } - /** - * Returns product of the integer represented as a polynomial and the constant. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - @JvmName("timesIntPolynomial") - public override operator fun Int.times(other: P): P = polynomialRing { this@times * other } - - /** - * Converts the integer [value] to polynomial. - */ - public override fun polynomialNumber(value: Int): P = polynomialRing { number(value) } - /** - * Converts the integer to polynomial. - */ - public override fun Int.asPolynomial(): P = polynomialRing { asPolynomial() } - - /** - * Returns the same constant. - */ - @JvmName("unaryPlusConstant") - public override operator fun C.unaryPlus(): C = polynomialRing { +this@unaryPlus } - /** - * Returns negation of the constant. - */ - @JvmName("unaryMinusConstant") - public override operator fun C.unaryMinus(): C = polynomialRing { -this@unaryMinus } - /** - * Returns sum of the constants. - */ - @JvmName("plusConstantConstant") - public override operator fun C.plus(other: C): C = polynomialRing { this@plus + other } - /** - * Returns difference of the constants. - */ - @JvmName("minusConstantConstant") - public override operator fun C.minus(other: C): C = polynomialRing { this@minus - other } - /** - * Returns product of the constants. - */ - @JvmName("timesConstantConstant") - public override operator fun C.times(other: C): C = polynomialRing { this@times * other } - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerConstant") - public override fun power(arg: C, exponent: UInt) : C = polynomialRing { power(arg, exponent) } - - /** - * Instance of zero constant (zero of the underlying ring). - */ - public override val constantZero: C get() = polynomialRing.constantZero - /** - * Instance of unit constant (unit of the underlying ring). - */ - public override val constantOne: C get() = polynomialRing.constantOne - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - @JvmName("plusConstantPolynomial") - public override operator fun C.plus(other: P): P = polynomialRing { this@plus + other } - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - @JvmName("minusConstantPolynomial") - public override operator fun C.minus(other: P): P = polynomialRing { this@minus - other } - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - @JvmName("timesConstantPolynomial") - public override operator fun C.times(other: P): P = polynomialRing { this@times * other } - - /** - * Returns sum of the constant represented as a polynomial and the polynomial. - */ - @JvmName("plusPolynomialConstant") - public override operator fun P.plus(other: C): P = polynomialRing { this@plus + other } - /** - * Returns difference between the constant represented as a polynomial and the polynomial. - */ - @JvmName("minusPolynomialConstant") - public override operator fun P.minus(other: C): P = polynomialRing { this@minus - other } - /** - * Returns product of the constant represented as a polynomial and the polynomial. - */ - @JvmName("timesPolynomialConstant") - public override operator fun P.times(other: C): P = polynomialRing { this@times * other } - - /** - * Converts the constant [value] to polynomial. - */ - public override fun polynomialNumber(value: C): P = polynomialRing { number(value) } - /** - * Converts the constant to polynomial. - */ - public override fun C.asPolynomial(): P = polynomialRing { asPolynomial() } - - /** - * Returns the same polynomial. - */ - @JvmName("unaryPlusPolynomial") - public override operator fun P.unaryPlus(): P = polynomialRing { +this@unaryPlus } - /** - * Returns negation of the polynomial. - */ - @JvmName("unaryMinusPolynomial") - public override operator fun P.unaryMinus(): P = polynomialRing { -this@unaryMinus } - /** - * Returns sum of the polynomials. - */ - @JvmName("plusPolynomialPolynomial") - public override operator fun P.plus(other: P): P = polynomialRing { this@plus + other } - /** - * Returns difference of the polynomials. - */ - @JvmName("minusPolynomialPolynomial") - public override operator fun P.minus(other: P): P = polynomialRing { this@minus - other } - /** - * Returns product of the polynomials. - */ - @JvmName("timesPolynomialPolynomial") - public override operator fun P.times(other: P): P = polynomialRing { this@times * other } - /** - * Raises [arg] to the integer power [exponent]. - */ - @JvmName("powerPolynomial") - public override fun power(arg: P, exponent: UInt) : P = polynomialRing { power(arg, exponent) } - - /** - * Instance of zero polynomial (zero of the polynomial ring). - */ - public override val polynomialZero: P get() = polynomialRing.zero - /** - * Instance of unit polynomial (unit of the polynomial ring). - */ - public override val polynomialOne: P get() = polynomialRing.one - - /** - * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is - * zero, degree is -1. - */ - public override val P.degree: Int get() = polynomialRing { this@degree.degree } -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] and constants of type - * [C]. It also assumes that there is provided constructor [constructRationalFunction] of rational functions from - * polynomial numerator and denominator. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators in them. - * @param R the type of rational functions. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public abstract class PolynomialSpaceOfFractions< - C, - P, - R: RationalFunction, - > : RationalFunctionSpace { - - /** - * Constructor of rational functions (of type [R]) from numerator and denominator (of type [P]). - */ - protected abstract fun constructRationalFunction(numerator: P, denominator: P = polynomialOne) : R - - /** - * Returns sum of the rational function and the integer represented as a rational function. - * - * The operation is equivalent to adding [other] copies of unit polynomial to [this]. - */ - public override operator fun R.plus(other: Int): R = - constructRationalFunction( - numerator + denominator * other, - denominator - ) - /** - * Returns difference between the rational function and the integer represented as a rational function. - * - * The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. - */ - public override operator fun R.minus(other: Int): R = - constructRationalFunction( - numerator - denominator * other, - denominator - ) - /** - * Returns product of the rational function and the integer represented as a rational function. - * - * The operation is equivalent to sum of [other] copies of [this]. - */ - public override operator fun R.times(other: Int): R = - constructRationalFunction( - numerator * other, - denominator - ) - /** - * Returns quotient of the rational function and the integer represented as a rational function. - * - * The operation is equivalent to creating a new rational function by preserving numerator of [this] and - * multiplication denominator of [this] to [other]. - */ - public override operator fun R.div(other: Int): R = - constructRationalFunction( - numerator, - denominator * other - ) - - /** - * Returns sum of the integer represented as a rational function and the rational function. - * - * The operation is equivalent to adding [this] copies of unit polynomial to [other]. - */ - public override operator fun Int.plus(other: R): R = - constructRationalFunction( - other.denominator * this + other.numerator, - other.denominator - ) - /** - * Returns difference between the integer represented as a rational function and the rational function. - * - * The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. - */ - public override operator fun Int.minus(other: R): R = - constructRationalFunction( - other.denominator * this - other.numerator, - other.denominator - ) - /** - * Returns product of the integer represented as a rational function and the rational function. - * - * The operation is equivalent to sum of [this] copies of [other]. - */ - public override operator fun Int.times(other: R): R = - constructRationalFunction( - this * other.numerator, - other.denominator - ) - /** - * Returns quotient of the integer represented as a rational function and the rational function. - * - * The operation is equivalent to creating a new rational function which numerator is [this] times denominator of - * [other] and which denominator is [other]'s numerator. - */ - public override operator fun Int.div(other: R): R = - constructRationalFunction( - this * other.denominator, - other.numerator - ) - - /** - * Converts the integer [value] to rational function. - */ - public override fun number(value: Int): R = constructRationalFunction(polynomialNumber(value)) - - /** - * Returns quotient of the polynomials as rational function. - */ - @JvmName("divPolynomialPolynomial") - public override operator fun P.div(other: P): R = constructRationalFunction(this, other) - - /** - * Returns sum of the constant represented as a rational function and the rational function. - */ - @JvmName("plusConstantRational") - public override operator fun C.plus(other: R): R = - constructRationalFunction( - other.denominator * this + other.numerator, - other.denominator - ) - /** - * Returns difference between the constant represented as a polynomial and the rational function. - */ - @JvmName("minusConstantRational") - public override operator fun C.minus(other: R): R = - constructRationalFunction( - other.denominator * this - other.numerator, - other.denominator - ) - /** - * Returns product of the constant represented as a polynomial and the rational function. - */ - @JvmName("timesConstantRational") - public override operator fun C.times(other: R): R = - constructRationalFunction( - this * other.numerator, - other.denominator - ) - /** - * Returns quotient of the constant represented as a polynomial and the rational function. - */ - @JvmName("divConstantRational") - public override operator fun C.div(other: R): R = - constructRationalFunction( - this * other.denominator, - other.numerator - ) - - /** - * Returns sum of the constant represented as a rational function and the rational function. - */ - @JvmName("plusRationalConstant") - public override operator fun R.plus(other: C): R = - constructRationalFunction( - numerator + denominator * other, - denominator - ) - /** - * Returns difference between the constant represented as a rational function and the rational function. - */ - @JvmName("minusRationalConstant") - public override operator fun R.minus(other: C): R = - constructRationalFunction( - numerator - denominator * other, - denominator - ) - /** - * Returns product of the constant represented as a rational function and the rational function. - */ - @JvmName("timesRationalConstant") - public override operator fun R.times(other: C): R = - constructRationalFunction( - numerator * other, - denominator - ) - /** - * Returns quotient of the rational function and the constant represented as a rational function. - */ - @JvmName("divRationalConstant") - public override operator fun R.div(other: C): R = - constructRationalFunction( - numerator, - denominator * other - ) - - /** - * Converts the constant [value] to rational function. - */ - @JvmName("numberConstant") - public override fun number(value: C): R = constructRationalFunction(polynomialNumber(value)) - - /** - * Returns sum of the polynomial represented as a rational function and the rational function. - */ - @JvmName("plusPolynomialRational") - public override operator fun P.plus(other: R): R = - constructRationalFunction( - other.denominator * this + other.numerator, - other.denominator - ) - /** - * Returns difference between the polynomial represented as a polynomial and the rational function. - */ - @JvmName("minusPolynomialRational") - public override operator fun P.minus(other: R): R = - constructRationalFunction( - other.denominator * this - other.numerator, - other.denominator - ) - /** - * Returns product of the polynomial represented as a polynomial and the rational function. - */ - @JvmName("timesPolynomialRational") - public override operator fun P.times(other: R): R = - constructRationalFunction( - this * other.numerator, - other.denominator - ) - /** - * Returns quotient of the polynomial represented as a polynomial and the rational function. - */ - @JvmName("divPolynomialRational") - public override operator fun P.div(other: R): R = - constructRationalFunction( - this * other.denominator, - other.numerator - ) - - /** - * Returns sum of the polynomial represented as a rational function and the rational function. - */ - @JvmName("plusRationalPolynomial") - public override operator fun R.plus(other: P): R = - constructRationalFunction( - numerator + denominator * other, - denominator - ) - /** - * Returns difference between the polynomial represented as a rational function and the rational function. - */ - @JvmName("minusRationalPolynomial") - public override operator fun R.minus(other: P): R = - constructRationalFunction( - numerator - denominator * other, - denominator - ) - /** - * Returns product of the polynomial represented as a rational function and the rational function. - */ - @JvmName("timesRationalPolynomial") - public override operator fun R.times(other: P): R = - constructRationalFunction( - numerator * other, - denominator - ) - /** - * Returns quotient of the rational function and the polynomial represented as a rational function. - */ - @JvmName("divRationalPolynomial") - public override operator fun R.div(other: P): R = - constructRationalFunction( - numerator, - denominator * other - ) - - /** - * Converts the polynomial [value] to rational function. - */ - @JvmName("numberPolynomial") - public override fun number(value: P): R = constructRationalFunction(value) - - /** - * Returns negation of the rational function. - */ - public override operator fun R.unaryMinus(): R = constructRationalFunction(-numerator, denominator) - /** - * Returns sum of the rational functions. - */ - public override operator fun R.plus(other: R): R = - constructRationalFunction( - numerator * other.denominator + denominator * other.numerator, - denominator * other.denominator - ) - /** - * Returns difference of the rational functions. - */ - public override operator fun R.minus(other: R): R = - constructRationalFunction( - numerator * other.denominator - denominator * other.numerator, - denominator * other.denominator - ) - /** - * Returns product of the rational functions. - */ - public override operator fun R.times(other: R): R = - constructRationalFunction( - numerator * other.numerator, - denominator * other.denominator - ) - /** - * Returns quotient of the rational functions. - */ - public override operator fun R.div(other: R): R = - constructRationalFunction( - numerator * other.denominator, - denominator * other.numerator - ) - /** - * Raises [arg] to the integer power [exponent]. - */ - public override fun power(arg: R, exponent: UInt): R = - constructRationalFunction( - power(arg.numerator, exponent), - power(arg.denominator, exponent), - ) - - /** - * Instance of zero rational function (zero of the rational functions ring). - */ - public override val zero: R by lazy { constructRationalFunction(polynomialZero) } - - /** - * Instance of unit polynomial (unit of the rational functions ring). - */ - public override val one: R by lazy { constructRationalFunction(polynomialOne) } -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] of variables of type - * [V] and over ring of constants of type [C]. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param V the type of variables. Polynomials have them in representations of terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators in them. - * @param R the type of rational functions. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public interface MultivariateRationalFunctionSpace< - C, - V, - P, - R: RationalFunction - >: RationalFunctionSpace { - /** - * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("plusVariableInt") - @JsName("plusVariableInt") - public operator fun V.plus(other: Int): P - /** - * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("minusVariableInt") - @JsName("minusVariableInt") - public operator fun V.minus(other: Int): P - /** - * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("timesVariableInt") - @JsName("timesVariableInt") - public operator fun V.times(other: Int): P - - /** - * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusIntVariable") - @JsName("plusIntVariable") - public operator fun Int.plus(other: V): P - /** - * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusIntVariable") - @JsName("minusIntVariable") - public operator fun Int.minus(other: V): P - /** - * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesIntVariable") - @JsName("timesIntVariable") - public operator fun Int.times(other: V): P - - /** - * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("plusVariableConstant") - @JsName("plusVariableConstant") - public operator fun V.plus(other: C): P - /** - * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("minusVariableConstant") - @JsName("minusVariableConstant") - public operator fun V.minus(other: C): P - /** - * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("timesVariableConstant") - @JsName("timesVariableConstant") - public operator fun V.times(other: C): P - - /** - * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusConstantVariable") - @JsName("plusConstantVariable") - public operator fun C.plus(other: V): P - /** - * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusConstantVariable") - @JsName("minusConstantVariable") - public operator fun C.minus(other: V): P - /** - * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesConstantVariable") - @JsName("timesConstantVariable") - public operator fun C.times(other: V): P - - /** - * Represents the variable as a monic monomial. - */ - @JvmName("unaryPlusVariable") - @JsName("unaryPlusVariable") - public operator fun V.unaryPlus(): P - /** - * Returns negation of representation of the variable as a monic monomial. - */ - @JvmName("unaryMinusVariable") - @JsName("unaryMinusVariable") - public operator fun V.unaryMinus(): P - /** - * Returns sum of the variables represented as monic monomials. - */ - @JvmName("plusVariableVariable") - @JsName("plusVariableVariable") - public operator fun V.plus(other: V): P - /** - * Returns difference between the variables represented as monic monomials. - */ - @JvmName("minusVariableVariable") - @JsName("minusVariableVariable") - public operator fun V.minus(other: V): P - /** - * Returns product of the variables represented as monic monomials. - */ - @JvmName("timesVariableVariable") - @JsName("timesVariableVariable") - public operator fun V.times(other: V): P - - /** - * Represents the [variable] as a monic monomial. - */ - @JvmName("polynomialNumberVariable") - public fun polynomialNumber(variable: V): P = +variable - /** - * Represents the variable as a monic monomial. - */ - @JvmName("asPolynomialVariable") - public fun V.asPolynomial(): P = polynomialNumber(this) - - /** - * Represents the [variable] as a rational function. - */ - @JvmName("numberVariable") - @JsName("numberVariable") - public fun number(variable: V): R = number(polynomialNumber(variable)) - /** - * Represents the variable as a rational function. - */ - @JvmName("asRationalFunctionVariable") - @JsName("asRationalFunctionVariable") - public fun V.asRationalFunction(): R = number(this) - - /** - * Returns sum of the variable represented as a monic monomial and the polynomial. - */ - @JvmName("plusVariablePolynomial") - public operator fun V.plus(other: P): P - /** - * Returns difference between the variable represented as a monic monomial and the polynomial. - */ - @JvmName("minusVariablePolynomial") - public operator fun V.minus(other: P): P - /** - * Returns product of the variable represented as a monic monomial and the polynomial. - */ - @JvmName("timesVariablePolynomial") - public operator fun V.times(other: P): P - - /** - * Returns sum of the polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusPolynomialVariable") - public operator fun P.plus(other: V): P - /** - * Returns difference between the polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusPolynomialVariable") - public operator fun P.minus(other: V): P - /** - * Returns product of the polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesPolynomialVariable") - public operator fun P.times(other: V): P - - /** - * Returns sum of the variable represented as a rational function and the rational function. - */ - @JvmName("plusVariableRational") - public operator fun V.plus(other: R): R - /** - * Returns difference between the variable represented as a rational function and the rational function. - */ - @JvmName("minusVariableRational") - public operator fun V.minus(other: R): R - /** - * Returns product of the variable represented as a rational function and the rational function. - */ - @JvmName("timesVariableRational") - public operator fun V.times(other: R): R - - /** - * Returns sum of the rational function and the variable represented as a rational function. - */ - @JvmName("plusRationalVariable") - public operator fun R.plus(other: V): R - /** - * Returns difference between the rational function and the variable represented as a rational function. - */ - @JvmName("minusRationalVariable") - public operator fun R.minus(other: V): R - /** - * Returns product of the rational function and the variable represented as a rational function. - */ - @JvmName("timesRationalVariable") - public operator fun R.times(other: V): R - - /** - * Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents - * in which they are appeared in the polynomial. - * - * As consequence all values in the map are positive integers. Also, if the polynomial is constant, the map is empty. - * And keys of the map is the same as in [variables]. - */ - public val P.degrees: Map - /** - * Counts degree of the polynomial by the specified [variable]. - */ - public fun P.degreeBy(variable: V): UInt = degrees.getOrElse(variable) { 0u } - /** - * Counts degree of the polynomial by the specified [variables]. - */ - public fun P.degreeBy(variables: Collection): UInt - /** - * Set of all variables that appear in the polynomial in positive exponents. - */ - public val P.variables: Set get() = degrees.keys - /** - * Count of all variables that appear in the polynomial in positive exponents. - */ - public val P.countOfVariables: Int get() = variables.size - - /** - * Set of all variables that appear in the polynomial in positive exponents. - */ - public val R.variables: Set get() = numerator.variables union denominator.variables - /** - * Count of all variables that appear in the polynomial in positive exponents. - */ - public val R.countOfVariables: Int get() = variables.size -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] of variables of type - * [V] and over ring of constants of type [C]. It also assumes that there is provided [polynomialRing] (of type [AP]), - * that provides constant-, variable- and polynomial-wise operations. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param V the type of variables. Polynomials have them in representations of terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators in them. - * @param R the type of rational functions. - * @param AP the type of algebraic structure (precisely, of ring) provided for polynomials. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public interface MultivariateRationalFunctionSpaceOverMultivariatePolynomialSpace< - C, - V, - P, - R: RationalFunction, - out AP: MultivariatePolynomialSpace, - > : RationalFunctionSpaceOverPolynomialSpace, MultivariateRationalFunctionSpace { - /** - * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("plusVariableInt") - public override operator fun V.plus(other: Int): P = polynomialRing { this@plus + other } - /** - * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("minusVariableInt") - public override operator fun V.minus(other: Int): P = polynomialRing { this@minus - other } - /** - * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial. - */ - @JvmName("timesVariableInt") - public override operator fun V.times(other: Int): P = polynomialRing { this@times * other } - - /** - * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusIntVariable") - public override operator fun Int.plus(other: V): P = polynomialRing { this@plus + other } - /** - * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusIntVariable") - public override operator fun Int.minus(other: V): P = polynomialRing { this@minus - other } - /** - * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesIntVariable") - public override operator fun Int.times(other: V): P = polynomialRing { this@times * other } - - /** - * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("plusVariableConstant") - public override operator fun V.plus(other: C): P = polynomialRing { this@plus + other } - /** - * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("minusVariableConstant") - public override operator fun V.minus(other: C): P = polynomialRing { this@minus - other } - /** - * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial. - */ - @JvmName("timesVariableConstant") - public override operator fun V.times(other: C): P = polynomialRing { this@times * other } - - /** - * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusConstantVariable") - public override operator fun C.plus(other: V): P = polynomialRing { this@plus + other } - /** - * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusConstantVariable") - public override operator fun C.minus(other: V): P = polynomialRing { this@minus - other } - /** - * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesConstantVariable") - public override operator fun C.times(other: V): P = polynomialRing { this@times * other } - - /** - * Represents the variable as a monic monomial. - */ - @JvmName("unaryPlusVariable") - public override operator fun V.unaryPlus(): P = polynomialRing { +this@unaryPlus } - /** - * Returns negation of representation of the variable as a monic monomial. - */ - @JvmName("unaryMinusVariable") - public override operator fun V.unaryMinus(): P = polynomialRing { -this@unaryMinus } - /** - * Returns sum of the variables represented as monic monomials. - */ - @JvmName("plusVariableVariable") - public override operator fun V.plus(other: V): P = polynomialRing { this@plus + other } - /** - * Returns difference between the variables represented as monic monomials. - */ - @JvmName("minusVariableVariable") - public override operator fun V.minus(other: V): P = polynomialRing { this@minus - other } - /** - * Returns product of the variables represented as monic monomials. - */ - @JvmName("timesVariableVariable") - public override operator fun V.times(other: V): P = polynomialRing { this@times * other } - - /** - * Represents the [variable] as a monic monomial. - */ - @JvmName("polynomialNumberVariable") - public override fun polynomialNumber(variable: V): P = polynomialRing { number(variable) } - /** - * Represents the variable as a monic monomial. - */ - @JvmName("asPolynomialVariable") - public override fun V.asPolynomial(): P = polynomialRing { this@asPolynomial.asPolynomial() } - - /** - * Returns sum of the variable represented as a monic monomial and the polynomial. - */ - @JvmName("plusVariablePolynomial") - public override operator fun V.plus(other: P): P = polynomialRing { this@plus + other } - /** - * Returns difference between the variable represented as a monic monomial and the polynomial. - */ - @JvmName("minusVariablePolynomial") - public override operator fun V.minus(other: P): P = polynomialRing { this@minus - other } - /** - * Returns product of the variable represented as a monic monomial and the polynomial. - */ - @JvmName("timesVariablePolynomial") - public override operator fun V.times(other: P): P = polynomialRing { this@times * other } - - /** - * Returns sum of the polynomial and the variable represented as a monic monomial. - */ - @JvmName("plusPolynomialVariable") - public override operator fun P.plus(other: V): P = polynomialRing { this@plus + other } - /** - * Returns difference between the polynomial and the variable represented as a monic monomial. - */ - @JvmName("minusPolynomialVariable") - public override operator fun P.minus(other: V): P = polynomialRing { this@minus - other } - /** - * Returns product of the polynomial and the variable represented as a monic monomial. - */ - @JvmName("timesPolynomialVariable") - public override operator fun P.times(other: V): P = polynomialRing { this@times * other } - - /** - * Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents - * in which they are appeared in the polynomial. - * - * As consequence all values in the map are positive integers. Also, if the polynomial is constant, the map is empty. - * And keys of the map is the same as in [variables]. - */ - public override val P.degrees: Map get() = polynomialRing { degrees } - /** - * Counts degree of the polynomial by the specified [variable]. - */ - public override fun P.degreeBy(variable: V): UInt = polynomialRing { degreeBy(variable) } - /** - * Counts degree of the polynomial by the specified [variables]. - */ - public override fun P.degreeBy(variables: Collection): UInt = polynomialRing { degreeBy(variables) } - /** - * Set of all variables that appear in the polynomial in positive exponents. - */ - public override val P.variables: Set get() = polynomialRing { variables } - /** - * Count of all variables that appear in the polynomial in positive exponents. - */ - public override val P.countOfVariables: Int get() = polynomialRing { countOfVariables } -} - -/** - * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] of variables of type - * [V] and over ring of constants of type [C]. It also assumes that there is provided constructor - * [constructRationalFunction] of rational functions from polynomial numerator and denominator. - * - * @param C the type of constants. Polynomials have them as coefficients in their terms. - * @param V the type of variables. Polynomials have them in representations of terms. - * @param P the type of polynomials. Rational functions have them as numerators and denominators in them. - * @param R the type of rational functions. - */ -@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420 -public abstract class MultivariatePolynomialSpaceOfFractions< - C, - V, - P, - R: RationalFunction, - > : MultivariateRationalFunctionSpace, PolynomialSpaceOfFractions() { - /** - * Returns sum of the variable represented as a rational function and the rational function. - */ - @JvmName("plusVariableRational") - public override operator fun V.plus(other: R): R = - constructRationalFunction( - this * other.denominator + other.numerator, - other.denominator - ) - /** - * Returns difference between the variable represented as a rational function and the rational function. - */ - @JvmName("minusVariableRational") - public override operator fun V.minus(other: R): R = - constructRationalFunction( - this * other.denominator - other.numerator, - other.denominator - ) - /** - * Returns product of the variable represented as a rational function and the rational function. - */ - @JvmName("timesVariableRational") - public override operator fun V.times(other: R): R = - constructRationalFunction( - this * other.numerator, - other.denominator - ) - - /** - * Returns sum of the rational function and the variable represented as a rational function. - */ - @JvmName("plusRationalVariable") - public override operator fun R.plus(other: V): R = - constructRationalFunction( - numerator + denominator * other, - denominator - ) - /** - * Returns difference between the rational function and the variable represented as a rational function. - */ - @JvmName("minusRationalVariable") - public override operator fun R.minus(other: V): R = - constructRationalFunction( - numerator - denominator * other, - denominator - ) - /** - * Returns product of the rational function and the variable represented as a rational function. - */ - public override operator fun R.times(other: V): R = - constructRationalFunction( - numerator * other, - denominator - ) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/algebraicStub.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/algebraicStub.kt deleted file mode 100644 index 80bf6ec53..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/algebraicStub.kt +++ /dev/null @@ -1,146 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.* - - -// TODO: All of this should be moved to algebraic structures' place for utilities -// FIXME: Move receiver to context receiver -/** - * Returns product of [arg] and integer [multiplier]. - * - * @param arg the multiplicand. - * @param multiplier the integer multiplier. - * @return product of the multiplicand [arg] and the multiplier [multiplier]. - * @author Gleb Minaev - */ -internal fun Group.multiplyByDoubling(arg: C, multiplier: Int): C = - if (multiplier >= 0) multiplyByDoubling(arg, multiplier.toUInt()) - else multiplyByDoubling(-arg, (-multiplier).toUInt()) - -// FIXME: Move receiver to context receiver -/** - * Adds product of [arg] and [multiplier] to [base]. - * - * @param base the augend. - * @param arg the multiplicand. - * @param multiplier the integer multiplier. - * @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier]. - * @author Gleb Minaev - */ -internal fun GroupOps.addMultipliedByDoubling(base: C, arg: C, multiplier: Int): C = - if (multiplier >= 0) addMultipliedByDoubling(base, arg, multiplier.toUInt()) - else addMultipliedByDoubling(base, -arg, (-multiplier).toUInt()) - -// FIXME: Move receiver to context receiver -/** - * Returns product of [arg] and integer [multiplier]. - * - * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) - * - * @param arg the multiplicand. - * @param multiplier the integer multiplier. - * @return product of the multiplicand [arg] and the multiplier [multiplier]. - * @author Gleb Minaev - */ -internal tailrec fun Group.multiplyByDoubling(arg: C, multiplier: UInt): C = - when { - multiplier == 0u -> zero - multiplier == 1u -> arg - multiplier and 1u == 0u -> multiplyByDoubling(arg + arg, multiplier shr 1) - multiplier and 1u == 1u -> addMultipliedByDoubling(arg, arg + arg, multiplier shr 1) - else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1") - } - -// FIXME: Move receiver to context receiver -/** - * Adds product of [arg] and [multiplier] to [base]. - * - * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) - * - * @param base the augend. - * @param arg the multiplicand. - * @param multiplier the integer multiplier. - * @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier]. - * @author Gleb Minaev - */ -internal tailrec fun GroupOps.addMultipliedByDoubling(base: C, arg: C, multiplier: UInt): C = - when { - multiplier == 0u -> base - multiplier == 1u -> base + arg - multiplier and 1u == 0u -> addMultipliedByDoubling(base, arg + arg, multiplier shr 1) - multiplier and 1u == 1u -> addMultipliedByDoubling(base + arg, arg + arg, multiplier shr 1) - else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1") - } - -// FIXME: Move receiver to context receiver -/** - * Raises [arg] to the integer power [exponent]. - * - * @param arg the base of the power. - * @param exponent the exponent of the power. - * @return [arg] raised to the power [exponent]. - * @author Gleb Minaev - */ -internal fun Field.exponentiateBySquaring(arg: C, exponent: Int): C = - if (exponent >= 0) exponentiateBySquaring(arg, exponent.toUInt()) - else exponentiateBySquaring(one / arg, (-exponent).toUInt()) - -// FIXME: Move receiver to context receiver -/** - * Multiplies [base] and [arg] raised to the integer power [exponent]. - * - * @param base the multiplicand. - * @param arg the base of the power. - * @param exponent the exponent of the power. - * @return product of [base] and [arg] raised to the power [exponent]. - * @author Gleb Minaev - */ -internal fun Field.multiplyExponentiatedBySquaring(base: C, arg: C, exponent: Int): C = - if (exponent >= 0) multiplyExponentiatedBySquaring(base, arg, exponent.toUInt()) - else multiplyExponentiatedBySquaring(base, one / arg, (-exponent).toUInt()) - -// FIXME: Move receiver to context receiver -/** - * Raises [arg] to the integer power [exponent]. - * - * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) - * - * @param arg the base of the power. - * @param exponent the exponent of the power. - * @return [arg] raised to the power [exponent]. - * @author Gleb Minaev - */ -internal tailrec fun Ring.exponentiateBySquaring(arg: C, exponent: UInt): C = - when { - exponent == 0u -> zero - exponent == 1u -> arg - exponent and 1u == 0u -> exponentiateBySquaring(arg * arg, exponent shr 1) - exponent and 1u == 1u -> multiplyExponentiatedBySquaring(arg, arg * arg, exponent shr 1) - else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1") - } - -// FIXME: Move receiver to context receiver -/** - * Multiplies [base] and [arg] raised to the integer power [exponent]. - * - * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) - * - * @param base the multiplicand. - * @param arg the base of the power. - * @param exponent the exponent of the power. - * @return product of [base] and [arg] raised to the power [exponent]. - * @author Gleb Minaev - */ -internal tailrec fun RingOps.multiplyExponentiatedBySquaring(base: C, arg: C, exponent: UInt): C = - when { - exponent == 0u -> base - exponent == 1u -> base * arg - exponent and 1u == 0u -> multiplyExponentiatedBySquaring(base, arg * arg, exponent shr 1) - exponent and 1u == 1u -> multiplyExponentiatedBySquaring(base * arg, arg * arg, exponent shr 1) - else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1") - } \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/collectionUtils.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/collectionUtils.kt deleted file mode 100644 index e294f3533..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/collectionUtils.kt +++ /dev/null @@ -1,906 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import kotlin.contracts.InvocationKind.* -import kotlin.contracts.contract - - -/** - * Computes the given lambda [compute] on value corresponding to the provided [key] or `null` if the key is not present. - * - * @param key key which corresponding value will be used if it's present. - * @param compute lambda that is computed on the received value. - * @return result of the computation of the lambda. - */ -internal inline fun Map.computeOn(key: K, compute: (V?) -> R): R { - contract { - callsInPlace(compute, EXACTLY_ONCE) - } - return compute(get(key)) -} - -/** - * Computes the given lambda [compute] on value corresponding to the provided [key] or computes the given lambda - * [defaultResult] if the key is not present. - * - * @param key key which corresponding value will be used if it's present. - * @param compute lambda that is computed on the value corresponding to the [key]. - * @param defaultResult lambda that is computed if the [key] is not present. - * @return result of [compute] lambda if the [key] is present or result of [defaultResult] otherwise. - */ -internal inline fun Map.computeOnOrElse(key: K, defaultResult: () -> R, compute: (value: V) -> R): R { - contract { - callsInPlace(defaultResult, AT_MOST_ONCE) - callsInPlace(compute, AT_MOST_ONCE) - } - @Suppress("UNCHECKED_CAST") - return (if (key !in this) defaultResult() else compute(get(key) as V)) -} - -/** - * Computes the given lambda [compute] on value corresponding to the provided [key] or computes the given lambda - * [defaultResult] if the key is not present. - * - * @param key key which corresponding value will be used if it's present. - * @param compute lambda that is computed on the value corresponding to the [key]. - * @param defaultResult default result that is returned in case of the [key]'s absence. - * @return result of [compute] lambda if the [key] is present or [defaultResult] otherwise. - */ -internal inline fun Map.computeOnOrElse(key: K, defaultResult: R, compute: (value: V) -> R): R { - contract { - callsInPlace(compute, AT_MOST_ONCE) - } - return computeOnOrElse(key, { defaultResult }, compute) -} - -/** - * Computes the given lambda [compute] on value corresponding to the provided [key] or computes the given lambda - * [defaultResult] if the key is not present. - * - * @param key key which corresponding value will be used if it's present. - * @param compute lambda that is computed on the value corresponding to the [key]. - * @param defaultResult default result that is returned in case of the [key]'s absence. - * @return result of [compute] lambda if the [key] is present or [defaultResult] otherwise. - */ -internal inline fun Map.computeOnOrElse(key: K, defaultResult: R, compute: (key: K, value: V) -> R): R { - contract { - callsInPlace(compute, AT_MOST_ONCE) - } - return computeOnOrElse(key, { defaultResult }, { it -> compute(key, it) }) -} - -/** - * Applies the [transformation][transform] to the value corresponding to the given [key] or null instead if it's not - * present. - * - * @param key key to check. - * @param transform transformation to apply. - * @return result of the transformation - */ -internal inline fun MutableMap.applyToKey(key: K, transform: (currentValue: V?) -> V): V { - contract { - callsInPlace(transform, EXACTLY_ONCE) - } - return computeOn(key, transform).also { this[key] = it } -} - -/** - * Depending on presence of value corresponding to the given [key] either puts new value calculated by [valueOnPut] or - * changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut lazily calculated value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * current value as a parameter. - * @return result value corresponding to the [key]. - */ -internal inline fun MutableMap.putOrChange(key: K, valueOnPut: () -> V, transformOnChange: (currentValue: V) -> V): V { - contract { - callsInPlace(valueOnPut, AT_MOST_ONCE) - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return computeOnOrElse(key, valueOnPut, transformOnChange).also { this[key] = it } -} - -/** - * Depending on presence of value corresponding to the given [key] either puts new value [valueOnPut] or - * changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * current value as a parameter. - * @return result value corresponding to the [key]. - */ -internal inline fun MutableMap.putOrChange(key: K, valueOnPut: V, transformOnChange: (currentValue: V) -> V): V { - contract { - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return putOrChange(key, { valueOnPut }, transformOnChange) -} - -/** - * Depending on presence of value corresponding to the given [key] either puts new value [valueOnPut] or - * changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * current value and new value as parameters. - * @return result value corresponding to the [key]. - */ -internal inline fun MutableMap.putOrChange(key: K, valueOnPut: V, transformOnChange: (currentValue: V, newValue: V) -> V): V { - contract { - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return putOrChange(key, { valueOnPut }, { transformOnChange(it, valueOnPut) }) -} - -/** - * Depending on presence of value corresponding to the given [key] either puts new value [valueOnPut] or - * changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * the [key], current value, and new value as parameters. - * @return result value corresponding to the [key]. - */ -internal inline fun MutableMap.putOrChange(key: K, valueOnPut: V, transformOnChange: (key: K, currentValue: V, newValue: V) -> V): V { - contract { - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return putOrChange(key, { valueOnPut }, { transformOnChange(key, it, valueOnPut) }) -} - -/** - * Creates copy of [the map][this] and applies the [transformation][transform] to the value corresponding to the given - * [key] in the copy or null instead if it's not present. - * - * @param key key to check. - * @param transform transformation to apply. - * @return the copy of [the map][this]. - */ -internal inline fun Map.withAppliedToKey(key: K, transform: (currentValue: V?) -> V): Map { - contract { - callsInPlace(transform, EXACTLY_ONCE) - } - return buildMap(size) { - putAll(this) - applyToKey(key, transform) - } -} - -/** - * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new - * value calculated by [valueOnPut] or changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut lazily calculated value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * current value as a parameter. - * @return the copy of [the map][this]. - */ -internal inline fun Map.withPutOrChanged(key: K, valueOnPut: () -> V, transformOnChange: (currentValue: V) -> V): Map { - contract { - callsInPlace(valueOnPut, AT_MOST_ONCE) - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return buildMap(size + 1) { - putAll(this@withPutOrChanged) - putOrChange(key, valueOnPut, transformOnChange) - } -} - -/** - * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new - * value [valueOnPut] or changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * current value as a parameter. - * @return the copy of [the map][this]. - */ -internal inline fun Map.withPutOrChanged(key: K, valueOnPut: V, transformOnChange: (currentValue: V) -> V): Map { - contract { - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return withPutOrChanged(key, { valueOnPut }, transformOnChange) -} - -/** - * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new - * value [valueOnPut] or changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * current value and new value as parameters. - * @return the copy of [the map][this]. - */ -internal inline fun Map.withPutOrChanged(key: K, valueOnPut: V, transformOnChange: (currentValue: V, newValue: V) -> V): Map { - contract { - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return withPutOrChanged(key, { valueOnPut }, { transformOnChange(it, valueOnPut) }) -} - -/** - * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new - * value [valueOnPut] or changes the present value with [transformOnChange]. - * - * @param key key to check. - * @param valueOnPut value to put in case of absence of the [key]. - * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses - * the [key], current value, and new value as parameters. - * @return the copy of [the map][this]. - */ -internal inline fun Map.withPutOrChanged(key: K, valueOnPut: V, transformOnChange: (key: K, currentValue: V, newValue: V) -> V): Map { - contract { - callsInPlace(transformOnChange, AT_MOST_ONCE) - } - return withPutOrChanged(key, { valueOnPut }, { transformOnChange(key, it, valueOnPut) }) -} - -/** - * Copies entries of [this map][this] to the [destination] map overriding present ones if needed. - * - * @receiver map to be copied. - * @param destination map to receive copies. - * @return the [destination]. - */ -internal fun > Map.copyTo(destination: D): D { - for ((key, value) in this) { - destination[key] = value - } - return destination -} - -/** - * Copies entries of [this map][this] to the [destination] map merging present entries with new ones using [resolve] - * lambda. - * - * @receiver map to be copied. - * @param destination map to receive copies. - * @param resolve lambda function that resolves overriding. It takes a key, current value corresponding to the key, and - * a new one and returns value to associate to the key. - * @return the [destination]. - */ -internal inline fun > Map.copyToBy(destination: D, resolve: (key: K, currentValue: W, newValue: V) -> W): D { - for ((key, value) in this) { - destination.putOrChange(key, value) { it -> resolve(key, it, value) } - } - return destination -} - -/** - * Copies entries of [this map][this] to the [destination] map merging present entries with new ones using [resolve] - * lambda. - * - * @receiver map to be copied. - * @param destination map to receive copies. - * @param resolve lambda function that resolves overriding. It takes current value corresponding to some key, and - * a new one and returns value to associate to the key. - * @return the [destination]. - */ -internal inline fun > Map.copyToBy(destination: D, resolve: (currentValue: W, newValue: V) -> W): D = - copyToBy(destination) { _, currentValue, newValue -> resolve(currentValue, newValue) } - -/** - * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting - * entries to the [destination] map overriding present ones if needed. Is equivalent to - * ```kotlin - * this.mapValues(transform).copyTo(destination) - * ``` - * - * @receiver map to be transformed and copied. - * @param destination map to receive copies. - * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is - * the same as initial entry. - * @return the [destination]. - */ -internal inline fun > Map.copyMapTo(destination: D, transform: (Map.Entry) -> W): D { - for (entry in this) { - destination[entry.key] = transform(entry) - } - return destination -} - -/** - * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting - * entries to the [destination] map overriding present ones if needed. Is equivalent to - * ```kotlin - * this.mapValues(transform).copyTo(destination) - * ``` - * - * @receiver map to be transformed and copied. - * @param destination map to receive copies. - * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is - * the same as initial entry. - * @return the [destination]. - */ -internal inline fun > Map.copyMapTo(destination: D, transform: (key: K, value: V) -> W): D = - copyMapTo(destination) { (key, value) -> transform(key, value) } - -/** - * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting - * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to - * ```kotlin - * this.mapValues(transform).copyToBy(destination, resolve) - * ``` - * - * @receiver map to be transformed and copied. - * @param destination map to receive copies. - * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is - * the same as initial entry. - * @param resolve lambda function that resolves overriding. It takes a key, current value corresponding to the key, and - * a new one and returns value to associate to the key. - * @return the [destination]. - */ -internal inline fun > Map.copyMapToBy(destination: D, transform: (Map.Entry) -> W, resolve: (key: K, currentValue: W, newValue: V) -> W): D { - for (entry in this) { - val (key, value) = entry - destination.putOrChange(key, transform(entry)) { it -> resolve(key, it, value) } - } - return destination -} - -/** - * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting - * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to - * ```kotlin - * this.mapValues(transform).copyToBy(destination, resolve) - * ``` - * - * @receiver map to be transformed and copied. - * @param destination map to receive copies. - * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is - * the same as initial entry. - * @param resolve lambda function that resolves overriding. It takes a key, current value corresponding to the key, and - * a new one and returns value to associate to the key. - * @return the [destination]. - */ -internal inline fun > Map.copyMapToBy(destination: D, transform: (key: K, value: V) -> W, resolve: (key: K, currentValue: W, newValue: V) -> W): D = - copyMapToBy(destination, { (key, value) -> transform(key, value) }, resolve) - -/** - * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting - * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to - * ```kotlin - * this.mapValues(transform).copyToBy(destination, resolve) - * ``` - * - * @receiver map to be transformed and copied. - * @param destination map to receive copies. - * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is - * the same as initial entry. - * @param resolve lambda function that resolves overriding. It takes current value corresponding to some key, and - * a new one and returns value to associate to the key. - * @return the [destination]. - */ -internal inline fun > Map.copyMapToBy(destination: D, transform: (Map.Entry) -> W, resolve: (currentValue: W, newValue: V) -> W): D = - copyMapToBy(destination, transform, { _, currentValue, newValue -> resolve(currentValue, newValue) }) - -/** - * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting - * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to - * ```kotlin - * this.mapValues(transform).copyToBy(destination, resolve) - * ``` - * - * @receiver map to be transformed and copied. - * @param destination map to receive copies. - * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is - * the same as initial entry. - * @param resolve lambda function that resolves overriding. It takes current value corresponding to some key, and - * a new one and returns value to associate to the key. - * @return the [destination]. - */ -internal inline fun > Map.copyMapToBy(destination: D, transform: (key: K, value: V) -> W, resolve: (currentValue: W, newValue: V) -> W): D = - copyMapToBy(destination, { (key, value) -> transform(key, value) }, { _, currentValue, newValue -> resolve(currentValue, newValue) }) - -/** - * Merges [the first map][map1] and [the second map][map2] prioritising the second one, puts result to the [destination] - * and returns the [destination]. - * - * Precisely, corresponding keys and values of the received maps are put into the destination overriding existing values - * in the [destination] if needed. For every key appearing in both maps corresponding value from the second map is - * chosen. - * - * @param map1 the first (less prioritised) map to merge. - * @param map2 the second (more prioritised) map to merge. - * @param destination the map where result of the merge is put. - * @return the destination. - */ -internal fun > mergeTo(map1: Map, map2: Map, destination: D): D { - for ((key, value) in map1) { - destination.put(key, value) - } - for ((key, value) in map2) { - destination.put(key, value) - } - return destination -} - -/** - * Merges [the first map][map1] and [the second map][map2] resolving conflicts with [resolve] lambda, puts result to the - * [destination] and returns the [destination]. - * - * Precisely, corresponding keys and values of the received maps are put into the destination overriding existing values - * in the [destination] if needed. For every key appearing in both maps corresponding value is a result of the [resolve] - * lambda calculated on the key and its corresponding values from the merged maps. - * - * @param map1 the first (less prioritised) map to merge. - * @param map2 the second (more prioritised) map to merge. - * @param resolve lambda function that resolves merge conflicts. - * @param destination the map where result of the merge is put. - * @return the destination. - */ -internal inline fun > mergeToBy(map1: Map, map2: Map, destination: D, resolve: (key: K, value1: V1, value2: V2) -> W): D { - for (key in map2.keys) { - destination.remove(key) - } - for ((key, value) in map1) { - destination.put(key, value) - } - for ((key, value) in map2) { - @Suppress("UNCHECKED_CAST") - destination.putOrChange(key, value) { it -> resolve(key, it as V1, value) } - } - return destination -} - -/** - * Merges [the first map][map1] and [the second map][map2] resolving conflicts with [resolve] lambda, puts result to the - * [destination] and returns the [destination]. - * - * Precisely, corresponding keys and values of the received maps are put into the destination overriding existing values - * in the [destination] if needed. For every key appearing in both maps corresponding value is a result of the [resolve] - * lambda calculated on the key's corresponding values from the merged maps. - * - * @param map1 the first (less prioritised) map to merge. - * @param map2 the second (more prioritised) map to merge. - * @param resolve lambda function that resolves merge conflicts. - * @param destination the map where result of the merge is put. - * @return the destination. - */ -internal inline fun > mergeToBy(map1: Map, map2: Map, destination: D, resolve: (value1: V1, value2: V2) -> W): D = - mergeToBy(map1, map2, destination) { _, value1, value2 -> resolve(value1, value2) } - -/** - * Merges [the first map][map1] and [the second map][map2] prioritising the second one. - * - * Precisely, corresponding keys and values of the received maps are put into a new empty map which is returned after - * afterwards. For every key appearing in both maps corresponding value from the second map is chosen. - * - * @param map1 the first (less prioritised) map to merge. - * @param map2 the second (more prioritised) map to merge. - * @return the result of the merge. - */ -internal fun merge(map1: Map, map2: Map): Map { - val result = LinkedHashMap(map1.size + map2.size) - return mergeTo(map1, map2, result) -} - -/** - * Merges [the first map][map1] and [the second map][map2] resolving conflicts with [resolve] lambda. - * - * Precisely, corresponding keys and values of the received maps are put into a new empty map which is returned after - * afterwards. For every key appearing in both maps corresponding value is a result of the [resolve] lambda calculated - * on the key and its corresponding values from the merged maps. - * - * @param map1 the first (less prioritised) map to merge. - * @param map2 the second (more prioritised) map to merge. - * @param resolve lambda function that resolves merge conflicts. - * @return the result of the merge. - */ -internal inline fun mergeBy(map1: Map, map2: Map, resolve: (key: K, value1: V1, value2: V2) -> W): Map { - val result = LinkedHashMap(map1.size + map2.size) - return mergeToBy(map1, map2, result, resolve) -} - -/** - * Merges [the first map][map1] and [the second map][map2] resolving conflicts with [resolve] lambda. - * - * Precisely, corresponding keys and values of the received maps are put into a new empty map which is returned after - * afterwards. For every key appearing in both maps corresponding value is a result of the [resolve] lambda calculated - * on the key's corresponding values from the merged maps. - * - * @param map1 the first (less prioritised) map to merge. - * @param map2 the second (more prioritised) map to merge. - * @param resolve lambda function that resolves merge conflicts. - * @return the result of the merge. - */ -internal inline fun mergeBy(map1: Map, map2: Map, resolve: (value1: V1, value2: V2) -> W): Map = - mergeBy(map1, map2) { _, value1, value2 -> resolve(value1, value2) } - -/** - * Populates the [destination] map with key-value pairs provided by [transform] function applied to each element of the - * given collection resolving conflicts with [resolve] function and returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each element to key-value. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Iterable.associateTo(destination: D, transform: (T) -> Pair, resolve: (key: K, currentValue: V, newValue: V) -> V): D { - for (element in this) { - val (key, value) = transform(element) - destination.putOrChange(key, value, resolve) - } - return destination -} - -/** - * Populates the [destination] map with key-value pairs, where key is provided by [keySelector] function and value is - * provided by [valueTransform] applied to each element of the given collection, resolving conflicts with [resolve] - * function and returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param valueTransform lambda functions that generates value for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Iterable.associateByTo(destination: D, keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (key: K, currentValue: V, newValue: V) -> V): D { - for (element in this) { - val key = keySelector(element) - val value = valueTransform(element) - destination.putOrChange(key, value, resolve) - } - return destination -} - -/** - * Populates the [destination] map with key-value pairs, where key is provided by [keySelector] function applied to each - * element of the given collection and value is the element itself, resolving conflicts with [resolve] function and - * returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Iterable.associateByTo(destination: D, keySelector: (T) -> K, resolve: (key: K, currentValue: T, newValue: T) -> T): D { - for (element in this) { - val key = keySelector(element) - destination.putOrChange(key, element, resolve) - } - return destination -} - -/** - * Populates the [destination] map with key-value pairs provided by [transform] function applied to each element of the - * given collection resolving conflicts with [resolve] function and returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each element to key-value pair. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Iterable.associateTo(destination: D, transform: (T) -> Pair, resolve: (currentValue: V, newValue: V) -> V): D = - associateTo(destination, transform) { _, currentValue, newValue -> resolve(currentValue, newValue) } - -/** - * Populates the [destination] map with key-value pairs, where key is provided by [keySelector] function and value is - * provided by [valueTransform] applied to each element of the given collection, resolving conflicts with [resolve] - * function and returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param valueTransform lambda functions that generates value for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Iterable.associateByTo(destination: D, keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (currentValue: V, newValue: V) -> V): D = - associateByTo(destination, keySelector, valueTransform) { _, currentValue, newValue -> resolve(currentValue, newValue) } - -/** - * Populates the [destination] map with key-value pairs, where key is provided by [keySelector] function applied to each - * element of the given collection and value is the element itself, resolving conflicts with [resolve] function and - * returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Iterable.associateByTo(destination: D, keySelector: (T) -> K, resolve: (currentValue: T, newValue: T) -> T): D = - associateByTo(destination, keySelector) { _, currentValue, newValue -> resolve(currentValue, newValue) } - -/** - * Returns a map containing key-value pairs provided by [transform] function applied to elements of the given collection. - * - * All pairs are added in order of iteration. If some key is already added to the map, adding new key-value pair with the - * key is resolved with [resolve] function which takes the key, current value corresponding to the key, and new value - * from the pair. - * - * @param transform function which transforms each element to key-value pair. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Iterable.associate(transform: (T) -> Pair, resolve: (key: K, currentValue: V, newValue: V) -> V): Map = - associateTo(LinkedHashMap(), transform, resolve) - -/** - * Returns a map containing the values provided by [valueTransform] and indexed by [keySelector] functions applied to - * elements of the given collection. - * - * All pairs are added in order of iteration. If some key is already added to the map, adding new key-value pair with - * the key is resolved with [resolve] function which takes the key, current value corresponding to the key, and new - * value from the pair. - * - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param valueTransform lambda functions that generates value for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Iterable.associateBy(keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (key: K, currentValue: V, newValue: V) -> V): Map = - associateByTo(LinkedHashMap(), keySelector, valueTransform, resolve) - -/** - * Returns a map containing the elements from the given collection indexed by the key returned from [keySelector] - * function applied to each element. - * - * All pairs are added in order of iteration. If some key is already added to the map, adding new key-value pair with - * the key is resolved with [resolve] function which takes the key, current value corresponding to the key, and new - * value from the pair. - * - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Iterable.associateBy(keySelector: (T) -> K, resolve: (key: K, currentValue: T, newValue: T) -> T): Map = - associateByTo(LinkedHashMap(), keySelector, resolve) - -/** - * Returns a map containing key-value pairs provided by [transform] function applied to elements of the given collection. - * - * All pairs are added in order of iteration. If some key is already added to the map, adding new key-value pair with - * the key is resolved with [resolve] function which takes current value corresponding to the key and new value from the - * pair. - * - * @param transform function which transforms each element to key-value pair. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Iterable.associate(transform: (T) -> Pair, resolve: (currentValue: V, newValue: V) -> V): Map = - associateTo(LinkedHashMap(), transform, resolve) - -/** - * Returns a map containing the values provided by [valueTransform] and indexed by [keySelector] functions applied to - * elements of the given collection. - * - * All pairs are added in order of iteration. If some key is already added to the map, adding new key-value pair with - * the key is resolved with [resolve] function which takes current value corresponding to the key and new value from the - * pair. - * - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param valueTransform lambda functions that generates value for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Iterable.associateBy(keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (currentValue: V, newValue: V) -> V): Map = - associateByTo(LinkedHashMap(), keySelector, valueTransform, resolve) - -/** - * Returns a map containing the elements from the given collection indexed by the key returned from [keySelector] - * function applied to each element. - * - * All pairs are added in order of iteration. If some key is already added to the map, adding new key-value pair with - * the key is resolved with [resolve] function which takes current value corresponding to the key and new value from the - * pair. - * - * @param keySelector lambda functions that generates keys for the key-value pairs. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Iterable.associateBy(keySelector: (T) -> K, resolve: (currentValue: T, newValue: T) -> T): Map = - associateByTo(LinkedHashMap(), keySelector, resolve) - -/** - * Populates the given [destination] map with entries having the keys of this map and the values obtained - * by applying the [transform] function to each entry in this map resolving conflicts with [resolve] function and - * returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new value. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Map.mapValuesTo(destination: D, transform: (Map.Entry) -> W, resolve: (key: K, currentValue: W, newValue: W) -> W): D = - entries.associateByTo(destination, { it.key }, transform, resolve) - -/** - * Populates the given [destination] map with entries having the keys of this map and the values obtained - * by applying the [transform] function to each entry in this map resolving conflicts with [resolve] function and - * returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new value. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Map.mapValuesTo(destination: D, transform: (key: K, value: V) -> W, resolve: (key: K, currentValue: W, newValue: W) -> W): D = - entries.associateByTo(destination, { it.key }, { (key, value) -> transform(key, value) }, resolve) - -/** - * Populates the given [destination] map with entries having the keys of this map and the values obtained - * by applying the [transform] function to each entry in this map resolving conflicts with [resolve] function and - * returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new value. - * @param resolve lambda function that resolves merge conflicts which current and new values corresponding to some key. - * @return the [destination]. - */ -internal inline fun > Map.mapValuesTo(destination: D, transform: (Map.Entry) -> W, resolve: (currentValue: W, newValue: W) -> W): D = - entries.associateByTo(destination, { it.key }, transform, resolve) - -/** - * Populates the given [destination] map with entries having the keys of this map and the values obtained - * by applying the [transform] function to each entry in this map resolving conflicts with [resolve] function and - * returns the [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new value. - * @param resolve lambda function that resolves merge conflicts which current and new values corresponding to some key. - * @return the [destination]. - */ -internal inline fun > Map.mapValuesTo(destination: D, transform: (key: K, value: V) -> W, resolve: (currentValue: W, newValue: W) -> W): D = - entries.associateByTo(destination, { it.key }, { (key, value) -> transform(key, value) }, resolve) - -/** - * Populates the given [destination] map with entries having the keys obtained by applying the [transform] function to - * each entry in this map and the values of this map, resolving conflicts with [resolve] function and returns the - * [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Map.mapKeysTo(destination: D, transform: (Map.Entry) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): D = - entries.associateByTo(destination, transform, { it.value }, resolve) - -/** - * Populates the given [destination] map with entries having the keys obtained by applying the [transform] function to - * each entry in this map and the values of this map, resolving conflicts with [resolve] function and returns the - * [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the [destination]. - */ -internal inline fun > Map.mapKeysTo(destination: D, transform: (key: K, value: V) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): D = - entries.associateByTo(destination, { (key, value) -> transform(key, value) }, { it.value }, resolve) - -/** - * Populates the given [destination] map with entries having the keys obtained by applying the [transform] function to - * each entry in this map and the values of this map, resolving conflicts with [resolve] function and returns the - * [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which current and new values corresponding to some key. - * @return the [destination]. - */ -internal inline fun > Map.mapKeysTo(destination: D, transform: (Map.Entry) -> L, resolve: (currentValue: V, newValue: V) -> V): D = - entries.associateByTo(destination, transform, { it.value }, resolve) - -/** - * Populates the given [destination] map with entries having the keys obtained by applying the [transform] function to - * each entry in this map and the values of this map, resolving conflicts with [resolve] function and returns the - * [destination]. - * - * All pairs are added and resolved in order of iteration. - * - * @param destination the destination of the generated key-value pairs. - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which current and new values corresponding to some key. - * @return the [destination]. - */ -internal inline fun > Map.mapKeysTo(destination: D, transform: (key: K, value: V) -> L, resolve: (currentValue: V, newValue: V) -> V): D = - entries.associateByTo(destination, { (key, value) -> transform(key, value) }, { it.value }, resolve) - -/** - * Returns a new map with entries having the keys obtained by applying the [transform] function to each entry in this - * map and the values of this map and resolving conflicts with [resolve] function. - * - * All pairs are added and resolved in order of iteration. - * - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Map.mapKeys(transform: (Map.Entry) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): Map = - mapKeysTo(LinkedHashMap(size), transform, resolve) - -/** - * Returns a new map with entries having the keys obtained by applying the [transform] function to each entry in this - * map and the values of this map and resolving conflicts with [resolve] function. - * - * All pairs are added and resolved in order of iteration. - * - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which receives some key, its current, and new - * corresponding values. - * @return the result map. - */ -internal inline fun Map.mapKeys(transform: (key: K, value: V) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): Map = - mapKeysTo(LinkedHashMap(size), transform, resolve) - -/** - * Returns a new map with entries having the keys obtained by applying the [transform] function to each entry in this - * map and the values of this map and resolving conflicts with [resolve] function. - * - * All pairs are added and resolved in order of iteration. - * - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which current and new values corresponding to some key. - * @return the result map. - */ -internal inline fun Map.mapKeys(transform: (Map.Entry) -> L, resolve: (currentValue: V, newValue: V) -> V): Map = - mapKeysTo(LinkedHashMap(size), transform, resolve) - -/** - * Returns a new map with entries having the keys obtained by applying the [transform] function to each entry in this - * map and the values of this map and resolving conflicts with [resolve] function. - * - * All pairs are added and resolved in order of iteration. - * - * @param transform function which transforms each key-value pair to new key. - * @param resolve lambda function that resolves merge conflicts which current and new values corresponding to some key. - * @return the result map. - */ -internal inline fun Map.mapKeys(transform: (key: K, value: V) -> L, resolve: (currentValue: V, newValue: V) -> V): Map = - mapKeysTo(LinkedHashMap(size), transform, resolve) \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/labeledConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/labeledConstructors.kt deleted file mode 100644 index 78bb3b290..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/labeledConstructors.kt +++ /dev/null @@ -1,779 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("FunctionName", "NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.operations.invoke - - -/** - * Returns the same degrees' description of the monomial, but without zero degrees. - */ -internal fun Map.cleanUp() = filterValues { it > 0U } - -/** - * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. The map is used as is. - */ -@PublishedApi -internal inline fun LabeledPolynomialAsIs(coefs: Map, C>) : LabeledPolynomial = LabeledPolynomial(coefs) - -/** - * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * The collections will be transformed to map with [toMap] and then will be used as is. - */ -@PublishedApi -internal inline fun LabeledPolynomialAsIs(pairs: Collection, C>>) : LabeledPolynomial = LabeledPolynomial(pairs.toMap()) - -/** - * Constructs [LabeledPolynomial] with provided array of [pairs] of pairs "term's signature — term's coefficient". - * The array will be transformed to map with [toMap] and then will be used as is. - */ -@PublishedApi -internal inline fun LabeledPolynomialAsIs(vararg pairs: Pair, C>) : LabeledPolynomial = LabeledPolynomial(pairs.toMap()) - -/** - * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. The map is used as is. - * - * **Be sure you read description of [LabeledPolynomial.coefficients]. Otherwise, you may make a mistake that will - * cause wrong computation result or even runtime error.** - */ -@DelicatePolynomialAPI -public inline fun LabeledPolynomialWithoutCheck(coefs: Map, C>) : LabeledPolynomial = LabeledPolynomial(coefs) - -/** - * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * The collections will be transformed to map with [toMap] and then will be used as is. - * - * **Be sure you read description of [LabeledPolynomial.coefficients]. Otherwise, you may make a mistake that will - * cause wrong computation result or even runtime error.** - */ -@DelicatePolynomialAPI -public inline fun LabeledPolynomialWithoutCheck(pairs: Collection, C>>) : LabeledPolynomial = LabeledPolynomial(pairs.toMap()) - -/** - * Constructs [LabeledPolynomial] with provided array of [pairs] of pairs "term's signature — term's coefficient". - * The array will be transformed to map with [toMap] and then will be used as is. - * - * **Be sure you read description of [LabeledPolynomial.coefficients]. Otherwise, you may make a mistake that will - * cause wrong computation result or even runtime error.** - */ -@DelicatePolynomialAPI -public inline fun LabeledPolynomialWithoutCheck(vararg pairs: Pair, C>) : LabeledPolynomial = LabeledPolynomial(pairs.toMap()) - -/** - * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public fun LabeledPolynomial(coefs: Map, C>, add: (C, C) -> C) : LabeledPolynomial = - LabeledPolynomialAsIs( - coefs.mapKeys({ key, _ -> key.cleanUp() }, add) - ) - -/** - * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public fun LabeledPolynomial(pairs: Collection, C>>, add: (C, C) -> C) : LabeledPolynomial = - LabeledPolynomialAsIs( - pairs.associateBy({ it.first.cleanUp() }, { it.second }, add) - ) - -/** - * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public fun LabeledPolynomial(vararg pairs: Pair, C>, add: (C, C) -> C) : LabeledPolynomial = - LabeledPolynomialAsIs( - pairs.asIterable().associateBy({ it.first.cleanUp() }, { it.second }, add) - ) - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -/** - * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > A.LabeledPolynomial(coefs: Map, C>) : LabeledPolynomial = LabeledPolynomial(coefs, ::add) -/** - * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > LabeledPolynomialSpace.LabeledPolynomial(coefs: Map, C>) : LabeledPolynomial = LabeledPolynomial(coefs) { left: C, right: C -> left + right } - -/** - * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > LabeledRationalFunctionSpace.LabeledPolynomial(coefs: Map, C>) : LabeledPolynomial = LabeledPolynomial(coefs) { left: C, right: C -> left + right } - -/** - * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > A.LabeledPolynomial(pairs: Collection, C>>) : LabeledPolynomial = LabeledPolynomial(pairs, ::add) - -/** - * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > LabeledPolynomialSpace.LabeledPolynomial(pairs: Collection, C>>) : LabeledPolynomial = LabeledPolynomial(pairs) { left: C, right: C -> left + right } -/** - * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > LabeledRationalFunctionSpace.LabeledPolynomial(pairs: Collection, C>>) : LabeledPolynomial = LabeledPolynomial(pairs) { left: C, right: C -> left + right } - -/** - * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > A.LabeledPolynomial(vararg pairs: Pair, C>) : LabeledPolynomial = LabeledPolynomial(*pairs) { left: C, right: C -> left + right } -/** - * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > LabeledPolynomialSpace.LabeledPolynomial(vararg pairs: Pair, C>) : LabeledPolynomial = LabeledPolynomial(*pairs) { left: C, right: C -> left + right } -/** - * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see LabeledPolynomialWithoutCheck - */ -public inline fun > LabeledRationalFunctionSpace.LabeledPolynomial(vararg pairs: Pair, C>) : LabeledPolynomial = LabeledPolynomial(*pairs) { left: C, right: C -> left + right } - -/** - * Converts [this] constant to [LabeledPolynomial]. - */ -public inline fun C.asLabeledPolynomial() : LabeledPolynomial = LabeledPolynomialAsIs(mapOf(emptyMap() to this)) - -///** -//// * Converts [this] variable to [LabeledPolynomial]. -//// */ -//context(A) -//public inline fun > Symbol.asLabeledPolynomial() : LabeledPolynomial = LabeledPolynomial(mapOf(mapOf(this to 1u) to one)) -///** -// * Converts [this] variable to [LabeledPolynomial]. -// */ -//context(LabeledPolynomialSpace) -//public inline fun > Symbol.asLabeledPolynomial() : LabeledPolynomial = LabeledPolynomial(mapOf(mapOf(this to 1u) to constantOne)) -///** -// * Converts [this] variable to [LabeledPolynomial]. -// */ -//context(LabeledRationalFunctionSpace) -//public inline fun > Symbol.asLabeledPolynomial() : LabeledPolynomial = LabeledPolynomial(mapOf(mapOf(this to 1u) to constantOne)) - -/** - * Marks DSL that allows to more simply create [LabeledPolynomial]s with good performance. - * - * For example, polynomial \(5 a^2 c^3 - 6 b\) can be described as - * ``` - * Int.algebra { - * val labeledPolynomial : LabeledPolynomial = LabeledPolynomialDSL1 { - * 5 { a inPowerOf 2u; c inPowerOf 3u } // 5 a^2 c^3 + - * (-6) { b inPowerOf 1u } // (-6) b^1 - * } - * } - * ``` - * @usesMathJax - */ -@DslMarker -@UnstableKMathAPI -internal annotation class LabeledPolynomialConstructorDSL1 - -/** - * Builder of [LabeledPolynomial] signature. It should be used as an implicit context for lambdas that describe term signature. - */ -@UnstableKMathAPI -@LabeledPolynomialConstructorDSL1 -public class DSL1LabeledPolynomialTermSignatureBuilder { - /** - * Signature storage. Any declaration of any variable's power updates the storage by increasing corresponding value. - * Afterward the storage will be used as a resulting signature. - */ - private val signature: MutableMap = LinkedHashMap() - - /** - * Builds the resulting signature. - * - * In fact, it just returns [signature] as regular signature of type `List`. - */ - @PublishedApi - internal fun build(): Map = signature - - /** - * Declares power of [this] variable of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public infix fun Symbol.inPowerOf(deg: UInt) { - if (deg == 0u) return - signature.putOrChange(this, deg) { it -> it + deg } - } - /** - * Declares power of [this] variable of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public inline infix fun Symbol.pow(deg: UInt): Unit = this inPowerOf deg - /** - * Declares power of [this] variable of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public inline infix fun Symbol.`in`(deg: UInt): Unit = this inPowerOf deg - /** - * Declares power of [this] variable of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public inline infix fun Symbol.of(deg: UInt): Unit = this inPowerOf deg -} - -/** - * Builder of [LabeledPolynomial]. It should be used as an implicit context for lambdas that describe [LabeledPolynomial]. - */ -@UnstableKMathAPI -@LabeledPolynomialConstructorDSL1 -public class DSL1LabeledPolynomialBuilder( - /** - * Summation operation that will be used to sum coefficients of monomials of same signatures. - */ - private val add: (C, C) -> C, - /** - * Initial capacity of coefficients map. - */ - initialCapacity: Int? = null -) { - /** - * Coefficients storage. Any declaration of any monomial updates the storage. - * Afterward the storage will be used as a resulting coefficients map. - */ - private val coefficients: MutableMap, C> = if (initialCapacity != null) LinkedHashMap(initialCapacity) else LinkedHashMap() - - /** - * Builds the resulting coefficients map. - * - * In fact, it just returns [coefficients] as regular coefficients map of type `Map, C>`. - */ - @PublishedApi - internal fun build(): LabeledPolynomial = LabeledPolynomial(coefficients) - - /** - * Declares monomial with [this] coefficient and provided [signature]. - * - * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such - * coefficients is zero at any moment the monomial won't be removed but will be left as it is. - */ - public infix fun C.with(signature: Map) { - coefficients.putOrChange(signature, this@with, add) - } - /** - * Declares monomial with [this] coefficient and signature constructed by [block]. - * - * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such - * coefficients is zero at any moment the monomial won't be removed but will be left as it is. - */ - public inline infix fun C.with(noinline block: DSL1LabeledPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block) - /** - * Declares monomial with [this] coefficient and signature constructed by [block]. - * - * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such - * coefficients is zero at any moment the monomial won't be removed but will be left as it is. - */ - public inline operator fun C.invoke(block: DSL1LabeledPolynomialTermSignatureBuilder.() -> Unit): Unit = - this with DSL1LabeledPolynomialTermSignatureBuilder().apply(block).build() -} - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -///** -// * Creates [LabeledPolynomial] with lambda [block] in context of [this] ring of constants. -// * -// * For example, polynomial \(5 a^2 c^3 - 6 b\) can be described as -// * ``` -// * Int.algebra { -// * val labeledPolynomial : LabeledPolynomial = LabeledPolynomialDSL1 { -// * 5 { a inPowerOf 2u; c inPowerOf 3u } // 5 a^2 c^3 + -// * (-6) { b inPowerOf 1u } // (-6) b^1 -// * } -// * } -// * ``` -// * @usesMathJax -// */ -// FIXME: For now this fabric does not let next two fabrics work. (See KT-52803.) Possible feature solutions: -// 1. `LowPriorityInOverloadResolution` becomes public. Then it should be applied to this function. -// 2. Union types are implemented. Then all three functions should be rewritten -// as one with single union type as a (context) receiver. -//@UnstableKMathAPI -//public inline fun > A.LabeledPolynomialDSL1(initialCapacity: Int? = null, block: LabeledPolynomialBuilder.() -> Unit) : LabeledPolynomial = LabeledPolynomialBuilder(::add, initialCapacity).apply(block).build() -/** - * Creates [LabeledPolynomial] with lambda [block] in context of [this] ring of [LabeledPolynomial]s. - * - * For example, polynomial \(5 a^2 c^3 - 6 b\) can be described as - * ``` - * Int.algebra { - * val labeledPolynomial : LabeledPolynomial = LabeledPolynomialDSL1 { - * 5 { a inPowerOf 2u; c inPowerOf 3u } // 5 a^2 c^3 + - * (-6) { b inPowerOf 1u } // (-6) b^1 - * } - * } - * ``` - * @usesMathJax - */ -@UnstableKMathAPI -public inline fun > LabeledPolynomialSpace.LabeledPolynomialDSL1(initialCapacity: Int? = null, block: DSL1LabeledPolynomialBuilder.() -> Unit) : LabeledPolynomial = DSL1LabeledPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build() -/** - * Creates [LabeledPolynomial] with lambda [block] in context of [this] field of [LabeledRationalFunction]s. - * - * For example, polynomial \(5 a^2 c^3 - 6 b\) can be described as - * ``` - * Int.algebra { - * val labeledPolynomial : LabeledPolynomial = LabeledPolynomialDSL1 { - * 5 { a inPowerOf 2u; c inPowerOf 3u } // 5 a^2 c^3 + - * (-6) { b inPowerOf 1u } // (-6) b^1 - * } - * } - * ``` - * @usesMathJax - */ -@UnstableKMathAPI -public inline fun > LabeledRationalFunctionSpace.LabeledPolynomialDSL1(initialCapacity: Int? = null, block: DSL1LabeledPolynomialBuilder.() -> Unit) : LabeledPolynomial = DSL1LabeledPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build() - -/** - * Marks DSL that allows to more simply create [LabeledPolynomial]s with good performance. - * - * For example, polynomial \(5 a^2 c^3 - 6 b\) can be described as - * ``` - * Int.algebra { - * val numberedPolynomial : NumberedPolynomial = NumberedPolynomial { - * 5 { a inPowerOf 2u; c inPowerOf 3u } // 5 a^2 c^3 + - * (-6) { b inPowerOf 1u } // (-6) b^1 - * } - * } - * ``` - * @usesMathJax - */ -@DslMarker -@UnstableKMathAPI -internal annotation class LabeledPolynomialBuilderDSL2 - -/** - * Builder of [LabeledPolynomial]. It should be used as an implicit context for lambdas that describe [LabeledPolynomial]. - */ -@UnstableKMathAPI -@LabeledPolynomialBuilderDSL2 -public class DSL2LabeledPolynomialBuilder( - private val ring: Ring, - /** - * Initial capacity of coefficients map. - */ - initialCapacity: Int? = null -) { - /** - * Coefficients storage. Any declaration of any monomial updates the storage. - * Afterward the storage will be used as a resulting coefficients map. - */ - private val coefficients: MutableMap, C> = if (initialCapacity != null) LinkedHashMap(initialCapacity) else LinkedHashMap() - - /** - * Builds the resulting coefficients map. - * - * In fact, it just returns [coefficients] as regular coefficients map of type `Map, C>`. - */ - @PublishedApi - internal fun build(): LabeledPolynomial = LabeledPolynomial(coefficients) - - public inner class Term internal constructor( - internal val signature: Map = HashMap(), - internal val coefficient: C - ) - - private inline fun submit(signature: Map, onPut: Ring.() -> C, onChange: Ring.(C) -> C) { - coefficients.putOrChange<_, C>(signature, { ring.onPut() }, { ring.onChange(it) }) - } - - private inline fun submit(signature: Map, lazyCoefficient: Ring.() -> C) { - submit(signature, lazyCoefficient) { it + lazyCoefficient() } - } - - private fun submit(signature: Map, coefficient: C) { - submit(signature) { coefficient } - } - - // TODO: `@submit` will be resolved differently. Change it to `@C`. - private fun C.submitSelf() = submit(emptyMap()) { this@submitSelf } - - private fun Symbol.submit() = submit(mapOf(this to 1u)) { one } - - private fun Term.submit(): Submit { - submit(signature, coefficient) - return Submit - } - - public object Submit - - public operator fun C.unaryPlus(): Submit { - submitSelf() - return Submit - } - - public operator fun C.unaryMinus(): Submit { - submit(emptyMap(), { -this@unaryMinus }, { it - this@unaryMinus }) - return Submit - } - - public operator fun C.plus(other: C): Submit { - submit(emptyMap()) { this@plus + other } - return Submit - } - - public operator fun C.minus(other: C): Submit { - submit(emptyMap()) { this@minus - other } - return Submit - } - - public operator fun C.times(other: C): C = ring { this@times * other } - - public operator fun C.plus(other: Symbol): Submit { - submit(emptyMap(), this) - submit(mapOf(other to 1u), ring.one) - return Submit - } - - public operator fun C.minus(other: Symbol): Submit { - submit(emptyMap(), this) - submit(mapOf(other to 1u), { -one }, { it - one }) - return Submit - } - - public operator fun C.times(other: Symbol): Term = Term(mapOf(other to 1u), this) - - public operator fun C.plus(other: Term): Submit { - submit(emptyMap(), this) - other.submit() - return Submit - } - - public operator fun C.minus(other: Term): Submit { - submit(emptyMap(), this) - submit(other.signature, { -other.coefficient }, { it - other.coefficient }) - return Submit - } - - public operator fun C.times(other: Term): Term = Term(other.signature, ring { this@times * other.coefficient }) - - public operator fun Symbol.plus(other: C): Submit { - this.submit() - other.submitSelf() - return Submit - } - - public operator fun Symbol.minus(other: C): Submit { - this.submit() - submit(emptyMap(), { -other }, { it - other }) - return Submit - } - - public operator fun Symbol.times(other: C): Term = Term(mapOf(this to 1u), other) - - public operator fun Symbol.unaryPlus(): Submit { - this.submit() - return Submit - } - - public operator fun Symbol.unaryMinus(): Submit { - submit(mapOf(this to 1u), { -one }, { it - one }) - return Submit - } - - public operator fun Symbol.plus(other: Symbol): Submit { - this.submit() - other.submit() - return Submit - } - - public operator fun Symbol.minus(other: Symbol): Submit { - this.submit() - submit(mapOf(other to 1u), { -one }, { it - one }) - return Submit - } - - public operator fun Symbol.times(other: Symbol): Term = - if (this == other) Term(mapOf(this to 2u), ring.one) - else Term(mapOf(this to 1u, other to 1u), ring.one) - - public operator fun Symbol.plus(other: Term): Submit { - this.submit() - other.submit() - return Submit - } - - public operator fun Symbol.minus(other: Term): Submit { - this.submit() - submit(other.signature, { -other.coefficient }, { it - other.coefficient }) - return Submit - } - - public operator fun Symbol.times(other: Term): Term = - Term( - other.signature.withPutOrChanged(this, 1u) { it -> it + 1u }, - other.coefficient - ) - - public operator fun Term.plus(other: C): Submit { - this.submit() - other.submitSelf() - return Submit - } - - public operator fun Term.minus(other: C): Submit { - this.submit() - submit(emptyMap(), { -other }, { it - other }) - return Submit - } - - public operator fun Term.times(other: C): Term = - Term( - signature, - ring { coefficient * other } - ) - - public operator fun Term.plus(other: Symbol): Submit { - this.submit() - other.submit() - return Submit - } - - public operator fun Term.minus(other: Symbol): Submit { - this.submit() - submit(mapOf(other to 1u), { -one }, { it - one }) - return Submit - } - - public operator fun Term.times(other: Symbol): Term = - Term( - signature.withPutOrChanged(other, 1u) { it -> it + 1u }, - coefficient - ) - - public operator fun Term.unaryPlus(): Submit { - this.submit() - return Submit - } - - public operator fun Term.unaryMinus(): Submit { - submit(signature, { -coefficient }, { it - coefficient }) - return Submit - } - - public operator fun Term.plus(other: Term): Submit { - this.submit() - other.submit() - return Submit - } - - public operator fun Term.minus(other: Term): Submit { - this.submit() - submit(other.signature, { -other.coefficient }, { it - other.coefficient }) - return Submit - } - - public operator fun Term.times(other: Term): Term = - Term( - mergeBy(signature, other.signature) { deg1, deg2 -> deg1 + deg2 }, - ring { coefficient * other.coefficient } - ) -} - -//@UnstableKMathAPI -//public fun Ring.LabeledPolynomialDSL2(initialCapacity: Int? = null, block: DSL2LabeledPolynomialBuilder.() -> Unit): LabeledPolynomial = DSL2LabeledPolynomialBuilder(this, initialCapacity).apply(block).build() - -@UnstableKMathAPI -public fun > LabeledPolynomialSpace.LabeledPolynomialDSL2(initialCapacity: Int? = null, block: DSL2LabeledPolynomialBuilder.() -> Unit): LabeledPolynomial = DSL2LabeledPolynomialBuilder(ring, initialCapacity).apply(block).build() - -@UnstableKMathAPI -public fun > LabeledRationalFunctionSpace.LabeledPolynomialDSL2(initialCapacity: Int? = null, block: DSL2LabeledPolynomialBuilder.() -> Unit): LabeledPolynomial = DSL2LabeledPolynomialBuilder(ring, initialCapacity).apply(block).build() - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -/** - * Constructs [LabeledRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients]. - * - * The maps will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > A.LabeledRationalFunction(numeratorCoefficients: Map, C>, denominatorCoefficients: Map, C>): LabeledRationalFunction = - LabeledRationalFunction( - LabeledPolynomial(numeratorCoefficients), - LabeledPolynomial(denominatorCoefficients) - ) -/** - * Constructs [LabeledRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients]. - * - * The maps will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > LabeledRationalFunctionSpace.LabeledRationalFunction(numeratorCoefficients: Map, C>, denominatorCoefficients: Map, C>): LabeledRationalFunction = - LabeledRationalFunction( - LabeledPolynomial(numeratorCoefficients), - LabeledPolynomial(denominatorCoefficients) - ) - -/** - * Constructs [LabeledRationalFunction] with provided [numerator] and unit denominator. - */ -public fun > A.LabeledRationalFunction(numerator: LabeledPolynomial): LabeledRationalFunction = - LabeledRationalFunction(numerator, LabeledPolynomial(mapOf(emptyMap() to one))) -/** - * Constructs [LabeledRationalFunction] with provided [numerator] and unit denominator. - */ -public fun > LabeledRationalFunctionSpace.LabeledRationalFunction(numerator: LabeledPolynomial): LabeledRationalFunction = - LabeledRationalFunction(numerator, polynomialOne) - -/** - * Constructs [LabeledRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit - * denominator. - * - * [numeratorCoefficients] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > LabeledRationalFunctionSpace.LabeledRationalFunction(numeratorCoefficients: Map, C>): LabeledRationalFunction = - LabeledRationalFunction( - LabeledPolynomial(numeratorCoefficients), - polynomialOne - ) -/** - * Constructs [LabeledRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit - * denominator. - * - * [numeratorCoefficients] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > A.LabeledRationalFunction(numeratorCoefficients: Map, C>): LabeledRationalFunction = - LabeledRationalFunction( - LabeledPolynomial(numeratorCoefficients), - LabeledPolynomialAsIs(mapOf(emptyMap() to one)) - ) - -///** -// * Converts [this] constant to [LabeledRationalFunction]. -// */ -//context(A) -//public fun > C.asLabeledRationalFunction() : LabeledRationalFunction = -// LabeledRationalFunction( -// LabeledPolynomialAsIs(mapOf(emptyMap() to this)), -// LabeledPolynomialAsIs(mapOf(emptyMap() to one)) -// ) -///** -// * Converts [this] constant to [LabeledRationalFunction]. -// */ -//context(LabeledRationalFunctionSpace) -//public fun > C.asLabeledRationalFunction() : LabeledRationalFunction = -// LabeledRationalFunction( -// LabeledPolynomialAsIs(mapOf(emptyMap() to this)), -// LabeledPolynomialAsIs(mapOf(emptyMap() to constantOne)) -// ) - -///** -// * Converts [this] variable to [LabeledRationalFunction]. -// */ -//context(A) -//public fun > Symbol.asLabeledRationalFunction() : LabeledRationalFunction = -// LabeledRationalFunction( -// LabeledPolynomialAsIs(mapOf(mapOf(this to 1u) to one)), -// LabeledPolynomialAsIs(mapOf(emptyMap() to one)) -// ) -///** -// * Converts [this] variable to [LabeledRationalFunction]. -// */ -//context(LabeledRationalFunctionSpace) -//public fun > Symbol.asLabeledRationalFunction() : LabeledRationalFunction = -// LabeledRationalFunction( -// LabeledPolynomialAsIs(mapOf(mapOf(this to 1u) to constantOne)), -// LabeledPolynomialAsIs(mapOf(emptyMap() to constantOne)) -// ) \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt deleted file mode 100644 index 188240bf7..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt +++ /dev/null @@ -1,321 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.* -import kotlin.contracts.InvocationKind -import kotlin.contracts.contract -import kotlin.jvm.JvmName - - -/** - * Creates a [LabeledPolynomialSpace] over a received ring. - */ -public inline val > A.labeledPolynomialSpace: LabeledPolynomialSpace - get() = LabeledPolynomialSpace(this) - -/** - * Creates a [LabeledPolynomialSpace]'s scope over a received ring. - */ -public inline fun , R> A.labeledPolynomialSpace(block: LabeledPolynomialSpace.() -> R): R { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return LabeledPolynomialSpace(this).block() -} -/** - * Creates a [LabeledRationalFunctionSpace] over a received ring. - */ -public inline val > A.labeledRationalFunctionSpace: LabeledRationalFunctionSpace - get() = LabeledRationalFunctionSpace(this) - -/** - * Creates a [LabeledRationalFunctionSpace]'s scope over a received ring. - */ -public inline fun , R> A.labeledRationalFunctionSpace(block: LabeledRationalFunctionSpace.() -> R): R { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return LabeledRationalFunctionSpace(this).block() -} - -/** - * Substitutes provided Double arguments [args] into [this] Double polynomial. - */ -public fun LabeledPolynomial.substitute(args: Map): LabeledPolynomial = Double.algebra { - if (coefficients.isEmpty()) return this@substitute - LabeledPolynomial( - buildMap { - coefficients.forEach { (degs, c) -> - val newDegs = degs.filterKeys { it !in args } - val newC = args.entries.fold(c) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - putOrChange(newDegs, newC, ::add) - } - } - ) -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ -public fun LabeledPolynomial.substitute(ring: Ring, args: Map): LabeledPolynomial = ring { - if (coefficients.isEmpty()) return this@substitute - LabeledPolynomial( - buildMap { - coefficients.forEach { (degs, c) -> - val newDegs = degs.filterKeys { it !in args } - val newC = args.entries.fold(c) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - putOrChange(newDegs, newC, ::add) - } - } - ) -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ // TODO: To optimize boxing -@JvmName("substitutePolynomial") -public fun LabeledPolynomial.substitute(ring: Ring, args: Map>) : LabeledPolynomial = - ring.labeledPolynomialSpace { - coefficients.entries.fold(zero) { acc, (degs, c) -> - val newDegs = degs.filterKeys { it !in args } - acc + args.entries.fold(LabeledPolynomial(mapOf(newDegs to c))) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - } - } - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ // TODO: To optimize boxing -@JvmName("substituteRationalFunction") -public fun LabeledPolynomial.substitute(ring: Ring, args: Map>) : LabeledRationalFunction = - ring.labeledRationalFunctionSpace { - coefficients.entries.fold(zero) { acc, (degs, c) -> - val newDegs = degs.filterKeys { it !in args } - acc + args.entries.fold(LabeledRationalFunction(LabeledPolynomial(mapOf(newDegs to c)))) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - } - } - -/** - * Substitutes provided Double arguments [args] into [this] Double rational function. - */ -public fun LabeledRationalFunction.substitute(args: Map): LabeledRationalFunction = - LabeledRationalFunction(numerator.substitute(args), denominator.substitute(args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ -public fun LabeledRationalFunction.substitute(ring: Ring, args: Map): LabeledRationalFunction = - LabeledRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ // TODO: To optimize calculation -@JvmName("substitutePolynomial") -public fun LabeledRationalFunction.substitute(ring: Ring, args: Map>) : LabeledRationalFunction = - LabeledRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ // TODO: To optimize calculation -@JvmName("substituteRationalFunction") -public fun LabeledRationalFunction.substitute(ring: Ring, args: Map>) : LabeledRationalFunction = - ring.labeledRationalFunctionSpace { - numerator.substitute(ring, args) / denominator.substitute(ring, args) - } - -/** - * Returns algebraic derivative of received polynomial with respect to provided variable. - */ -@UnstableKMathAPI -public fun > LabeledPolynomial.derivativeWithRespectTo( - algebra: A, - variable: Symbol, -): LabeledPolynomial = algebra { - LabeledPolynomial( - buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= 1u }) { - coefficients - .forEach { (degs, c) -> - if (variable !in degs) return@forEach - put( - buildMap { - degs.forEach { (vari, deg) -> - when { - vari != variable -> put(vari, deg) - deg > 1u -> put(vari, deg - 1u) - } - } - }, - multiplyByDoubling(c, degs[variable]!!) - ) - } - } - ) -} - -/** - * Returns algebraic derivative of received polynomial with respect to provided variable of specified order. - */ -@UnstableKMathAPI -public fun > LabeledPolynomial.nthDerivativeWithRespectTo( - algebra: A, - variable: Symbol, - order: UInt -): LabeledPolynomial = algebra { - if (order == 0u) return this@nthDerivativeWithRespectTo - LabeledPolynomial( - buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= order }) { - coefficients - .forEach { (degs, c) -> - if (degs.getOrElse(variable) { 0u } < order) return@forEach - put( - buildMap { - degs.forEach { (vari, deg) -> - when { - vari != variable -> put(vari, deg) - deg > order -> put(vari, deg - order) - } - } - }, - degs[variable]!!.let { deg -> - (deg downTo deg - order + 1u) - .fold(c) { acc, ord -> multiplyByDoubling(acc, ord) } - } - ) - } - } - ) -} - -/** - * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders. - */ -@UnstableKMathAPI -public fun > LabeledPolynomial.nthDerivativeWithRespectTo( - algebra: A, - variablesAndOrders: Map, -): LabeledPolynomial = algebra { - val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u } - if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo - LabeledPolynomial( - buildMap( - coefficients.count { - variablesAndOrders.all { (variable, order) -> - it.key.getOrElse(variable) { 0u } >= order - } - } - ) { - coefficients - .forEach { (degs, c) -> - if (filteredVariablesAndOrders.any { (variable, order) -> degs.getOrElse(variable) { 0u } < order }) return@forEach - put( - buildMap { - degs.forEach { (vari, deg) -> - if (vari !in filteredVariablesAndOrders) put(vari, deg) - else { - val order = filteredVariablesAndOrders[vari]!! - if (deg > order) put(vari, deg - order) - } - } - }, - filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> - degs[index]!!.let { deg -> - (deg downTo deg - order + 1u) - .fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) } - } - } - ) - } - } - ) -} - -/** - * Returns algebraic antiderivative of received polynomial with respect to provided variable. - */ -@UnstableKMathAPI -public fun > LabeledPolynomial.antiderivativeWithRespectTo( - algebra: A, - variable: Symbol, -): LabeledPolynomial = algebra { - LabeledPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - val newDegs = degs.withPutOrChanged(variable, 1u) { it -> it + 1u } - put( - newDegs, - c / multiplyByDoubling(one, newDegs[variable]!!) - ) - } - } - ) -} - -/** - * Returns algebraic antiderivative of received polynomial with respect to provided variable of specified order. - */ -@UnstableKMathAPI -public fun > LabeledPolynomial.nthAntiderivativeWithRespectTo( - algebra: A, - variable: Symbol, - order: UInt -): LabeledPolynomial = algebra { - if (order == 0u) return this@nthAntiderivativeWithRespectTo - LabeledPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - val newDegs = degs.withPutOrChanged(variable, order) { it -> it + order } - put( - newDegs, - newDegs[variable]!!.let { deg -> - (deg downTo deg - order + 1u) - .fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) } - } - ) - } - } - ) -} - -/** - * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders. - */ -@UnstableKMathAPI -public fun > LabeledPolynomial.nthAntiderivativeWithRespectTo( - algebra: A, - variablesAndOrders: Map, -): LabeledPolynomial = algebra { - val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u } - if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo - LabeledPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - val newDegs = mergeBy(degs, filteredVariablesAndOrders) { deg, order -> deg + order } - put( - newDegs, - filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> - newDegs[index]!!.let { deg -> - (deg downTo deg - order + 1u) - .fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) } - } - } - ) - } - } - ) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/listConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/listConstructors.kt deleted file mode 100644 index 30b1e2fe4..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/listConstructors.kt +++ /dev/null @@ -1,92 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.operations.Ring - - -/** - * Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed - * if [reverse] parameter is true. - */ -@Suppress("FunctionName") -public fun ListPolynomial(coefficients: List, reverse: Boolean = false): ListPolynomial = - ListPolynomial(with(coefficients) { if (reverse) reversed() else this }) - -/** - * Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed - * if [reverse] parameter is true. - */ -@Suppress("FunctionName") -public fun ListPolynomial(vararg coefficients: C, reverse: Boolean = false): ListPolynomial = - ListPolynomial(with(coefficients) { if (reverse) reversed() else toList() }) - -/** - * Represents [this] constant as a [ListPolynomial]. - */ -public fun C.asListPolynomial() : ListPolynomial = ListPolynomial(listOf(this)) - - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -/** - * Constructs [ListRationalFunction] instance with numerator and denominator constructed with provided - * [numeratorCoefficients] and [denominatorCoefficients]. The both collections of coefficients will be reversed if - * [reverse] parameter is true. - */ -@Suppress("FunctionName") -public fun ListRationalFunction(numeratorCoefficients: List, denominatorCoefficients: List, reverse: Boolean = false): ListRationalFunction = - ListRationalFunction( - ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ), - ListPolynomial( with(denominatorCoefficients) { if (reverse) reversed() else this } ) - ) -/** - * Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator. - */ -@Suppress("FunctionName") -public fun > A.ListRationalFunction(numerator: ListPolynomial): ListRationalFunction = - ListRationalFunction(numerator, ListPolynomial(listOf(one))) -/** - * Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator. - */ -@Suppress("FunctionName") -public fun > ListRationalFunctionSpace.ListRationalFunction(numerator: ListPolynomial): ListRationalFunction = - ListRationalFunction(numerator, polynomialOne) -/** - * Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit - * denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true. - */ -@Suppress("FunctionName") -public fun > A.ListRationalFunction(numeratorCoefficients: List, reverse: Boolean = false): ListRationalFunction = - ListRationalFunction( - ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ), - ListPolynomial(listOf(one)) - ) -/** - * Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit - * denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true. - */ -@Suppress("FunctionName") -public fun > ListRationalFunctionSpace.ListRationalFunction(numeratorCoefficients: List, reverse: Boolean = false): ListRationalFunction = - ListRationalFunction( - ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ), - polynomialOne - ) - -/** - * Represents [this] constant as a rational function. - */ // FIXME: When context receivers will be ready, delete this function and uncomment the following two -public fun > C.asListRationalFunction(ring: A) : ListRationalFunction = ring.ListRationalFunction(asListPolynomial()) -///** -// * Represents [this] constant as a rational function. -// */ -//context(A) -//public fun > C.asListRationalFunction() : ListRationalFunction = ListRationalFunction(asListPolynomial()) -///** -// * Represents [this] constant as a rational function. -// */ -//context(ListRationalFunctionSpace) -//public fun > C.asListRationalFunction() : ListRationalFunction = ListRationalFunction(asListPolynomial()) \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/listUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/listUtil.kt deleted file mode 100644 index e7c11f5ea..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/listUtil.kt +++ /dev/null @@ -1,255 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.* -import kotlin.contracts.InvocationKind -import kotlin.contracts.contract -import kotlin.math.max -import kotlin.math.pow - - -/** - * Creates a [ListPolynomialSpace] over a received ring. - */ -public inline val > A.listPolynomialSpace: ListPolynomialSpace - get() = ListPolynomialSpace(this) - -/** - * Creates a [ListPolynomialSpace]'s scope over a received ring. - */ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block] -public inline fun , R> A.listPolynomialSpace(block: ListPolynomialSpace.() -> R): R { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return ListPolynomialSpace(this).block() -} - -/** - * Creates a [ScalableListPolynomialSpace] over a received scalable ring. - */ -public inline val A.scalableListPolynomialSpace: ScalableListPolynomialSpace where A : Ring, A : ScaleOperations - get() = ScalableListPolynomialSpace(this) - -/** - * Creates a [ScalableListPolynomialSpace]'s scope over a received scalable ring. - */ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block] -public inline fun A.scalableListPolynomialSpace(block: ScalableListPolynomialSpace.() -> R): R where A : Ring, A : ScaleOperations { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return ScalableListPolynomialSpace(this).block() -} - -/** - * Creates a [ListRationalFunctionSpace] over a received ring. - */ -public inline val > A.listRationalFunctionSpace: ListRationalFunctionSpace - get() = ListRationalFunctionSpace(this) - -/** - * Creates a [ListRationalFunctionSpace]'s scope over a received ring. - */ // TODO: When context will be ready move [ListRationalFunctionSpace] and add [A] to context receivers of [block] -public inline fun , R> A.listRationalFunctionSpace(block: ListRationalFunctionSpace.() -> R): R { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return ListRationalFunctionSpace(this).block() -} - - -/** - * Evaluates value of [this] Double polynomial on provided Double argument. - */ -public fun ListPolynomial.substitute(arg: Double): Double = - coefficients.reduceIndexedOrNull { index, acc, c -> - acc + c * arg.pow(index) - } ?: .0 - -/** - * Evaluates value of [this] polynomial on provided argument. - * - * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method). - */ -public fun ListPolynomial.substitute(ring: Ring, arg: C): C = ring { - if (coefficients.isEmpty()) return zero - var result: C = coefficients.last() - for (j in coefficients.size - 2 downTo 0) { - result = (arg * result) + coefficients[j] - } - return result -} - -/** - * Substitutes provided polynomial [arg] into [this] polynomial. - * - * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method). - */ // TODO: To optimize boxing -public fun ListPolynomial.substitute(ring: Ring, arg: ListPolynomial) : ListPolynomial = - ring.listPolynomialSpace { - if (coefficients.isEmpty()) return zero - var result: ListPolynomial = coefficients.last().asPolynomial() - for (j in coefficients.size - 2 downTo 0) { - result = (arg * result) + coefficients[j] - } - return result - } - -/** - * Substitutes provided rational function [arg] into [this] polynomial. - * - * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method). - */ // TODO: To optimize boxing -public fun ListPolynomial.substitute(ring: Ring, arg: ListRationalFunction) : ListRationalFunction = - ring.listRationalFunctionSpace { - if (coefficients.isEmpty()) return zero - var result: ListRationalFunction = coefficients.last().asRationalFunction() - for (j in coefficients.size - 2 downTo 0) { - result = (arg * result) + coefficients[j] - } - return result - } - -/** - * Evaluates value of [this] Double rational function in provided Double argument. - */ -public fun ListRationalFunction.substitute(arg: Double): Double = - numerator.substitute(arg) / denominator.substitute(arg) - -/** - * Evaluates value of [this] polynomial for provided argument. - * - * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method). - */ -public fun ListRationalFunction.substitute(ring: Field, arg: C): C = ring { - numerator.substitute(ring, arg) / denominator.substitute(ring, arg) -} - -/** - * Substitutes provided polynomial [arg] into [this] rational function. - */ // TODO: To optimize boxing -public fun ListRationalFunction.substitute(ring: Ring, arg: ListPolynomial) : ListRationalFunction = - ring.listRationalFunctionSpace { - numerator.substitute(ring, arg) / denominator.substitute(ring, arg) - } - -/** - * Substitutes provided rational function [arg] into [this] rational function. - */ // TODO: To optimize boxing -public fun ListRationalFunction.substitute(ring: Ring, arg: ListRationalFunction) : ListRationalFunction = - ring.listRationalFunctionSpace { - numerator.substitute(ring, arg) / denominator.substitute(ring, arg) - } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > ListPolynomial.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > ListPolynomial.asFunctionOfConstantOver(ring: A): (C) -> C = { substitute(ring, it) } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > ListPolynomial.asFunctionOfPolynomialOver(ring: A): (ListPolynomial) -> ListPolynomial = { substitute(ring, it) } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > ListPolynomial.asFunctionOfRationalFunctionOver(ring: A): (ListRationalFunction) -> ListRationalFunction = { substitute(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > ListRationalFunction.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > ListRationalFunction.asFunctionOfConstantOver(ring: A): (C) -> C = { substitute(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > ListRationalFunction.asFunctionOfPolynomialOver(ring: A): (ListPolynomial) -> ListRationalFunction = { substitute(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > ListRationalFunction.asFunctionOfRationalFunctionOver(ring: A): (ListRationalFunction) -> ListRationalFunction = { substitute(ring, it) } - -/** - * Returns algebraic derivative of received polynomial. - */ -@UnstableKMathAPI -public fun ListPolynomial.derivative( - ring: A, -): ListPolynomial where A : Ring, A : NumericAlgebra = ring { - ListPolynomial( - buildList(max(0, coefficients.size - 1)) { - for (deg in 1 .. coefficients.lastIndex) add(number(deg) * coefficients[deg]) - } - ) -} - -/** - * Returns algebraic derivative of received polynomial of specified [order]. The [order] should be non-negative integer. - */ -@UnstableKMathAPI -public fun ListPolynomial.nthDerivative( - ring: A, - order: Int, -): ListPolynomial where A : Ring, A : NumericAlgebra = ring { - require(order >= 0) { "Order of derivative must be non-negative" } - ListPolynomial( - buildList(max(0, coefficients.size - order)) { - for (deg in order.. coefficients.lastIndex) - add((deg - order + 1 .. deg).fold(coefficients[deg]) { acc, d -> acc * number(d) }) - } - ) -} - -/** - * Returns algebraic antiderivative of received polynomial. - */ -@UnstableKMathAPI -public fun ListPolynomial.antiderivative( - ring: A, -): ListPolynomial where A : Field, A : NumericAlgebra = ring { - ListPolynomial( - buildList(coefficients.size + 1) { - add(zero) - coefficients.mapIndexedTo(this) { index, t -> t / number(index + 1) } - } - ) -} - -/** - * Returns algebraic antiderivative of received polynomial of specified [order]. The [order] should be non-negative integer. - */ -@UnstableKMathAPI -public fun ListPolynomial.nthAntiderivative( - ring: A, - order: Int, -): ListPolynomial where A : Field, A : NumericAlgebra = ring { - require(order >= 0) { "Order of antiderivative must be non-negative" } - ListPolynomial( - buildList(coefficients.size + order) { - repeat(order) { add(zero) } - coefficients.mapIndexedTo(this) { index, c -> (1..order).fold(c) { acc, i -> acc / number(index + i) } } - } - ) -} - -/** - * Computes a definite integral of [this] polynomial in the specified [range]. - */ -@UnstableKMathAPI -public fun > ListPolynomial.integrate( - ring: Field, - range: ClosedRange, -): C = ring { - val antiderivative = antiderivative(ring) - antiderivative.substitute(ring, range.endInclusive) - antiderivative.substitute(ring, range.start) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/misc.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/misc.kt deleted file mode 100644 index 0a251b3b7..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/misc.kt +++ /dev/null @@ -1,22 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - - -/** - * Marks declarations that give access to internal entities of polynomials delicate structure. Thus, it allows to - * optimize performance a bit by skipping standard steps, but such skips may cause critical errors if something is - * implemented badly. Make sure you fully read and understand documentation and don't break internal contracts. - */ -@RequiresOptIn( - message = "This declaration gives access to delicate internal structure of polynomials. " + - "It allows to optimize performance by skipping unnecessary arguments check. " + - "But at the same time makes it easy to make a mistake " + - "that will cause wrong computation result or even runtime error. " + - "Make sure you fully read and understand documentation.", - level = RequiresOptIn.Level.ERROR -) -public annotation class DelicatePolynomialAPI \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/numberedConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/numberedConstructors.kt deleted file mode 100644 index df4afbd12..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/numberedConstructors.kt +++ /dev/null @@ -1,491 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("FunctionName", "NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.Ring - - -/** - * Returns the same degrees' description of the monomial, but without extra zero degrees on the end. - */ -internal fun List.cleanUp() = subList(0, indexOfLast { it != 0U } + 1) - -/** - * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is. - */ -@PublishedApi -internal inline fun NumberedPolynomialAsIs(coefs: Map, C>) : NumberedPolynomial = NumberedPolynomial(coefs) - -/** - * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * The collections will be transformed to map with [toMap] and then will be used as is. - */ -@PublishedApi -internal inline fun NumberedPolynomialAsIs(pairs: Collection, C>>) : NumberedPolynomial = NumberedPolynomial(pairs.toMap()) - -/** - * Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature — term's coefficient". - * The array will be transformed to map with [toMap] and then will be used as is. - */ -@PublishedApi -internal inline fun NumberedPolynomialAsIs(vararg pairs: Pair, C>) : NumberedPolynomial = NumberedPolynomial(pairs.toMap()) - -/** - * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is. - * - * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will - * cause wrong computation result or even runtime error.** - */ -@DelicatePolynomialAPI -public inline fun NumberedPolynomialWithoutCheck(coefs: Map, C>) : NumberedPolynomial = NumberedPolynomial(coefs) - -/** - * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * The collections will be transformed to map with [toMap] and then will be used as is. - * - * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will - * cause wrong computation result or even runtime error.** - */ -@DelicatePolynomialAPI -public inline fun NumberedPolynomialWithoutCheck(pairs: Collection, C>>) : NumberedPolynomial = NumberedPolynomial(pairs.toMap()) - -/** - * Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature — term's coefficient". - * The array will be transformed to map with [toMap] and then will be used as is. - * - * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will - * cause wrong computation result or even runtime error.** - */ -@DelicatePolynomialAPI -public inline fun NumberedPolynomialWithoutCheck(vararg pairs: Pair, C>) : NumberedPolynomial = NumberedPolynomial(pairs.toMap()) - -/** - * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public fun NumberedPolynomial(coefs: Map, C>, add: (C, C) -> C) : NumberedPolynomial = - NumberedPolynomialAsIs( - coefs.mapKeys({ key, _ -> key.cleanUp() }, add) - ) - -/** - * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public fun NumberedPolynomial(pairs: Collection, C>>, add: (C, C) -> C) : NumberedPolynomial = - NumberedPolynomialAsIs( - pairs.associateBy({ it.first.cleanUp() }, { it.second }, add) - ) - -/** - * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public fun NumberedPolynomial(vararg pairs: Pair, C>, add: (C, C) -> C) : NumberedPolynomial = - NumberedPolynomialAsIs( - pairs.asIterable().associateBy({ it.first.cleanUp() }, { it.second }, add) - ) - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -/** - * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > A.NumberedPolynomial(coefs: Map, C>) : NumberedPolynomial = NumberedPolynomial(coefs, ::add) -/** - * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > NumberedPolynomialSpace.NumberedPolynomial(coefs: Map, C>) : NumberedPolynomial = NumberedPolynomial(coefs) { left: C, right: C -> left + right } - -/** - * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. - * - * [coefs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > NumberedRationalFunctionSpace.NumberedPolynomial(coefs: Map, C>) : NumberedPolynomial = NumberedPolynomial(coefs) { left: C, right: C -> left + right } - -/** - * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > A.NumberedPolynomial(pairs: Collection, C>>) : NumberedPolynomial = NumberedPolynomial(pairs, ::add) - -/** - * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > NumberedPolynomialSpace.NumberedPolynomial(pairs: Collection, C>>) : NumberedPolynomial = NumberedPolynomial(pairs) { left: C, right: C -> left + right } -/** - * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public inline fun > NumberedRationalFunctionSpace.NumberedPolynomial(pairs: Collection, C>>) : NumberedPolynomial = NumberedPolynomial(pairs) { left: C, right: C -> left + right } - -/** - * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > A.NumberedPolynomial(vararg pairs: Pair, C>) : NumberedPolynomial = NumberedPolynomial(*pairs) { left: C, right: C -> left + right } -/** - * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > NumberedPolynomialSpace.NumberedPolynomial(vararg pairs: Pair, C>) : NumberedPolynomial = NumberedPolynomial(*pairs) { left: C, right: C -> left + right } -/** - * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient". - * - * [pairs] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - * - * @see NumberedPolynomialWithoutCheck - */ -public inline fun > NumberedRationalFunctionSpace.NumberedPolynomial(vararg pairs: Pair, C>) : NumberedPolynomial = NumberedPolynomial(*pairs) { left: C, right: C -> left + right } - -/** - * Converts [this] constant to [NumberedPolynomial]. - */ -public inline fun C.asNumberedPolynomial() : NumberedPolynomial = NumberedPolynomialAsIs(mapOf(emptyList() to this)) - -/** - * Marks DSL that allows to more simply create [NumberedPolynomial]s with good performance. - * - * For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as - * ``` - * Int.algebra { - * val numberedPolynomial : NumberedPolynomial = NumberedPolynomial { - * 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 + - * (-6) { 1 inPowerOf 1u } // (-6) x_1^1 - * } - * } - * ``` - * @usesMathJax - */ -@DslMarker -@UnstableKMathAPI -internal annotation class NumberedPolynomialConstructorDSL1 - -/** - * Builder of [NumberedPolynomial] signature. It should be used as an implicit context for lambdas that describe term signature. - */ -@UnstableKMathAPI -@NumberedPolynomialConstructorDSL1 -public class DSL1NumberedPolynomialTermSignatureBuilder { - /** - * Signature storage. Any declaration of any variable's power updates the storage by increasing corresponding value. - * Afterward the storage will be used as a resulting signature. - */ - private val signature: MutableList = ArrayList() - - /** - * Builds the resulting signature. - * - * In fact, it just returns [signature] as regular signature of type `List`. - */ - @PublishedApi - internal fun build(): List = signature - - /** - * Declares power of variable #[this] of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public infix fun Int.inPowerOf(deg: UInt) { - if (deg == 0u) return - val index = this - if (index > signature.lastIndex) { - signature.addAll(List(index - signature.lastIndex - 1) { 0u }) - signature.add(deg) - } else { - signature[index] += deg - } - } - /** - * Declares power of variable #[this] of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public inline infix fun Int.pow(deg: UInt): Unit = this inPowerOf deg - /** - * Declares power of variable #[this] of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public inline infix fun Int.`in`(deg: UInt): Unit = this inPowerOf deg - /** - * Declares power of variable #[this] of degree [deg]. - * - * Declaring another power of the same variable will increase its degree by received degree. - */ - public inline infix fun Int.of(deg: UInt): Unit = this inPowerOf deg -} - -/** - * Builder of [NumberedPolynomial]. It should be used as an implicit context for lambdas that describe [NumberedPolynomial]. - */ -@UnstableKMathAPI -@NumberedPolynomialConstructorDSL1 -public class DSL1NumberedPolynomialBuilder( - /** - * Summation operation that will be used to sum coefficients of monomials of same signatures. - */ - private val add: (C, C) -> C, - /** - * Initial capacity of coefficients map. - */ - initialCapacity: Int? = null -) { - /** - * Coefficients storage. Any declaration of any monomial updates the storage. - * Afterward the storage will be used as a resulting coefficients map. - */ - private val coefficients: MutableMap, C> = if (initialCapacity != null) LinkedHashMap(initialCapacity) else LinkedHashMap() - - /** - * Builds the resulting coefficients map. - * - * In fact, it just returns [coefficients] as regular coefficients map of type `Map, C>`. - */ - @PublishedApi - internal fun build(): NumberedPolynomial = NumberedPolynomial(coefficients) - - /** - * Declares monomial with [this] coefficient and provided [signature]. - * - * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such - * coefficients is zero at any moment the monomial won't be removed but will be left as it is. - */ - public infix fun C.with(signature: List) { - coefficients.putOrChange(signature, this@with, add) - } - /** - * Declares monomial with [this] coefficient and signature constructed by [block]. - * - * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such - * coefficients is zero at any moment the monomial won't be removed but will be left as it is. - */ - public inline infix fun C.with(noinline block: DSL1NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block) - /** - * Declares monomial with [this] coefficient and signature constructed by [block]. - * - * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such - * coefficients is zero at any moment the monomial won't be removed but will be left as it is. - */ - public inline operator fun C.invoke(block: DSL1NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit = - this with DSL1NumberedPolynomialTermSignatureBuilder().apply(block).build() -} - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -///** -// * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of constants. -// * -// * For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as -// * ``` -// * Int.algebra { -// * val numberedPolynomial : NumberedPolynomial = NumberedPolynomial { -// * 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 + -// * (-6) { 1 inPowerOf 1u } // (-6) x_1^1 -// * } -// * } -// * ``` -// * @usesMathJax -// */ -// FIXME: For now this fabric does not let next two fabrics work. (See KT-52803.) Possible feature solutions: -// 1. `LowPriorityInOverloadResolution` becomes public. Then it should be applied to this function. -// 2. Union types are implemented. Then all three functions should be rewritten -// as one with single union type as a (context) receiver. -//@UnstableKMathAPI -//public inline fun > A.NumberedPolynomialDSL1(initialCapacity: Int? = null, block: NumberedPolynomialBuilder.() -> Unit) : NumberedPolynomial = NumberedPolynomialBuilder(::add, initialCapacity).apply(block).build() -/** - * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of [NumberedPolynomial]s. - * - * For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as - * ``` - * Int.algebra { - * val numberedPolynomial : NumberedPolynomial = NumberedPolynomial { - * 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 + - * (-6) { 1 inPowerOf 1u } // (-6) x_1^1 - * } - * } - * ``` - * @usesMathJax - */ -@UnstableKMathAPI -public inline fun > NumberedPolynomialSpace.NumberedPolynomialDSL1(initialCapacity: Int? = null, block: DSL1NumberedPolynomialBuilder.() -> Unit) : NumberedPolynomial = DSL1NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build() -/** - * Creates [NumberedPolynomial] with lambda [block] in context of [this] field of [NumberedRationalFunction]s. - * - * For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as - * ``` - * Int.algebra { - * val numberedPolynomial : NumberedPolynomial = NumberedPolynomial { - * 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 + - * (-6) { 1 inPowerOf 1u } // (-6) x_1^1 - * } - * } - * ``` - * @usesMathJax - */ -@UnstableKMathAPI -public inline fun > NumberedRationalFunctionSpace.NumberedPolynomialDSL1(initialCapacity: Int? = null, block: DSL1NumberedPolynomialBuilder.() -> Unit) : NumberedPolynomial = DSL1NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build() - -// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available - -/** - * Constructs [NumberedRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients]. - * - * The maps will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > A.NumberedRationalFunction(numeratorCoefficients: Map, C>, denominatorCoefficients: Map, C>): NumberedRationalFunction = - NumberedRationalFunction( - NumberedPolynomial(numeratorCoefficients), - NumberedPolynomial(denominatorCoefficients) - ) -/** - * Constructs [NumberedRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients]. - * - * The maps will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > NumberedRationalFunctionSpace.NumberedRationalFunction(numeratorCoefficients: Map, C>, denominatorCoefficients: Map, C>): NumberedRationalFunction = - NumberedRationalFunction( - NumberedPolynomial(numeratorCoefficients), - NumberedPolynomial(denominatorCoefficients) - ) - -/** - * Constructs [NumberedRationalFunction] with provided [numerator] and unit denominator. - */ -public fun > A.NumberedRationalFunction(numerator: NumberedPolynomial): NumberedRationalFunction = - NumberedRationalFunction(numerator, NumberedPolynomial(mapOf(emptyList() to one))) -/** - * Constructs [NumberedRationalFunction] with provided [numerator] and unit denominator. - */ -public fun > NumberedRationalFunctionSpace.NumberedRationalFunction(numerator: NumberedPolynomial): NumberedRationalFunction = - NumberedRationalFunction(numerator, polynomialOne) - -/** - * Constructs [NumberedRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit - * denominator. - * - * [numeratorCoefficients] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > NumberedRationalFunctionSpace.NumberedRationalFunction(numeratorCoefficients: Map, C>): NumberedRationalFunction = - NumberedRationalFunction( - NumberedPolynomial(numeratorCoefficients), - polynomialOne - ) -/** - * Constructs [NumberedRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit - * denominator. - * - * [numeratorCoefficients] will be "cleaned up": - * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].) - * 1. Terms that happen to have the same signature will be summed up. - * 1. New map will be formed of resulting terms. - */ -public fun > A.NumberedRationalFunction(numeratorCoefficients: Map, C>): NumberedRationalFunction = - NumberedRationalFunction( - NumberedPolynomial(numeratorCoefficients), - NumberedPolynomialAsIs(mapOf(emptyList() to one)) - ) - -///** -// * Converts [this] constant to [NumberedRationalFunction]. -// */ -//context(A) -//public fun > C.asNumberedRationalFunction() : NumberedRationalFunction = -// NumberedRationalFunction( -// NumberedPolynomialAsIs(mapOf(emptyList() to this)), -// NumberedPolynomialAsIs(mapOf(emptyList() to one)) -// ) -///** -// * Converts [this] constant to [NumberedRationalFunction]. -// */ -//context(NumberedRationalFunctionSpace) -//public fun > C.asNumberedRationalFunction() : NumberedRationalFunction = -// NumberedRationalFunction( -// NumberedPolynomialAsIs(mapOf(emptyList() to this)), -// NumberedPolynomialAsIs(mapOf(emptyList() to constantOne)) -// ) \ No newline at end of file diff --git a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt deleted file mode 100644 index 88424d23c..000000000 --- a/kmath-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt +++ /dev/null @@ -1,513 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.Field -import space.kscience.kmath.operations.Ring -import space.kscience.kmath.operations.algebra -import space.kscience.kmath.operations.invoke -import space.kscience.kmath.structures.Buffer -import kotlin.contracts.InvocationKind -import kotlin.contracts.contract -import kotlin.jvm.JvmName -import kotlin.math.max -import kotlin.math.min - - -/** - * Creates a [NumberedPolynomialSpace] over a received ring. - */ -public inline val > A.numberedPolynomialSpace: NumberedPolynomialSpace - get() = NumberedPolynomialSpace(this) - -/** - * Creates a [NumberedPolynomialSpace]'s scope over a received ring. - */ -public inline fun , R> A.numberedPolynomialSpace(block: NumberedPolynomialSpace.() -> R): R { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return NumberedPolynomialSpace(this).block() -} - -/** - * Creates a [NumberedRationalFunctionSpace] over a received ring. - */ -public inline val > A.numberedRationalFunctionSpace: NumberedRationalFunctionSpace - get() = NumberedRationalFunctionSpace(this) - -/** - * Creates a [NumberedRationalFunctionSpace]'s scope over a received ring. - */ -public inline fun , R> A.numberedRationalFunctionSpace(block: NumberedRationalFunctionSpace.() -> R): R { - contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) } - return NumberedRationalFunctionSpace(this).block() -} - -/** - * Substitutes provided Double arguments [args] into [this] Double polynomial. - */ -public fun NumberedPolynomial.substitute(args: Map): NumberedPolynomial = Double.algebra { - NumberedPolynomial( - buildMap(coefficients.size) { - for ((degs, c) in coefficients) { - val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp() - val newC = args.entries.fold(c) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * substitution.pow(deg.toInt()) - } - putOrChange(newDegs, newC) { it -> it + newC } - } - } - ) -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ -public fun NumberedPolynomial.substitute(ring: Ring, args: Map): NumberedPolynomial = ring { - NumberedPolynomial( - buildMap(coefficients.size) { - for ((degs, c) in coefficients) { - val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp() - val newC = args.entries.fold(c) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - putOrChange(newDegs, newC) { it -> it + newC } - } - } - ) -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ // TODO: To optimize boxing -@JvmName("substitutePolynomial") -public fun NumberedPolynomial.substitute(ring: Ring, args: Map>) : NumberedPolynomial = - ring.numberedPolynomialSpace { - coefficients.entries.fold(zero) { acc, (degs, c) -> - val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp() - acc + args.entries.fold(NumberedPolynomial(mapOf(newDegs to c))) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - } - } - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ // TODO: To optimize boxing -@JvmName("substituteRationalFunction") -public fun NumberedPolynomial.substitute(ring: Ring, args: Map>) : NumberedRationalFunction = - ring.numberedRationalFunctionSpace { - coefficients.entries.fold(zero) { acc, (degs, c) -> - val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp() - acc + args.entries.fold(NumberedRationalFunction(NumberedPolynomial(mapOf(newDegs to c)))) { product, (variable, substitution) -> - val deg = degs.getOrElse(variable) { 0u } - if (deg == 0u) product else product * power(substitution, deg) - } - } - } - -/** - * Substitutes provided Double arguments [args] into [this] Double rational function. - */ -public fun NumberedRationalFunction.substitute(args: Map): NumberedRationalFunction = - NumberedRationalFunction(numerator.substitute(args), denominator.substitute(args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ -public fun NumberedRationalFunction.substitute(ring: Ring, args: Map): NumberedRationalFunction = - NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ // TODO: To optimize calculation -@JvmName("substitutePolynomial") -public fun NumberedRationalFunction.substitute(ring: Ring, args: Map>) : NumberedRationalFunction = - NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ // TODO: To optimize calculation -@JvmName("substituteRationalFunction") -public fun NumberedRationalFunction.substitute(ring: Ring, args: Map>) : NumberedRationalFunction = - ring.numberedRationalFunctionSpace { - numerator.substitute(ring, args) / denominator.substitute(ring, args) - } - -/** - * Substitutes provided Double arguments [args] into [this] Double polynomial. - */ -public fun NumberedPolynomial.substitute(args: Buffer): NumberedPolynomial = Double.algebra { - val lastSubstitutionVariable = args.size - 1 - NumberedPolynomial( - buildMap(coefficients.size) { - for ((degs, c) in coefficients) { - val lastDegsIndex = degs.lastIndex - val newDegs = - if (lastDegsIndex <= lastSubstitutionVariable) emptyList() - else degs.toMutableList().apply { - for (i in 0..lastSubstitutionVariable) this[i] = 0u - } - val newC = (0..min(lastDegsIndex, lastSubstitutionVariable)).fold(c) { product, variable -> - val deg = degs[variable] - if (deg == 0u) product else product * args[variable].pow(deg.toInt()) - } - putOrChange(newDegs, newC) { it -> it + newC } - } - } - ) -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ -public fun NumberedPolynomial.substitute(ring: Ring, args: Buffer): NumberedPolynomial = ring { - val lastSubstitutionVariable = args.size - 1 - NumberedPolynomial( - buildMap, C>(coefficients.size) { - for ((degs, c) in coefficients) { - val lastDegsIndex = degs.lastIndex - val newDegs = - if (lastDegsIndex <= lastSubstitutionVariable) emptyList() - else degs.toMutableList().apply { - for (i in 0..lastSubstitutionVariable) this[i] = 0u - } - val newC = (0..min(lastDegsIndex, lastSubstitutionVariable)).fold(c) { product, variable -> - val deg = degs[variable] - if (deg == 0u) product else product * power(args[variable], deg) - } - putOrChange(newDegs, newC) { it -> it + newC } - } - } - ) -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ // TODO: To optimize boxing -@JvmName("substitutePolynomial") -public fun NumberedPolynomial.substitute(ring: Ring, args: Buffer>) : NumberedPolynomial = - ring.numberedPolynomialSpace { - val lastSubstitutionVariable = args.size - 1 - coefficients.entries.fold(zero) { acc, (degs, c) -> - val lastDegsIndex = degs.lastIndex - val newDegs = - if (lastDegsIndex <= lastSubstitutionVariable) emptyList() - else degs.toMutableList().apply { - for (i in 0..lastSubstitutionVariable) this[i] = 0u - } - acc + (0..min(lastDegsIndex, lastSubstitutionVariable)) - .fold(NumberedPolynomial(mapOf(newDegs to c))) { product, variable -> - val deg = degs[variable] - if (deg == 0u) product else product * power(args[variable], deg) - } - } - } - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ // TODO: To optimize boxing -@JvmName("substituteRationalFunction") -public fun NumberedPolynomial.substitute(ring: Ring, args: Buffer>) : NumberedRationalFunction = - ring.numberedRationalFunctionSpace { - val lastSubstitutionVariable = args.size - 1 - coefficients.entries.fold(zero) { acc, (degs, c) -> - val lastDegsIndex = degs.lastIndex - val newDegs = - if (lastDegsIndex <= lastSubstitutionVariable) emptyList() - else degs.toMutableList().apply { - for (i in 0..lastSubstitutionVariable) this[i] = 0u - } - acc + (0..min(lastDegsIndex, lastSubstitutionVariable)) - .fold(NumberedRationalFunction(NumberedPolynomial(mapOf(newDegs to c)))) { product, variable -> - val deg = degs[variable] - if (deg == 0u) product else product * power(args[variable], deg) - } - } - } - -/** - * Substitutes provided Double arguments [args] into [this] Double rational function. - */ -public fun NumberedRationalFunction.substitute(args: Buffer): NumberedRationalFunction = - NumberedRationalFunction(numerator.substitute(args), denominator.substitute(args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ -public fun NumberedRationalFunction.substitute(ring: Ring, args: Buffer): NumberedRationalFunction = - NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ // TODO: To optimize calculation -@JvmName("substitutePolynomial") -public fun NumberedRationalFunction.substitute(ring: Ring, args: Buffer>) : NumberedRationalFunction = - NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args)) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ // TODO: To optimize calculation -@JvmName("substituteRationalFunction") -public fun NumberedRationalFunction.substitute(ring: Ring, args: Buffer>) : NumberedRationalFunction = - ring.numberedRationalFunctionSpace { - numerator.substitute(ring, args) / denominator.substitute(ring, args) - } - -internal const val fullSubstitutionExceptionMessage: String = "Fully substituting buffer should cover all variables of the polynomial." - -/** - * Substitutes provided Double arguments [args] into [this] Double polynomial. - */ -public fun NumberedPolynomial.substituteFully(args: Buffer): Double = Double.algebra { - val lastSubstitutionVariable = args.size - 1 - require(coefficients.keys.all { it.lastIndex <= lastSubstitutionVariable }) { fullSubstitutionExceptionMessage } - coefficients.entries.fold(.0) { acc, (degs, c) -> - acc + degs.foldIndexed(c) { variable, product, deg -> - if (deg == 0u) product else product * args[variable].pow(deg.toInt()) - } - } -} - -/** - * Substitutes provided arguments [args] into [this] polynomial. - */ -public fun NumberedPolynomial.substituteFully(ring: Ring, args: Buffer): C = ring { - val lastSubstitutionVariable = args.size - 1 - require(coefficients.keys.all { it.lastIndex <= lastSubstitutionVariable }) { fullSubstitutionExceptionMessage } - coefficients.entries.fold(zero) { acc, (degs, c) -> - acc + degs.foldIndexed(c) { variable, product, deg -> - if (deg == 0u) product else product * power(args[variable], deg) - } - } -} - -/** - * Substitutes provided Double arguments [args] into [this] Double rational function. - */ -public fun NumberedRationalFunction.substituteFully(args: Buffer): Double = - numerator.substituteFully(args) / denominator.substituteFully(args) - -/** - * Substitutes provided arguments [args] into [this] rational function. - */ -public fun NumberedRationalFunction.substituteFully(ring: Field, args: Buffer): C = ring { - numerator.substituteFully(ring, args) / denominator.substituteFully(ring, args) -} - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > NumberedPolynomial.asFunctionOver(ring: A): (Buffer) -> C = { substituteFully(ring, it) } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > NumberedPolynomial.asFunctionOfConstantOver(ring: A): (Buffer) -> C = { substituteFully(ring, it) } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > NumberedPolynomial.asFunctionOfPolynomialOver(ring: A): (Buffer>) -> NumberedPolynomial = { substitute(ring, it) } - -/** - * Represent [this] polynomial as a regular context-less function. - */ -public fun > NumberedPolynomial.asFunctionOfRationalFunctionOver(ring: A): (Buffer>) -> NumberedRationalFunction = { substitute(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > NumberedRationalFunction.asFunctionOver(ring: A): (Buffer) -> C = { substituteFully(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > NumberedRationalFunction.asFunctionOfConstantOver(ring: A): (Buffer) -> C = { substituteFully(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > NumberedRationalFunction.asFunctionOfPolynomialOver(ring: A): (Buffer>) -> NumberedRationalFunction = { substitute(ring, it) } - -/** - * Represent [this] rational function as a regular context-less function. - */ -public fun > NumberedRationalFunction.asFunctionOfRationalFunctionOver(ring: A): (Buffer>) -> NumberedRationalFunction = { substitute(ring, it) } - -/** - * Returns algebraic derivative of received polynomial with respect to provided variable. - */ -@UnstableKMathAPI -public fun > NumberedPolynomial.derivativeWithRespectTo( - ring: A, - variable: Int, -): NumberedPolynomial = ring { - NumberedPolynomial( - buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= 1u }) { - coefficients - .forEach { (degs, c) -> - if (degs.lastIndex < variable) return@forEach - put( - degs.mapIndexed { index, deg -> - when { - index != variable -> deg - deg > 0u -> deg - 1u - else -> return@forEach - } - }.cleanUp(), - multiplyByDoubling(c, degs[variable]) - ) - } - } - ) -} - -/** - * Returns algebraic derivative of received polynomial with respect to provided variable of specified order. - */ -@UnstableKMathAPI -public fun > NumberedPolynomial.nthDerivativeWithRespectTo( - ring: A, - variable: Int, - order: UInt -): NumberedPolynomial = ring { - if (order == 0u) return this@nthDerivativeWithRespectTo - NumberedPolynomial( - buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= order }) { - coefficients - .forEach { (degs, c) -> - if (degs.lastIndex < variable) return@forEach - put( - degs.mapIndexed { index, deg -> - when { - index != variable -> deg - deg >= order -> deg - order - else -> return@forEach - } - }.cleanUp(), - degs[variable].let { deg -> - (deg downTo deg - order + 1u) - .fold(c) { acc, ord -> multiplyByDoubling(acc, ord) } - } - ) - } - } - ) -} - -/** - * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders. - */ -@UnstableKMathAPI -public fun > NumberedPolynomial.nthDerivativeWithRespectTo( - ring: A, - variablesAndOrders: Map, -): NumberedPolynomial = ring { - val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u } - if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo - val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!! - NumberedPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - if (degs.lastIndex < maxRespectedVariable) return@forEach - put( - degs.mapIndexed { index, deg -> - if (index !in filteredVariablesAndOrders) return@mapIndexed deg - val order = filteredVariablesAndOrders[index]!! - if (deg >= order) deg - order else return@forEach - }.cleanUp(), - filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> - degs[index].let { deg -> - (deg downTo deg - order + 1u) - .fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) } - } - } - ) - } - } - ) -} - -/** - * Returns algebraic antiderivative of received polynomial with respect to provided variable. - */ -@UnstableKMathAPI -public fun > NumberedPolynomial.antiderivativeWithRespectTo( - ring: A, - variable: Int, -): NumberedPolynomial = ring { - NumberedPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - put( - List(max(variable + 1, degs.size)) { degs.getOrElse(it) { 0u } + if (it != variable) 0u else 1u }, - c / multiplyByDoubling(one, degs.getOrElse(variable) { 0u } + 1u) - ) - } - } - ) -} - -/** - * Returns algebraic antiderivative of received polynomial with respect to provided variable of specified order. - */ -@UnstableKMathAPI -public fun > NumberedPolynomial.nthAntiderivativeWithRespectTo( - ring: A, - variable: Int, - order: UInt -): NumberedPolynomial = ring { - if (order == 0u) return this@nthAntiderivativeWithRespectTo - NumberedPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - put( - List(max(variable + 1, degs.size)) { degs.getOrElse(it) { 0u } + if (it != variable) 0u else order }, - degs.getOrElse(variable) { 0u }.let { deg -> - (deg + 1u .. deg + order) - .fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) } - } - ) - } - } - ) -} - -/** - * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders. - */ -@UnstableKMathAPI -public fun > NumberedPolynomial.nthAntiderivativeWithRespectTo( - ring: A, - variablesAndOrders: Map, -): NumberedPolynomial = ring { - val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u } - if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo - val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!! - NumberedPolynomial( - buildMap(coefficients.size) { - coefficients - .forEach { (degs, c) -> - put( - List(max(maxRespectedVariable + 1, degs.size)) { degs.getOrElse(it) { 0u } + filteredVariablesAndOrders.getOrElse(it) { 0u } }, - filteredVariablesAndOrders.entries.fold(c) { acc1, (variable, order) -> - degs.getOrElse(variable) { 0u }.let { deg -> - (deg + 1u .. deg + order) - .fold(acc1) { acc, ord -> acc / multiplyByDoubling(one, ord) } - } - } - ) - } - } - ) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/AlgebraicStubTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/AlgebraicStubTest.kt deleted file mode 100644 index 9dd2bb743..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/AlgebraicStubTest.kt +++ /dev/null @@ -1,589 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - - -import space.kscience.kmath.operations.invoke -import space.kscience.kmath.operations.Field -import kotlin.jvm.JvmInline -import kotlin.test.Test -import kotlin.test.assertEquals - -@JvmInline -value class Expr(val expr: String) - -object ExprRing : Field { - override fun Expr.unaryMinus(): Expr = Expr("-${expr}") - override fun add(left: Expr, right: Expr): Expr = Expr("(${left.expr} + ${right.expr})") - override fun multiply(left: Expr, right: Expr): Expr = Expr("(${left.expr} * ${right.expr})") - override val zero: Expr = Expr("0") - override val one: Expr = Expr("1") - override fun divide(left: Expr, right: Expr): Expr = Expr("(${left.expr} / ${right.expr})") - override fun scale(a: Expr, value: Double): Expr = Expr("(${a.expr} / $value)") -} - -class AlgebraicStubTest { - @Test - fun test_addMultipliedBySquaring_for_UInt() { - ExprRing { - assertEquals( - "57", - addMultipliedByDoubling(Expr("57"), Expr("179"), 0u).expr, - "tried addMultipliedBySquaring(57, 179, 0u)" - ) - assertEquals( - "(57 + 179)", - addMultipliedByDoubling(Expr("57"), Expr("179"), 1u).expr, - "tried addMultipliedBySquaring(57, 179, 1u)" - ) - assertEquals( - "(57 + (179 + 179))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 2u).expr, - "tried addMultipliedBySquaring(57, 179, 2u)" - ) - assertEquals( - "((57 + 179) + (179 + 179))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 3u).expr, - "tried addMultipliedBySquaring(57, 179, 3u)" - ) - assertEquals( - "(57 + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 4u).expr, - "tried addMultipliedBySquaring(57, 179, 4u)" - ) - assertEquals( - "((57 + 179) + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 5u).expr, - "tried addMultipliedBySquaring(57, 179, 5u)" - ) - assertEquals( - "((57 + (179 + 179)) + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 6u).expr, - "tried addMultipliedBySquaring(57, 179, 6u)" - ) - assertEquals( - "(((57 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 7u).expr, - "tried addMultipliedBySquaring(57, 179, 7u)" - ) - assertEquals( - "(57 + (((179 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179))))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 8u).expr, - "tried addMultipliedBySquaring(57, 179, 8u)" - ) - } - } - @Test - fun test_multiplyBySquaring_for_UInt() { - ExprRing { - assertEquals( - "0", - multiplyByDoubling(Expr("57"), 0u).expr, - "tried multiplyBySquaring(57, 0u)" - ) - assertEquals( - "57", - multiplyByDoubling(Expr("57"), 1u).expr, - "tried multiplyBySquaring(57, 1u)" - ) - assertEquals( - "(57 + 57)", - multiplyByDoubling(Expr("57"), 2u).expr, - "tried multiplyBySquaring(57, 2u)" - ) - assertEquals( - "(57 + (57 + 57))", - multiplyByDoubling(Expr("57"), 3u).expr, - "tried multiplyBySquaring(57, 3u)" - ) - assertEquals( - "((57 + 57) + (57 + 57))", - multiplyByDoubling(Expr("57"), 4u).expr, - "tried multiplyBySquaring(57, 4u)" - ) - assertEquals( - "(57 + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 5u).expr, - "tried multiplyBySquaring(57, 5u)" - ) - assertEquals( - "((57 + 57) + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 6u).expr, - "tried multiplyBySquaring(57, 6u)" - ) - assertEquals( - "((57 + (57 + 57)) + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 7u).expr, - "tried multiplyBySquaring(57, 7u)" - ) - assertEquals( - "(((57 + 57) + (57 + 57)) + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 8u).expr, - "tried multiplyBySquaring(57, 8u)" - ) - } - } - @Test - fun test_addMultipliedBySquaring_for_Int() { - ExprRing { - assertEquals( - "57", - addMultipliedByDoubling(Expr("57"), Expr("179"), 0).expr, - "tried addMultipliedBySquaring(57, 179, 0)" - ) - assertEquals( - "(57 + 179)", - addMultipliedByDoubling(Expr("57"), Expr("179"), 1).expr, - "tried addMultipliedBySquaring(57, 179, 1)" - ) - assertEquals( - "(57 + -179)", - addMultipliedByDoubling(Expr("57"), Expr("179"), -1).expr, - "tried addMultipliedBySquaring(57, 179, -1)" - ) - assertEquals( - "(57 + (179 + 179))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 2).expr, - "tried addMultipliedBySquaring(57, 179, 2)" - ) - assertEquals( - "(57 + (-179 + -179))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -2).expr, - "tried addMultipliedBySquaring(57, 179, -2)" - ) - assertEquals( - "((57 + 179) + (179 + 179))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 3).expr, - "tried addMultipliedBySquaring(57, 179, 3)" - ) - assertEquals( - "((57 + -179) + (-179 + -179))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -3).expr, - "tried addMultipliedBySquaring(57, 179, -3)" - ) - assertEquals( - "(57 + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 4).expr, - "tried addMultipliedBySquaring(57, 179, 4)" - ) - assertEquals( - "(57 + ((-179 + -179) + (-179 + -179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -4).expr, - "tried addMultipliedBySquaring(57, 179, -4)" - ) - assertEquals( - "((57 + 179) + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 5).expr, - "tried addMultipliedBySquaring(57, 179, 5)" - ) - assertEquals( - "((57 + -179) + ((-179 + -179) + (-179 + -179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -5).expr, - "tried addMultipliedBySquaring(57, 179, -5)" - ) - assertEquals( - "((57 + (179 + 179)) + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 6).expr, - "tried addMultipliedBySquaring(57, 179, 6)" - ) - assertEquals( - "((57 + (-179 + -179)) + ((-179 + -179) + (-179 + -179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -6).expr, - "tried addMultipliedBySquaring(57, 179, -6)" - ) - assertEquals( - "(((57 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 7).expr, - "tried addMultipliedBySquaring(57, 179, 7)" - ) - assertEquals( - "(((57 + -179) + (-179 + -179)) + ((-179 + -179) + (-179 + -179)))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -7).expr, - "tried addMultipliedBySquaring(57, 179, -7)" - ) - assertEquals( - "(57 + (((179 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179))))", - addMultipliedByDoubling(Expr("57"), Expr("179"), 8).expr, - "tried addMultipliedBySquaring(57, 179, 8)" - ) - assertEquals( - "(57 + (((-179 + -179) + (-179 + -179)) + ((-179 + -179) + (-179 + -179))))", - addMultipliedByDoubling(Expr("57"), Expr("179"), -8).expr, - "tried addMultipliedBySquaring(57, 179, -8)" - ) - } - } - @Test - fun test_multiplyBySquaring_for_Int() { - ExprRing { - assertEquals( - "0", - multiplyByDoubling(Expr("57"), 0).expr, - "tried multiplyBySquaring(57, 0)" - ) - assertEquals( - "57", - multiplyByDoubling(Expr("57"), 1).expr, - "tried multiplyBySquaring(57, 1)" - ) - assertEquals( - "-57", - multiplyByDoubling(Expr("57"), -1).expr, - "tried multiplyBySquaring(57, -1)" - ) - assertEquals( - "(57 + 57)", - multiplyByDoubling(Expr("57"), 2).expr, - "tried multiplyBySquaring(57, 2)" - ) - assertEquals( - "(-57 + -57)", - multiplyByDoubling(Expr("57"), -2).expr, - "tried multiplyBySquaring(57, -2)" - ) - assertEquals( - "(57 + (57 + 57))", - multiplyByDoubling(Expr("57"), 3).expr, - "tried multiplyBySquaring(57, 3)" - ) - assertEquals( - "(-57 + (-57 + -57))", - multiplyByDoubling(Expr("57"), -3).expr, - "tried multiplyBySquaring(57, -3)" - ) - assertEquals( - "((57 + 57) + (57 + 57))", - multiplyByDoubling(Expr("57"), 4).expr, - "tried multiplyBySquaring(57, 4)" - ) - assertEquals( - "((-57 + -57) + (-57 + -57))", - multiplyByDoubling(Expr("57"), -4).expr, - "tried multiplyBySquaring(57, -4)" - ) - assertEquals( - "(57 + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 5).expr, - "tried multiplyBySquaring(57, 5)" - ) - assertEquals( - "(-57 + ((-57 + -57) + (-57 + -57)))", - multiplyByDoubling(Expr("57"), -5).expr, - "tried multiplyBySquaring(57, -5)" - ) - assertEquals( - "((57 + 57) + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 6).expr, - "tried multiplyBySquaring(57, 6)" - ) - assertEquals( - "((-57 + -57) + ((-57 + -57) + (-57 + -57)))", - multiplyByDoubling(Expr("57"), -6).expr, - "tried multiplyBySquaring(57, -6)" - ) - assertEquals( - "((57 + (57 + 57)) + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 7).expr, - "tried multiplyBySquaring(57, 7)" - ) - assertEquals( - "((-57 + (-57 + -57)) + ((-57 + -57) + (-57 + -57)))", - multiplyByDoubling(Expr("57"), -7).expr, - "tried multiplyBySquaring(57, -7)" - ) - assertEquals( - "(((57 + 57) + (57 + 57)) + ((57 + 57) + (57 + 57)))", - multiplyByDoubling(Expr("57"), 8).expr, - "tried multiplyBySquaring(57, 8)" - ) - assertEquals( - "(((-57 + -57) + (-57 + -57)) + ((-57 + -57) + (-57 + -57)))", - multiplyByDoubling(Expr("57"), -8).expr, - "tried multiplyBySquaring(57, -8)" - ) - } - } - @Test - fun test_multiplyExponentiationBySquaring_for_UInt() { - ExprRing { - assertEquals( - "57", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 0u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 0u)" - ) - assertEquals( - "(57 * 179)", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 1u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 1u)" - ) - assertEquals( - "(57 * (179 * 179))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 2u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 2u)" - ) - assertEquals( - "((57 * 179) * (179 * 179))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 3u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 3u)" - ) - assertEquals( - "(57 * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 4u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 4u)" - ) - assertEquals( - "((57 * 179) * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 5u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 5u)" - ) - assertEquals( - "((57 * (179 * 179)) * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 6u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 6u)" - ) - assertEquals( - "(((57 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 7u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 7u)" - ) - assertEquals( - "(57 * (((179 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 8u).expr, - "tried multiplyExponentiationBySquaring(57, 179, 8u)" - ) - } - } - @Test - fun test_exponentiationBySquaring_for_UInt() { - ExprRing { - assertEquals( - "0", - exponentiateBySquaring(Expr("57"), 0u).expr, - "tried exponentiationBySquaring(57, 0u)" - ) - assertEquals( - "57", - exponentiateBySquaring(Expr("57"), 1u).expr, - "tried exponentiationBySquaring(57, 1u)" - ) - assertEquals( - "(57 * 57)", - exponentiateBySquaring(Expr("57"), 2u).expr, - "tried exponentiationBySquaring(57, 2u)" - ) - assertEquals( - "(57 * (57 * 57))", - exponentiateBySquaring(Expr("57"), 3u).expr, - "tried exponentiationBySquaring(57, 3u)" - ) - assertEquals( - "((57 * 57) * (57 * 57))", - exponentiateBySquaring(Expr("57"), 4u).expr, - "tried exponentiationBySquaring(57, 4u)" - ) - assertEquals( - "(57 * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 5u).expr, - "tried exponentiationBySquaring(57, 5u)" - ) - assertEquals( - "((57 * 57) * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 6u).expr, - "tried exponentiationBySquaring(57, 6u)" - ) - assertEquals( - "((57 * (57 * 57)) * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 7u).expr, - "tried exponentiationBySquaring(57, 7u)" - ) - assertEquals( - "(((57 * 57) * (57 * 57)) * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 8u).expr, - "tried exponentiationBySquaring(57, 8u)" - ) - } - } - @Test - fun test_multiplyExponentiationBySquaring_for_Int() { - ExprRing { - assertEquals( - "57", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 0).expr, - "tried multiplyExponentiationBySquaring(57, 179, 0)" - ) - assertEquals( - "(57 * 179)", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 1).expr, - "tried multiplyExponentiationBySquaring(57, 179, 1)" - ) - assertEquals( - "(57 * (1 / 179))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -1).expr, - "tried multiplyExponentiationBySquaring(57, 179, -1)" - ) - assertEquals( - "(57 * (179 * 179))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 2).expr, - "tried multiplyExponentiationBySquaring(57, 179, 2)" - ) - assertEquals( - "(57 * ((1 / 179) * (1 / 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -2).expr, - "tried multiplyExponentiationBySquaring(57, 179, -2)" - ) - assertEquals( - "((57 * 179) * (179 * 179))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 3).expr, - "tried multiplyExponentiationBySquaring(57, 179, 3)" - ) - assertEquals( - "((57 * (1 / 179)) * ((1 / 179) * (1 / 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -3).expr, - "tried multiplyExponentiationBySquaring(57, 179, -3)" - ) - assertEquals( - "(57 * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 4).expr, - "tried multiplyExponentiationBySquaring(57, 179, 4)" - ) - assertEquals( - "(57 * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -4).expr, - "tried multiplyExponentiationBySquaring(57, 179, -4)" - ) - assertEquals( - "((57 * 179) * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 5).expr, - "tried multiplyExponentiationBySquaring(57, 179, 5)" - ) - assertEquals( - "((57 * (1 / 179)) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -5).expr, - "tried multiplyExponentiationBySquaring(57, 179, -5)" - ) - assertEquals( - "((57 * (179 * 179)) * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 6).expr, - "tried multiplyExponentiationBySquaring(57, 179, 6)" - ) - assertEquals( - "((57 * ((1 / 179) * (1 / 179))) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -6).expr, - "tried multiplyExponentiationBySquaring(57, 179, -6)" - ) - assertEquals( - "(((57 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179)))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 7).expr, - "tried multiplyExponentiationBySquaring(57, 179, 7)" - ) - assertEquals( - "(((57 * (1 / 179)) * ((1 / 179) * (1 / 179))) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -7).expr, - "tried multiplyExponentiationBySquaring(57, 179, -7)" - ) - assertEquals( - "(57 * (((179 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), 8).expr, - "tried multiplyExponentiationBySquaring(57, 179, 8)" - ) - assertEquals( - "(57 * ((((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179)))))", - multiplyExponentiatedBySquaring(Expr("57"), Expr("179"), -8).expr, - "tried multiplyExponentiationBySquaring(57, 179, -8)" - ) - } - } - @Test - fun test_exponentiationBySquaring_for_Int() { - ExprRing { - assertEquals( - "0", - exponentiateBySquaring(Expr("57"), 0).expr, - "tried exponentiationBySquaring(57, 0)" - ) - assertEquals( - "57", - exponentiateBySquaring(Expr("57"), 1).expr, - "tried exponentiationBySquaring(57, 1)" - ) - assertEquals( - "(1 / 57)", - exponentiateBySquaring(Expr("57"), -1).expr, - "tried exponentiationBySquaring(57, -1)" - ) - assertEquals( - "(57 * 57)", - exponentiateBySquaring(Expr("57"), 2).expr, - "tried exponentiationBySquaring(57, 2)" - ) - assertEquals( - "((1 / 57) * (1 / 57))", - exponentiateBySquaring(Expr("57"), -2).expr, - "tried exponentiationBySquaring(57, -2)" - ) - assertEquals( - "(57 * (57 * 57))", - exponentiateBySquaring(Expr("57"), 3).expr, - "tried exponentiationBySquaring(57, 3)" - ) - assertEquals( - "((1 / 57) * ((1 / 57) * (1 / 57)))", - exponentiateBySquaring(Expr("57"), -3).expr, - "tried exponentiationBySquaring(57, -3)" - ) - assertEquals( - "((57 * 57) * (57 * 57))", - exponentiateBySquaring(Expr("57"), 4).expr, - "tried exponentiationBySquaring(57, 4)" - ) - assertEquals( - "(((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57)))", - exponentiateBySquaring(Expr("57"), -4).expr, - "tried exponentiationBySquaring(57, -4)" - ) - assertEquals( - "(57 * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 5).expr, - "tried exponentiationBySquaring(57, 5)" - ) - assertEquals( - "((1 / 57) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))", - exponentiateBySquaring(Expr("57"), -5).expr, - "tried exponentiationBySquaring(57, -5)" - ) - assertEquals( - "((57 * 57) * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 6).expr, - "tried exponentiationBySquaring(57, 6)" - ) - assertEquals( - "(((1 / 57) * (1 / 57)) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))", - exponentiateBySquaring(Expr("57"), -6).expr, - "tried exponentiationBySquaring(57, -6)" - ) - assertEquals( - "((57 * (57 * 57)) * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 7).expr, - "tried exponentiationBySquaring(57, 7)" - ) - assertEquals( - "(((1 / 57) * ((1 / 57) * (1 / 57))) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))", - exponentiateBySquaring(Expr("57"), -7).expr, - "tried exponentiationBySquaring(57, -7)" - ) - assertEquals( - "(((57 * 57) * (57 * 57)) * ((57 * 57) * (57 * 57)))", - exponentiateBySquaring(Expr("57"), 8).expr, - "tried exponentiationBySquaring(57, 8)" - ) - assertEquals( - "((((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))", - exponentiateBySquaring(Expr("57"), -8).expr, - "tried exponentiationBySquaring(57, -8)" - ) - } - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt deleted file mode 100644 index 054f0dc4c..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt +++ /dev/null @@ -1,127 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.functions.testUtils.t -import space.kscience.kmath.functions.testUtils.x -import space.kscience.kmath.functions.testUtils.y -import space.kscience.kmath.functions.testUtils.z -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.algebra -import space.kscience.kmath.operations.invoke -import kotlin.test.Test -import kotlin.test.assertEquals - -class LabeledConstructorsTest { - @Test - @UnstableKMathAPI - fun testDSL1() { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u, z to 3u) to 5, - mapOf(y to 1u) to -6, - ), - Int.algebra.labeledPolynomialSpace { - LabeledPolynomialDSL1 { - 5 { x pow 2u; z pow 3u } - (-6) { y pow 1u } - } - }, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to -1, - ), - Int.algebra.labeledPolynomialSpace { - LabeledPolynomialDSL1 { - 5 { } - (-6) { } - } - }, - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to -1, - ), - Int.algebra.labeledPolynomialSpace { - LabeledPolynomialDSL1 { - 5 { x pow 1u; x pow 1u } - (-6) { x pow 2u } - } - }, - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to -1, - ), - Int.algebra.labeledPolynomialSpace { - LabeledPolynomialDSL1 { - 5 { x pow 1u; x pow 1u } - (-6) { x pow 2u; z pow 0u } - } - }, - "test 3" - ) - } - @Test - @UnstableKMathAPI - fun testFabric() { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u, z to 3u) to 5, - mapOf(y to 1u) to -6, - ), - Int.algebra { - LabeledPolynomial( - mapOf(x to 2u, z to 3u) to 5, - mapOf(y to 1u) to -6, - ) - }, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u, z to 3u) to 5, - mapOf(y to 1u) to -6, - ), - Int.algebra { - LabeledPolynomial( - mapOf(x to 2u, y to 0u, z to 3u, t to 0u) to 5, - mapOf(x to 0u, y to 1u, z to 0u, t to 0u) to -6, - ) - }, - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to -1, - ), - Int.algebra { - LabeledPolynomial( - mapOf(x to 0u) to 5, - mapOf(y to 0u, z to 0u) to -6, - ) - }, - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 0, - ), - Int.algebra { - LabeledPolynomial( - mapOf(x to 0u) to 5, - mapOf(z to 0u, t to 0u) to -5, - ) - }, - "test 4" - ) - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt deleted file mode 100644 index bb30f7742..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt +++ /dev/null @@ -1,2555 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("LocalVariableName") - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.functions.testUtils.IntModuloRing -import space.kscience.kmath.functions.testUtils.Rational -import space.kscience.kmath.functions.testUtils.RationalField -import space.kscience.kmath.functions.testUtils.iota -import space.kscience.kmath.functions.testUtils.m -import space.kscience.kmath.functions.testUtils.o -import space.kscience.kmath.functions.testUtils.s -import space.kscience.kmath.functions.testUtils.t -import space.kscience.kmath.functions.testUtils.x -import space.kscience.kmath.functions.testUtils.y -import space.kscience.kmath.functions.testUtils.z -import kotlin.test.* - - -// TODO: Тесты на конвертацию. -class LabeledPolynomialTest { - @Test - fun test_Variable_Int_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(5), - mapOf(x to 1u) to Rational(1), - ), - x + 5, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - ), - x + 0, - "test 2" - ) - } - } - @Test - fun test_Variable_Int_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-5), - mapOf(x to 1u) to Rational(1), - ), - x - 5, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - ), - x - 0, - "test 2" - ) - } - } - @Test - fun test_Variable_Int_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(5), - ), - x * 5, - "test 1" - ) - assertSame( - zero, - x * 0, - "test 2" - ) - } - } - @Test - fun test_Int_Variable_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(5), - mapOf(x to 1u) to Rational(1), - ), - 5 + x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - ), - 0 + x, - "test 2" - ) - } - } - @Test - fun test_Int_Variable_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(5), - mapOf(x to 1u) to Rational(-1), - ), - 5 - x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-1), - ), - 0 - x, - "test 2" - ) - } - } - @Test - fun test_Int_Variable_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(5), - ), - 5 * x, - "test 1" - ) - assertSame( - zero, - 0 * x, - "test 2" - ) - } - } - @Test - fun test_Polynomial_Int_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + -3, - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-3, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + -3, - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + -3, - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ) + -3, - "test 4" - ) - val polynomial_5 = LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_5, - polynomial_5 + 0, - "test 5" - ) - val polynomial_6 = LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_6, - polynomial_6 + 0, - "test 6" - ) - val polynomial_7 = LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_7, - polynomial_7 + 0, - "test 7" - ) - } - } - @Test - fun test_Polynomial_Int_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - 3, - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-3, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - 3, - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - 3, - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ) - 3, - "test 4" - ) - val polynomial_5 = LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_5, - polynomial_5 - 0, - "test 5" - ) - val polynomial_6 = LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_6, - polynomial_6 - 0, - "test 6" - ) - val polynomial_7 = LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_7, - polynomial_7 - 0, - "test 7" - ) - } - } - @Test - fun test_Polynomial_Int_times() { - IntModuloRing(35).labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to m(34), - mapOf(x to 3u) to m(2), - mapOf(x to 0u, y to 1u) to m(1), - mapOf(x to 1u) to m(20), - mapOf(x to 0u, y to 0u, z to 2u) to m(2), - ), - LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ) * 27, - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(0), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(0), - mapOf(x to 1u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - ), - LabeledPolynomial( - mapOf() to m(7), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(49), - mapOf(x to 1u) to m(21), - mapOf(x to 0u, y to 0u, z to 2u) to m(14), - ) * 15, - "test 2" - ) - val polynomial = LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ) - assertSame( - zero, - polynomial * 0, - "test 3" - ) - assertSame( - polynomial, - polynomial * 1, - "test 4" - ) - } - } - @Test - fun test_Int_Polynomial_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - -3 + LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-3, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - -3 + LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - -3 + LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - -3 + LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - "test 4" - ) - val polynomial_5 = LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_5, - 0 + polynomial_5, - "test 5" - ) - val polynomial_6 = LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_6, - 0 + polynomial_6, - "test 6" - ) - val polynomial_7 = LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_7, - 0 + polynomial_7, - "test 7" - ) - } - } - @Test - fun test_Int_Polynomial_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(22, 9), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - 3 - LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(3, 1), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - 3 - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - 3 - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - 3 - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - "test 4" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(22, 9), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - 0 - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 5" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - 0 - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 6" - ) - assertEquals( - LabeledPolynomial( - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - 0 - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 7" - ) - } - } - @Test - fun test_Int_Polynomial_times() { - IntModuloRing(35).labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to m(34), - mapOf(x to 3u) to m(2), - mapOf(x to 0u, y to 1u) to m(1), - mapOf(x to 1u) to m(20), - mapOf(x to 0u, y to 0u, z to 2u) to m(2), - ), - 27 * LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(0), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(0), - mapOf(x to 1u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - ), - 15 * LabeledPolynomial( - mapOf() to m(7), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(49), - mapOf(x to 1u) to m(21), - mapOf(x to 0u, y to 0u, z to 2u) to m(14), - ), - "test 2" - ) - val polynomial = LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ) - assertSame( - zero, - 0 * polynomial, - "test 3" - ) - assertSame( - polynomial, - 1 * polynomial, - "test 4" - ) - } - } - @Test - fun test_Variable_Constant_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(5), - mapOf(x to 1u) to Rational(1), - ), - x + Rational(5), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(1), - ), - x + Rational(0), - "test 2" - ) - } - } - @Test - fun test_Variable_Constant_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-5), - mapOf(x to 1u) to Rational(1), - ), - x - Rational(5), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(1), - ), - x - Rational(0), - "test 2" - ) - } - } - @Test - fun test_Variable_Constant_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(5), - ), - x * Rational(5), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(0), - ), - x * Rational(0), - "test 2" - ) - } - } - @Test - fun test_Constant_Variable_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(5), - mapOf(x to 1u) to Rational(1), - ), - Rational(5) + x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(1), - ), - Rational(0) + x, - "test 2" - ) - } - } - @Test - fun test_Constant_Variable_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(5), - mapOf(x to 1u) to Rational(-1), - ), - Rational(5) - x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(-1), - ), - Rational(0) - x, - "test 2" - ) - } - } - @Test - fun test_Constant_Variable_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(5), - ), - Rational(5) * x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(0), - ), - Rational(0) * x, - "test 2" - ) - } - } - @Test - fun test_Polynomial_Constant_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + Rational(-3), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-3, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + Rational(-3), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + Rational(-3), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ) + Rational(-3), - "test 4" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + Rational(0), - "test 5" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + Rational(0), - "test 6" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) + Rational(0), - "test 7" - ) - } - } - @Test - fun test_Polynomial_Constant_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - Rational(3), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-3, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - Rational(3), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - Rational(3), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ) - Rational(3), - "test 4" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - Rational(0), - "test 5" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - Rational(0), - "test 6" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ) - Rational(0), - "test 7" - ) - } - } - @Test - fun test_Polynomial_Constant_times() { - IntModuloRing(35).labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to m(34), - mapOf(x to 3u) to m(2), - mapOf(x to 0u, y to 1u) to m(1), - mapOf(x to 1u) to m(20), - mapOf(x to 0u, y to 0u, z to 2u) to m(2), - ), - LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ) * m(27), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(0), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(0), - mapOf(x to 1u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - ), - LabeledPolynomial( - mapOf() to m(7), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(49), - mapOf(x to 1u) to m(21), - mapOf(x to 0u, y to 0u, z to 2u) to m(14), - ) * m(15), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(0), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(0), - mapOf(x to 1u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - ), - LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ) * m(0), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ), - LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ) * m(1), - "test 4" - ) - } - } - @Test - fun test_Constant_Polynomial_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - Rational(-3) + LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-3, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - Rational(-3) + LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - Rational(-3) + LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - Rational(-3) + LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - "test 4" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - Rational(0) + LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 5" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - Rational(0) + LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 6" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - Rational(0) + LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 7" - ) - } - } - @Test - fun test_Constant_Polynomial_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(22, 9), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - Rational(3) - LabeledPolynomial( - mapOf() to Rational(5, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(3, 1), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - Rational(3) - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 1), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - Rational(3) - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - Rational(3) - LabeledPolynomial( - mapOf() to Rational(27, 9), - mapOf(x to 3u) to Rational(0), - mapOf(x to 0u, y to 4u) to Rational(0), - ), - "test 4" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(22, 9), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - Rational(0) - LabeledPolynomial( - mapOf() to Rational(-22, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 5" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - Rational(0) - LabeledPolynomial( - mapOf() to Rational(0, 9), - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 6" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 3u) to Rational(8, 9), - mapOf(x to 0u, y to 4u) to Rational(8, 7), - ), - Rational(0) - LabeledPolynomial( - mapOf(x to 3u) to Rational(-8, 9), - mapOf(x to 0u, y to 4u) to Rational(-8, 7), - ), - "test 7" - ) - } - } - @Test - fun test_Constant_Polynomial_times() { - IntModuloRing(35).labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to m(34), - mapOf(x to 3u) to m(2), - mapOf(x to 0u, y to 1u) to m(1), - mapOf(x to 1u) to m(20), - mapOf(x to 0u, y to 0u, z to 2u) to m(2), - ), - m(27) * LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(0), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(0), - mapOf(x to 1u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - ), - m(15) * LabeledPolynomial( - mapOf() to m(7), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(49), - mapOf(x to 1u) to m(21), - mapOf(x to 0u, y to 0u, z to 2u) to m(14), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(0), - mapOf(x to 3u) to m(0), - mapOf(x to 0u, y to 1u) to m(0), - mapOf(x to 1u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - ), - m(0) * LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ), - m(1) * LabeledPolynomial( - mapOf() to m(22), - mapOf(x to 3u) to m(26), - mapOf(x to 0u, y to 1u) to m(13), - mapOf(x to 1u) to m(15), - mapOf(x to 0u, y to 0u, z to 2u) to m(26), - ), - "test 4" - ) - } - } - @Test - fun test_Variable_unaryPlus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - ), - +x - ) - } - } - @Test - fun test_Variable_unaryMinus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-1), - ), - -x - ) - } - } - @Test - fun test_Variable_Variable_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - mapOf(y to 1u) to Rational(1), - ), - x + y, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(2), - ), - x + x, - "test 2" - ) - } - } - @Test - fun test_Variable_Variable_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - mapOf(y to 1u) to Rational(-1), - ), - x - y, - "test 1" - ) - assertSame( - zero, - x - x, - "test 2" - ) - } - } - @Test - fun test_Variable_Variable_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u, y to 1u) to Rational(1), - ), - x * y, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(1), - ), - x * x, - "test 2" - ) - } - } - @Test - fun test_Variable_Polynomial_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(7, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - x + LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(6, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - y + LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - mapOf(iota to 1u) to Rational(1), - ), - iota + LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 3" - ) - } - } - @Test - fun test_Variable_Polynomial_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(16, 4), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-3, 8), - mapOf(y to 1u) to Rational(1, 7), - mapOf(x to 1u, y to 1u) to Rational(15, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 5), - mapOf(y to 2u) to Rational(13, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(-11, 8), - ), - x - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(16, 4), - mapOf(x to 1u) to Rational(-4, 3), - mapOf(x to 2u) to Rational(-3, 8), - mapOf(y to 1u) to Rational(8, 7), - mapOf(x to 1u, y to 1u) to Rational(15, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 5), - mapOf(y to 2u) to Rational(13, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(-11, 8), - ), - y - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(16, 4), - mapOf(x to 1u) to Rational(-4, 3), - mapOf(x to 2u) to Rational(-3, 8), - mapOf(y to 1u) to Rational(1, 7), - mapOf(x to 1u, y to 1u) to Rational(15, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 5), - mapOf(y to 2u) to Rational(13, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(-11, 8), - mapOf(iota to 1u) to Rational(1), - ), - iota - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 3" - ) - } - } - @Test - fun test_Variable_Polynomial_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-16, 4), - mapOf(x to 2u) to Rational(4, 3), - mapOf(x to 3u) to Rational(3, 8), - mapOf(x to 1u, y to 1u) to Rational(-1, 7), - mapOf(x to 2u, y to 1u) to Rational(-15, 3), - mapOf(x to 3u, y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 2u) to Rational(-13, 3), - mapOf(x to 2u, y to 2u) to Rational(13, 4), - mapOf(x to 3u, y to 2u) to Rational(11, 8), - ), - x * LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(-16, 4), - mapOf(x to 1u, y to 1u) to Rational(4, 3), - mapOf(x to 2u, y to 1u) to Rational(3, 8), - mapOf(y to 2u) to Rational(-1, 7), - mapOf(x to 1u, y to 2u) to Rational(-15, 3), - mapOf(x to 2u, y to 2u) to Rational(6, 5), - mapOf(y to 3u) to Rational(-13, 3), - mapOf(x to 1u, y to 3u) to Rational(13, 4), - mapOf(x to 2u, y to 3u) to Rational(11, 8), - ), - y * LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(iota to 1u) to Rational(-16, 4), - mapOf(x to 1u, iota to 1u) to Rational(4, 3), - mapOf(x to 2u, iota to 1u) to Rational(3, 8), - mapOf(y to 1u, iota to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u, iota to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u, iota to 1u) to Rational(6, 5), - mapOf(y to 2u, iota to 1u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u, iota to 1u) to Rational(13, 4), - mapOf(x to 2u, y to 2u, iota to 1u) to Rational(11, 8), - ), - iota * LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - "test 3" - ) - } - } - @Test - fun test_Polynomial_Variable_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(7, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) + x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(6, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) + y, - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - mapOf(iota to 1u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) + iota, - "test 3" - ) - } - } - @Test - fun test_Polynomial_Variable_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(1, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) - x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-8, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) - y, - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - mapOf(iota to 1u) to Rational(-1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) - iota, - "test 3" - ) - } - } - @Test - fun test_Polynomial_Variable_times() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-16, 4), - mapOf(x to 2u) to Rational(4, 3), - mapOf(x to 3u) to Rational(3, 8), - mapOf(x to 1u, y to 1u) to Rational(-1, 7), - mapOf(x to 2u, y to 1u) to Rational(-15, 3), - mapOf(x to 3u, y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 2u) to Rational(-13, 3), - mapOf(x to 2u, y to 2u) to Rational(13, 4), - mapOf(x to 3u, y to 2u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) * x, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(-16, 4), - mapOf(x to 1u, y to 1u) to Rational(4, 3), - mapOf(x to 2u, y to 1u) to Rational(3, 8), - mapOf(y to 2u) to Rational(-1, 7), - mapOf(x to 1u, y to 2u) to Rational(-15, 3), - mapOf(x to 2u, y to 2u) to Rational(6, 5), - mapOf(y to 3u) to Rational(-13, 3), - mapOf(x to 1u, y to 3u) to Rational(13, 4), - mapOf(x to 2u, y to 3u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) * y, - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(iota to 1u) to Rational(-16, 4), - mapOf(x to 1u, iota to 1u) to Rational(4, 3), - mapOf(x to 2u, iota to 1u) to Rational(3, 8), - mapOf(y to 1u, iota to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u, iota to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u, iota to 1u) to Rational(6, 5), - mapOf(y to 2u, iota to 1u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u, iota to 1u) to Rational(13, 4), - mapOf(x to 2u, y to 2u, iota to 1u) to Rational(11, 8), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-16, 4), - mapOf(x to 1u) to Rational(4, 3), - mapOf(x to 2u) to Rational(3, 8), - mapOf(y to 1u) to Rational(-1, 7), - mapOf(x to 1u, y to 1u) to Rational(-15, 3), - mapOf(x to 2u, y to 1u) to Rational(6, 5), - mapOf(y to 2u) to Rational(-13, 3), - mapOf(x to 1u, y to 2u) to Rational(13, 4), - mapOf(x to 2u, y to 2u) to Rational(11, 8), - ) * iota, - "test 3" - ) - } - } - @Test - fun test_Polynomial_unaryMinus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf(x to 5u) to Rational(-5, 9), - mapOf() to Rational(8, 9), - mapOf(iota to 13u) to Rational(8, 7), - ), - -LabeledPolynomial( - mapOf(x to 5u) to Rational(5, 9), - mapOf() to Rational(-8, 9), - mapOf(iota to 13u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf(x to 5u) to Rational(-5, 9), - mapOf() to Rational(8, 9), - mapOf(iota to 13u) to Rational(8, 7), - mapOf(x to 0u, y to 4u) to Rational(0), - mapOf(x to 5u) to Rational(0), - ), - -LabeledPolynomial( - mapOf(x to 5u) to Rational(5, 9), - mapOf() to Rational(-8, 9), - mapOf(iota to 13u) to Rational(-8, 7), - mapOf(x to 0u, y to 4u) to Rational(0), - mapOf(x to 5u) to Rational(0), - ), - "test 2" - ) - } - } - @Test - fun test_Polynomial_Polynomial_plus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-17, 2), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-25, 21), - mapOf(x to 0u, y to 1u) to Rational(146, 63), - mapOf(x to 1u, y to 1u) to Rational(-3, 5), - mapOf(x to 2u, y to 1u) to Rational(61, 15), - mapOf(x to 0u, y to 2u) to Rational(157, 63), - mapOf(x to 1u, y to 2u) to Rational(-55, 21), - mapOf(x to 2u, y to 2u) to Rational(11, 24), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(-7, 7), - mapOf(x to 2u, y to 1u) to Rational(12, 5), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) + LabeledPolynomial( - mapOf() to Rational(-20, 2), - mapOf(x to 1u) to Rational(0, 9), - mapOf(x to 2u) to Rational(-20, 7), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(7, 9), - mapOf(x to 1u, y to 2u) to Rational(5, 7), - mapOf(x to 2u, y to 2u) to Rational(-2, 3), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-17, 2), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-25, 21), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(157, 63), - mapOf(x to 1u, y to 2u) to Rational(-55, 21), - mapOf(x to 2u, y to 2u) to Rational(11, 24), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) + LabeledPolynomial( - mapOf() to Rational(-20, 2), - mapOf(x to 1u) to Rational(0, 9), - mapOf(x to 2u) to Rational(-20, 7), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(7, 9), - mapOf(x to 1u, y to 2u) to Rational(5, 7), - mapOf(x to 2u, y to 2u) to Rational(-2, 3), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-17, 2), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-25, 21), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) + LabeledPolynomial( - mapOf() to Rational(-20, 2), - mapOf(x to 1u) to Rational(0, 9), - mapOf(x to 2u) to Rational(-20, 7), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 0u, y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 0u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(-7, 7), - mapOf(x to 2u, y to 1u) to Rational(12, 5), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) + LabeledPolynomial( - mapOf() to Rational(-6, 4), - mapOf(x to 1u) to Rational(2, 6), - mapOf(x to 2u) to Rational(-10, 6), - mapOf(x to 0u, y to 1u) to Rational(-17, 7), - mapOf(x to 1u, y to 1u) to Rational(7, 7), - mapOf(x to 2u, y to 1u) to Rational(-12, 5), - mapOf(x to 0u, y to 2u) to Rational(-12, 7), - mapOf(x to 1u, y to 2u) to Rational(10, 3), - mapOf(x to 2u, y to 2u) to Rational(-9, 8), - ), - "test 4" - ) - } - } - @Test - fun test_Polynomial_Polynomial_minus() { - RationalField.labeledPolynomialSpace { - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-17, 2), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-25, 21), - mapOf(x to 0u, y to 1u) to Rational(146, 63), - mapOf(x to 1u, y to 1u) to Rational(-3, 5), - mapOf(x to 2u, y to 1u) to Rational(61, 15), - mapOf(x to 0u, y to 2u) to Rational(157, 63), - mapOf(x to 1u, y to 2u) to Rational(-55, 21), - mapOf(x to 2u, y to 2u) to Rational(11, 24), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(-7, 7), - mapOf(x to 2u, y to 1u) to Rational(12, 5), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) - LabeledPolynomial( - mapOf() to Rational(20, 2), - mapOf(x to 1u) to Rational(0, 9), - mapOf(x to 2u) to Rational(20, 7), - mapOf(x to 0u, y to 1u) to Rational(1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 5), - mapOf(x to 2u, y to 1u) to Rational(-10, 6), - mapOf(x to 0u, y to 2u) to Rational(-7, 9), - mapOf(x to 1u, y to 2u) to Rational(-5, 7), - mapOf(x to 2u, y to 2u) to Rational(2, 3), - ), - "test 1" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-17, 2), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-25, 21), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(157, 63), - mapOf(x to 1u, y to 2u) to Rational(-55, 21), - mapOf(x to 2u, y to 2u) to Rational(11, 24), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) - LabeledPolynomial( - mapOf() to Rational(20, 2), - mapOf(x to 1u) to Rational(0, 9), - mapOf(x to 2u) to Rational(20, 7), - mapOf(x to 0u, y to 1u) to Rational(1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 5), - mapOf(x to 2u, y to 1u) to Rational(-10, 6), - mapOf(x to 0u, y to 2u) to Rational(-7, 9), - mapOf(x to 1u, y to 2u) to Rational(-5, 7), - mapOf(x to 2u, y to 2u) to Rational(2, 3), - ), - "test 2" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(-17, 2), - mapOf(x to 1u) to Rational(-1, 3), - mapOf(x to 2u) to Rational(-25, 21), - mapOf(x to 0u, y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(2, 5), - mapOf(x to 2u, y to 1u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) - LabeledPolynomial( - mapOf() to Rational(20, 2), - mapOf(x to 1u) to Rational(0, 9), - mapOf(x to 2u) to Rational(20, 7), - mapOf(x to 0u, y to 1u) to Rational(1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 5), - mapOf(x to 2u, y to 1u) to Rational(-10, 6), - mapOf(x to 0u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - ), - "test 3" - ) - assertEquals( - LabeledPolynomial( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 0u, y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 0u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - ), - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(-7, 7), - mapOf(x to 2u, y to 1u) to Rational(12, 5), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ) - LabeledPolynomial( - mapOf() to Rational(6, 4), - mapOf(x to 1u) to Rational(-2, 6), - mapOf(x to 2u) to Rational(10, 6), - mapOf(x to 0u, y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(-7, 7), - mapOf(x to 2u, y to 1u) to Rational(12, 5), - mapOf(x to 0u, y to 2u) to Rational(12, 7), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(9, 8), - ), - "test 4" - ) - } - } - @Test - fun test_Polynomial_Polynomial_times() { - IntModuloRing(35).labeledPolynomialSpace { - // (p + q + r) * (p^2 + q^2 + r^2 - pq - pr - qr) = p^3 + q^3 + r^3 - 3pqr - assertEquals( - LabeledPolynomial( - mapOf(x to 3u) to m(1), - mapOf(x to 0u, y to 3u) to m(1), - mapOf(x to 0u, y to 0u, z to 3u) to m(1), - mapOf(x to 1u, y to 2u) to m(0), - mapOf(x to 0u, y to 1u, z to 2u) to m(0), - mapOf(x to 2u, y to 0u, z to 1u) to m(0), - mapOf(x to 1u, y to 0u, z to 2u) to m(0), - mapOf(x to 2u, y to 1u) to m(0), - mapOf(x to 0u, y to 2u, z to 1u) to m(0), - mapOf(x to 1u, y to 1u, z to 1u) to m(-3), - ), - LabeledPolynomial( - mapOf(x to 1u) to m(1), - mapOf(x to 0u, y to 1u) to m(1), - mapOf(x to 0u, y to 0u, z to 1u) to m(1), - ) * LabeledPolynomial( - mapOf(x to 2u) to m(1), - mapOf(x to 0u, y to 2u) to m(1), - mapOf(x to 0u, y to 0u, z to 2u) to m(1), - mapOf(x to 1u, y to 1u) to m(-1), - mapOf(x to 0u, y to 1u, z to 1u) to m(-1), - mapOf(x to 1u, y to 0u, z to 1u) to m(-1), - ), - "test 1" - ) - // Spoiler: 5 * 7 = 0 - assertEquals( - LabeledPolynomial( - mapOf(x to 2u) to m(0), - mapOf(x to 0u, y to 2u) to m(0), - mapOf(x to 0u, y to 0u, z to 2u) to m(0), - mapOf(x to 1u, y to 1u) to m(0), - mapOf(x to 0u, y to 1u, z to 1u) to m(0), - mapOf(x to 1u, y to 0u, z to 1u) to m(0), - ), - LabeledPolynomial( - mapOf(x to 1u) to m(5), - mapOf(x to 0u, y to 1u) to m(-25), - mapOf(x to 0u, y to 0u, z to 1u) to m(10), - ) * LabeledPolynomial( - mapOf(x to 1u) to m(21), - mapOf(x to 0u, y to 1u) to m(14), - mapOf(x to 0u, y to 0u, z to 1u) to m(-7), - ), - "test 2" - ) - } - } - @Test - fun test_degree() { - RationalField.labeledPolynomialSpace { - assertEquals( - -1, - LabeledPolynomial().degree, - "test 1" - ) - assertEquals( - 0, - LabeledPolynomial( - mapOf() to o - ).degree, - "test 2" - ) - assertEquals( - 6, - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ).degree, - "test 3" - ) - assertEquals( - 4, - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u, t to 1u, s to 0u) to o - ).degree, - "test 4" - ) - assertEquals( - 3, - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ).degree, - "test 5" - ) - assertEquals( - 4, - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ).degree, - "test 6" - ) - } - } - @Test - fun test_degrees() { - RationalField.labeledPolynomialSpace { - assertEquals( - mapOf(), - LabeledPolynomial().degrees, - "test 1" - ) - assertEquals( - mapOf(), - LabeledPolynomial( - mapOf() to o - ).degrees, - "test 2" - ) - assertEquals( - mapOf(x to 1u, y to 2u, z to 3u), - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ).degrees, - "test 3" - ) - assertEquals( - mapOf(y to 1u, z to 2u, t to 1u), - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u, t to 1u, s to 0u) to o - ).degrees, - "test 4" - ) - assertEquals( - mapOf(x to 2u, y to 1u, z to 1u), - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ).degrees, - "test 5" - ) - assertEquals( - mapOf(x to 2u, y to 2u, z to 2u, t to 4u), - LabeledPolynomial( - mapOf() to o, - mapOf(x to 1u, y to 2u) to o, - mapOf(x to 0u, y to 1u, z to 2u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ).degrees, - "test 6" - ) - } - } - @Test - fun test_degreeBy() { - RationalField.labeledPolynomialSpace { - fun LabeledPolynomial.collectDegrees(variables: Set = this.variables + iota): Map = variables.associateWith { degreeBy(it) } - assertEquals( - mapOf(iota to 0u), - LabeledPolynomial().collectDegrees(), - "test 1" - ) - assertEquals( - mapOf(iota to 0u), - LabeledPolynomial( - mapOf() to o - ).collectDegrees(), - "test 2" - ) - assertEquals( - mapOf(x to 1u, y to 2u, z to 3u, iota to 0u), - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ).collectDegrees(), - "test 3" - ) - assertEquals( - mapOf(y to 1u, z to 2u, t to 1u, iota to 0u), - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u, t to 1u, s to 0u) to o - ).collectDegrees(), - "test 4" - ) - assertEquals( - mapOf(x to 2u, y to 1u, z to 1u, iota to 0u), - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ).collectDegrees(), - "test 5" - ) - assertEquals( - mapOf(x to 2u, y to 2u, z to 2u, t to 4u, iota to 0u), - LabeledPolynomial( - mapOf() to o, - mapOf(x to 1u, y to 2u) to o, - mapOf(x to 0u, y to 1u, z to 2u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ).collectDegrees(), - "test 6" - ) - } - } - @Test - fun test_degreeBy_Collection() { - RationalField.labeledPolynomialSpace { - fun LabeledPolynomial.checkDegreeBy(message: String? = null) { - val variables = variables.toList() + iota - val variablesCollectionSequence: Sequence> = sequence { - val appearances = MutableList(variables.size) { 0 } - while (true) { - yield( - buildList { - for ((variableIndex, count) in appearances.withIndex()) repeat(count) { add(variables[variableIndex]) } - } - ) - val indexChange = appearances.indexOfFirst { it < 4 } - if (indexChange == -1) break - appearances[indexChange] += 1 - for (index in 0 until indexChange) appearances[index] = 0 - } - } - for (variablesCollection in variablesCollectionSequence) { - val expected = coefficients.keys.maxOfOrNull { degs -> degs.filterKeys { it in variablesCollection }.values.sum() } ?: 0u - val actual = degreeBy(variablesCollection) - if (actual != expected) - fail("${message ?: ""} Incorrect answer for variable collection $variablesCollection: expected $expected, actual $actual") - } - } - LabeledPolynomial().checkDegreeBy("test 1") - LabeledPolynomial( - mapOf() to o - ).checkDegreeBy("test 2") - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ).checkDegreeBy("test 3") - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u, t to 1u, s to 0u) to o - ).checkDegreeBy("test 4") - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ).checkDegreeBy("test 5") - LabeledPolynomial( - mapOf() to o, - mapOf(x to 1u, y to 2u) to o, - mapOf(x to 0u, y to 1u, z to 2u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ).checkDegreeBy("test 6") - } - } - @Test - fun test_variables() { - RationalField.labeledPolynomialSpace { - assertEquals( - setOf(), - LabeledPolynomial().variables, - "test 1" - ) - assertEquals( - setOf(), - LabeledPolynomial( - mapOf() to o - ).variables, - "test 2" - ) - assertEquals( - setOf(x, y, z), - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ).variables, - "test 3" - ) - assertEquals( - setOf(y, z, t), - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u, t to 1u, s to 0u) to o - ).variables, - "test 4" - ) - assertEquals( - setOf(x, y, z), - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ).variables, - "test 5" - ) - assertEquals( - setOf(x, y, z, t), - LabeledPolynomial( - mapOf() to o, - mapOf(x to 1u, y to 2u) to o, - mapOf(x to 0u, y to 1u, z to 2u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ).variables, - "test 6" - ) - } - } - @Test - fun test_countOfVariables() { - RationalField.labeledPolynomialSpace { - assertEquals( - 0, - LabeledPolynomial().countOfVariables, - "test 1" - ) - assertEquals( - 0, - LabeledPolynomial( - mapOf() to o - ).countOfVariables, - "test 2" - ) - assertEquals( - 3, - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ).countOfVariables, - "test 3" - ) - assertEquals( - 3, - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u, t to 1u, s to 0u) to o - ).countOfVariables, - "test 4" - ) - assertEquals( - 3, - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ).countOfVariables, - "test 5" - ) - assertEquals( - 4, - LabeledPolynomial( - mapOf() to o, - mapOf(x to 1u, y to 2u) to o, - mapOf(x to 0u, y to 1u, z to 2u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ).countOfVariables, - "test 6" - ) - } - } - @Test - fun test_RF_countOfVariables() { - RationalField.labeledRationalFunctionSpace { - assertEquals( - 0, - LabeledRationalFunction( - LabeledPolynomial() - ).countOfVariables, - "test 1" - ) - assertEquals( - 0, - LabeledRationalFunction( - LabeledPolynomial(), - LabeledPolynomial() - ).countOfVariables, - "test 2" - ) - assertEquals( - 0, - LabeledRationalFunction( - LabeledPolynomial( - mapOf() to o - ) - ).countOfVariables, - "test 3" - ) - assertEquals( - 3, - LabeledRationalFunction( - LabeledPolynomial( - mapOf(x to 1u, y to 2u, z to 3u) to o - ) - ).countOfVariables, - "test 4" - ) - assertEquals( - 3, - LabeledRationalFunction( - LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 0u, t to 1u) to o - ), - LabeledPolynomial( - mapOf(x to 0u, y to 0u, z to 2u) to o - ) - ).countOfVariables, - "test 5" - ) - assertEquals( - 3, - LabeledRationalFunction( - LabeledPolynomial( - mapOf() to o, - mapOf(x to 0u, y to 1u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ) - ).countOfVariables, - "test 6" - ) - assertEquals( - 4, - LabeledRationalFunction( - LabeledPolynomial( - mapOf() to o, - mapOf(x to 1u, y to 2u) to o, - mapOf(x to 2u, y to 0u, z to 1u) to o, - ), LabeledPolynomial( - mapOf(x to 0u, y to 1u, z to 2u) to o, - mapOf(x to 0u, y to 0u, z to 0u, t to 4u) to o, - ) - ).countOfVariables, - "test 7" - ) - } - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt deleted file mode 100644 index 637981b66..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt +++ /dev/null @@ -1,8222 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.functions.testUtils.assertEquals -import space.kscience.kmath.functions.testUtils.Rational -import space.kscience.kmath.functions.testUtils.RationalField -import space.kscience.kmath.functions.testUtils.iota -import space.kscience.kmath.functions.testUtils.x -import space.kscience.kmath.functions.testUtils.y -import space.kscience.kmath.misc.UnstableKMathAPI -import kotlin.test.Ignore -import kotlin.test.Test -import kotlin.test.assertEquals - -class LabeledPolynomialUtilTest { - @Test - fun test_Polynomial_substitute_Double() { - assertEquals( - LabeledPolynomialAsIs(emptyMap() to 0.0), - LabeledPolynomialAsIs( - mapOf() to 1.0, - mapOf(x to 1u) to -2.0, - mapOf(x to 2u) to 1.0, - ).substitute(mapOf( - x to 1.0 - )), - 0.001, - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf()), - 0.001, - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - iota to 0.9211194782050933 - )), - 0.001, - "test 2'" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(y to 2u) to 0.2700930201481795, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - x to 0.0 - )), - 0.001, - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(y to 2u) to 0.2700930201481795, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - x to 0.0, - iota to 0.9211194782050933 - )), - 0.001, - "test 3'" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 1.433510890645169, - mapOf(x to 1u) to 0.6264844682514724, - mapOf(x to 2u) to 0.8405727903771333, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - y to 0.8400458576651112 - )), - 0.001, - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 1.433510890645169, - mapOf(x to 1u) to 0.6264844682514724, - mapOf(x to 2u) to 0.8405727903771333, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - y to 0.8400458576651112, - iota to 0.9211194782050933 - )), - 0.001, - "test 4'" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 1.934530767358133, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - x to 0.4846192734143442, - y to 0.8400458576651112, - )), - 0.001, - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to 1.934530767358133, - ), - LabeledPolynomialAsIs( - mapOf() to 0.8597048543814783, - mapOf(x to 1u) to 0.22997637465889875, - mapOf(x to 2u) to 0.32675302591924016, - mapOf(y to 1u) to 0.4561746111587508, - mapOf(x to 1u, y to 1u) to 0.5304946210170756, - mapOf(x to 2u, y to 1u) to 0.6244313712888998, - mapOf(y to 2u) to 0.2700930201481795, - mapOf(x to 1u, y to 2u) to -0.06962351375204712, - mapOf(x to 2u, y to 2u) to -0.015206988092131501, - ).substitute(mapOf( - x to 0.4846192734143442, - y to 0.8400458576651112, - iota to 0.9211194782050933 - )), - 0.001, - "test 5'" - ) - } - @Test - fun test_Polynomial_substitute_Constant_Map() { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1) - ).substitute(RationalField, mapOf( - x to Rational(1) - )), - "test 1" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9 - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(143, 150) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to Rational(-2, 5), - y to Rational(12, 9), - )), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(143, 150) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to Rational(-2, 5), - y to Rational(12, 9), - iota to Rational(57, 179), - )), - "test 2'" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+y+%3D+12%2F9 - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-67, 18), - mapOf(x to 1u) to Rational(-70, 9), - mapOf(x to 2u) to Rational(88, 9), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - y to Rational(12, 9), - )), - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-67, 18), - mapOf(x to 1u) to Rational(-70, 9), - mapOf(x to 2u) to Rational(88, 9), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - y to Rational(12, 9), - iota to Rational(57, 179), - )), - "test 3'" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5 - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-83, 50), - mapOf(y to 1u) to Rational(29, 25), - mapOf(y to 2u) to Rational(3, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to Rational(-2, 5), - )), - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-83, 50), - mapOf(y to 1u) to Rational(29, 25), - mapOf(y to 2u) to Rational(3, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to Rational(-2, 5), - iota to Rational(57, 179), - )), - "test 4'" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf()), - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - iota to Rational(57, 179), - )), - "test 5'" - ) - // https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9 - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(47639065216, 2562890625) - ), - LabeledPolynomialAsIs( - mapOf(x to 8u) to Rational(-3, 2), - mapOf(x to 7u, y to 1u) to Rational(8, 6), - mapOf(x to 6u, y to 2u) to Rational(14, 6), - mapOf(x to 5u, y to 3u) to Rational(-3, 1), - mapOf(x to 4u, y to 4u) to Rational(-19, 2), - mapOf(x to 3u, y to 5u) to Rational(9, 4), - mapOf(x to 2u, y to 6u) to Rational(5, 5), - mapOf(x to 1u, y to 7u) to Rational(18, 9), - mapOf(y to 8u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to Rational(-2, 5), - y to Rational(12, 9), - )), - "test 6" - ) - } - @Test - fun test_Polynomial_substitute_Polynomial_Map() { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - )), - "test 1" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-5%2F1+s+%2B+2%2F8+t%2C+y+%3D+11%2F7+t - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(y to 1u) to Rational(-92, 21), - mapOf(y to 2u) to Rational(-2627, 2352), - mapOf(y to 3u) to Rational(4565, 3136), - mapOf(y to 4u) to Rational(605, 1568), - mapOf(x to 1u) to Rational(-20, 3), - mapOf(x to 1u, y to 1u) to Rational(1445, 21), - mapOf(x to 1u, y to 2u) to Rational(-13145, 392), - mapOf(x to 1u, y to 3u) to Rational(-3025, 196), - mapOf(x to 2u) to Rational(175, 3), - mapOf(x to 2u, y to 1u) to Rational(2475, 28), - mapOf(x to 2u, y to 2u) to Rational(15125, 98), - mapOf(x to 3u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-5, 1), - mapOf(y to 1u) to Rational(2, 8), - ), - y to LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(0, 5), - mapOf(y to 1u) to Rational(11, 7), - ), - )), - "test 2" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = (0/6 + 14/8 s + -14/2 s^2) + (-3/5 + 11/1 s + 3/7 s^2) t + (-3/7 + -18/5 s + -9/1 s^2) t^2, y = (-9/2 + 2/7 s + 9/1 s^2) + (13/1 + -1/8 s + 2/8 s^2) t + (19/4 + 15/7 s + -19/4 s^2) t^2 - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(129, 4), - mapOf(x to 1u) to Rational(48583, 336), - mapOf(x to 2u) to Rational(-913477, 1568), - mapOf(x to 3u) to Rational(-967567, 672), - mapOf(x to 4u) to Rational(4722043, 1344), - mapOf(x to 5u) to Rational(8855, 2), - mapOf(x to 6u) to Rational(-311971, 32), - mapOf(x to 7u) to Rational(-17325, 4), - mapOf(x to 8u) to Rational(19845, 2), - mapOf(y to 1u) to Rational(-827, 4), - mapOf(x to 1u, y to 1u) to Rational(191927, 840), - mapOf(x to 2u, y to 1u) to Rational(9592627, 2352), - mapOf(x to 3u, y to 1u) to Rational(-105400711, 53760), - mapOf(x to 4u, y to 1u) to Rational(-10054101459, 439040), - mapOf(x to 5u, y to 1u) to Rational(2127351, 128), - mapOf(x to 6u, y to 1u) to Rational(116680973, 3136), - mapOf(x to 7u, y to 1u) to Rational(-220445, 7), - mapOf(x to 8u, y to 1u) to Rational(-2655, 4), - mapOf(y to 2u) to Rational(30567, 100), - mapOf(x to 1u, y to 2u) to Rational(-156284953, 39200), - mapOf(x to 2u, y to 2u) to Rational(-57661541711, 6585600), - mapOf(x to 3u, y to 2u) to Rational(131931579, 3136), - mapOf(x to 4u, y to 2u) to Rational(98818124791, 3512320), - mapOf(x to 5u, y to 2u) to Rational(-94458855053, 878080), - mapOf(x to 6u, y to 2u) to Rational(13937705305, 1229312), - mapOf(x to 7u, y to 2u) to Rational(335706887, 21952), - mapOf(x to 8u, y to 2u) to Rational(23549165, 1568), - mapOf(y to 3u) to Rational(111367, 1400), - mapOf(x to 1u, y to 3u) to Rational(4937369, 700), - mapOf(x to 2u, y to 3u) to Rational(-4449423711, 274400), - mapOf(x to 3u, y to 3u) to Rational(-351873325703, 4390400), - mapOf(x to 4u, y to 3u) to Rational(23495875029, 307328), - mapOf(x to 5u, y to 3u) to Rational(17576300919, 878080), - mapOf(x to 6u, y to 3u) to Rational(230316993, 12544), - mapOf(x to 7u, y to 3u) to Rational(-191130515, 21952), - mapOf(x to 8u, y to 3u) to Rational(332435, 392), - mapOf(y to 4u) to Rational(-275084, 1225), - mapOf(x to 1u, y to 4u) to Rational(-266774603, 137200), - mapOf(x to 2u, y to 4u) to Rational(2176279167121, 30732800), - mapOf(x to 3u, y to 4u) to Rational(10904913303, 2195200), - mapOf(x to 4u, y to 4u) to Rational(-10769286147, 2195200), - mapOf(x to 5u, y to 4u) to Rational(-26277119793, 439040), - mapOf(x to 6u, y to 4u) to Rational(25859735869, 6146560), - mapOf(x to 7u, y to 4u) to Rational(38906289, 2744), - mapOf(x to 8u, y to 4u) to Rational(-3072025, 392), - mapOf(y to 5u) to Rational(9573, 98), - mapOf(x to 1u, y to 5u) to Rational(-4154651399, 548800), - mapOf(x to 2u, y to 5u) to Rational(3446069019, 548800), - mapOf(x to 3u, y to 5u) to Rational(-7851500623, 137200), - mapOf(x to 4u, y to 5u) to Rational(-53205142903, 1920800), - mapOf(x to 5u, y to 5u) to Rational(-31953611, 3430), - mapOf(x to 6u, y to 5u) to Rational(1447380313, 109760), - mapOf(x to 7u, y to 5u) to Rational(764158625, 21952), - mapOf(x to 8u, y to 5u) to Rational(1153515, 784), - mapOf(y to 6u) to Rational(1722351, 7840), - mapOf(x to 1u, y to 6u) to Rational(-164554821, 109760), - mapOf(x to 2u, y to 6u) to Rational(-79096147243, 7683200), - mapOf(x to 3u, y to 6u) to Rational(-624721089, 15680), - mapOf(x to 4u, y to 6u) to Rational(11147305567, 548800), - mapOf(x to 5u, y to 6u) to Rational(8318333679, 109760), - mapOf(x to 6u, y to 6u) to Rational(32981871553, 1536640), - mapOf(x to 7u, y to 6u) to Rational(-225359619, 21952), - mapOf(x to 8u, y to 6u) to Rational(-3973995, 392), - mapOf(y to 7u) to Rational(67203, 784), - mapOf(x to 1u, y to 7u) to Rational(39281469, 54880), - mapOf(x to 2u, y to 7u) to Rational(70162551, 27440), - mapOf(x to 3u, y to 7u) to Rational(413630709, 54880), - mapOf(x to 4u, y to 7u) to Rational(4640410269, 192080), - mapOf(x to 5u, y to 7u) to Rational(802712247, 54880), - mapOf(x to 6u, y to 7u) to Rational(-473517603, 27440), - mapOf(x to 7u, y to 7u) to Rational(-17055459, 1568), - mapOf(x to 8u, y to 7u) to Rational(-12825, 14), - mapOf(y to 8u) to Rational(16245, 1568), - mapOf(x to 1u, y to 8u) to Rational(503253, 2744), - mapOf(x to 2u, y to 8u) to Rational(125292591, 96040), - mapOf(x to 3u, y to 8u) to Rational(12033171, 2744), - mapOf(x to 4u, y to 8u) to Rational(154352673, 27440), - mapOf(x to 5u, y to 8u) to Rational(-1302291, 392), - mapOf(x to 6u, y to 8u) to Rational(-20265741, 1960), - mapOf(x to 7u, y to 8u) to Rational(-26163, 56), - mapOf(x to 8u, y to 8u) to Rational(146205, 32), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(0, 6), - mapOf(x to 1u) to Rational(14, 8), - mapOf(x to 2u) to Rational(-14, 2), - mapOf(y to 1u) to Rational(-3, 5), - mapOf(x to 1u, y to 1u) to Rational(11, 1), - mapOf(x to 2u, y to 1u) to Rational(3, 7), - mapOf(y to 2u) to Rational(-3, 7), - mapOf(x to 1u, y to 2u) to Rational(-18, 5), - mapOf(x to 2u, y to 2u) to Rational(-9, 1), - ), - y to LabeledPolynomialAsIs( - mapOf() to Rational(-9, 2), - mapOf(x to 1u) to Rational(2, 7), - mapOf(x to 2u) to Rational(9, 1), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-1, 8), - mapOf(x to 2u, y to 1u) to Rational(2, 8), - mapOf(y to 2u) to Rational(19, 4), - mapOf(x to 1u, y to 2u) to Rational(15, 7), - mapOf(x to 2u, y to 2u) to Rational(-19, 4), - ), - )), - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(129, 4), - mapOf(x to 1u) to Rational(48583, 336), - mapOf(x to 2u) to Rational(-913477, 1568), - mapOf(x to 3u) to Rational(-967567, 672), - mapOf(x to 4u) to Rational(4722043, 1344), - mapOf(x to 5u) to Rational(8855, 2), - mapOf(x to 6u) to Rational(-311971, 32), - mapOf(x to 7u) to Rational(-17325, 4), - mapOf(x to 8u) to Rational(19845, 2), - mapOf(y to 1u) to Rational(-827, 4), - mapOf(x to 1u, y to 1u) to Rational(191927, 840), - mapOf(x to 2u, y to 1u) to Rational(9592627, 2352), - mapOf(x to 3u, y to 1u) to Rational(-105400711, 53760), - mapOf(x to 4u, y to 1u) to Rational(-10054101459, 439040), - mapOf(x to 5u, y to 1u) to Rational(2127351, 128), - mapOf(x to 6u, y to 1u) to Rational(116680973, 3136), - mapOf(x to 7u, y to 1u) to Rational(-220445, 7), - mapOf(x to 8u, y to 1u) to Rational(-2655, 4), - mapOf(y to 2u) to Rational(30567, 100), - mapOf(x to 1u, y to 2u) to Rational(-156284953, 39200), - mapOf(x to 2u, y to 2u) to Rational(-57661541711, 6585600), - mapOf(x to 3u, y to 2u) to Rational(131931579, 3136), - mapOf(x to 4u, y to 2u) to Rational(98818124791, 3512320), - mapOf(x to 5u, y to 2u) to Rational(-94458855053, 878080), - mapOf(x to 6u, y to 2u) to Rational(13937705305, 1229312), - mapOf(x to 7u, y to 2u) to Rational(335706887, 21952), - mapOf(x to 8u, y to 2u) to Rational(23549165, 1568), - mapOf(y to 3u) to Rational(111367, 1400), - mapOf(x to 1u, y to 3u) to Rational(4937369, 700), - mapOf(x to 2u, y to 3u) to Rational(-4449423711, 274400), - mapOf(x to 3u, y to 3u) to Rational(-351873325703, 4390400), - mapOf(x to 4u, y to 3u) to Rational(23495875029, 307328), - mapOf(x to 5u, y to 3u) to Rational(17576300919, 878080), - mapOf(x to 6u, y to 3u) to Rational(230316993, 12544), - mapOf(x to 7u, y to 3u) to Rational(-191130515, 21952), - mapOf(x to 8u, y to 3u) to Rational(332435, 392), - mapOf(y to 4u) to Rational(-275084, 1225), - mapOf(x to 1u, y to 4u) to Rational(-266774603, 137200), - mapOf(x to 2u, y to 4u) to Rational(2176279167121, 30732800), - mapOf(x to 3u, y to 4u) to Rational(10904913303, 2195200), - mapOf(x to 4u, y to 4u) to Rational(-10769286147, 2195200), - mapOf(x to 5u, y to 4u) to Rational(-26277119793, 439040), - mapOf(x to 6u, y to 4u) to Rational(25859735869, 6146560), - mapOf(x to 7u, y to 4u) to Rational(38906289, 2744), - mapOf(x to 8u, y to 4u) to Rational(-3072025, 392), - mapOf(y to 5u) to Rational(9573, 98), - mapOf(x to 1u, y to 5u) to Rational(-4154651399, 548800), - mapOf(x to 2u, y to 5u) to Rational(3446069019, 548800), - mapOf(x to 3u, y to 5u) to Rational(-7851500623, 137200), - mapOf(x to 4u, y to 5u) to Rational(-53205142903, 1920800), - mapOf(x to 5u, y to 5u) to Rational(-31953611, 3430), - mapOf(x to 6u, y to 5u) to Rational(1447380313, 109760), - mapOf(x to 7u, y to 5u) to Rational(764158625, 21952), - mapOf(x to 8u, y to 5u) to Rational(1153515, 784), - mapOf(y to 6u) to Rational(1722351, 7840), - mapOf(x to 1u, y to 6u) to Rational(-164554821, 109760), - mapOf(x to 2u, y to 6u) to Rational(-79096147243, 7683200), - mapOf(x to 3u, y to 6u) to Rational(-624721089, 15680), - mapOf(x to 4u, y to 6u) to Rational(11147305567, 548800), - mapOf(x to 5u, y to 6u) to Rational(8318333679, 109760), - mapOf(x to 6u, y to 6u) to Rational(32981871553, 1536640), - mapOf(x to 7u, y to 6u) to Rational(-225359619, 21952), - mapOf(x to 8u, y to 6u) to Rational(-3973995, 392), - mapOf(y to 7u) to Rational(67203, 784), - mapOf(x to 1u, y to 7u) to Rational(39281469, 54880), - mapOf(x to 2u, y to 7u) to Rational(70162551, 27440), - mapOf(x to 3u, y to 7u) to Rational(413630709, 54880), - mapOf(x to 4u, y to 7u) to Rational(4640410269, 192080), - mapOf(x to 5u, y to 7u) to Rational(802712247, 54880), - mapOf(x to 6u, y to 7u) to Rational(-473517603, 27440), - mapOf(x to 7u, y to 7u) to Rational(-17055459, 1568), - mapOf(x to 8u, y to 7u) to Rational(-12825, 14), - mapOf(y to 8u) to Rational(16245, 1568), - mapOf(x to 1u, y to 8u) to Rational(503253, 2744), - mapOf(x to 2u, y to 8u) to Rational(125292591, 96040), - mapOf(x to 3u, y to 8u) to Rational(12033171, 2744), - mapOf(x to 4u, y to 8u) to Rational(154352673, 27440), - mapOf(x to 5u, y to 8u) to Rational(-1302291, 392), - mapOf(x to 6u, y to 8u) to Rational(-20265741, 1960), - mapOf(x to 7u, y to 8u) to Rational(-26163, 56), - mapOf(x to 8u, y to 8u) to Rational(146205, 32), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(0, 6), - mapOf(x to 1u) to Rational(14, 8), - mapOf(x to 2u) to Rational(-14, 2), - mapOf(y to 1u) to Rational(-3, 5), - mapOf(x to 1u, y to 1u) to Rational(11, 1), - mapOf(x to 2u, y to 1u) to Rational(3, 7), - mapOf(y to 2u) to Rational(-3, 7), - mapOf(x to 1u, y to 2u) to Rational(-18, 5), - mapOf(x to 2u, y to 2u) to Rational(-9, 1), - ), - y to LabeledPolynomialAsIs( - mapOf() to Rational(-9, 2), - mapOf(x to 1u) to Rational(2, 7), - mapOf(x to 2u) to Rational(9, 1), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-1, 8), - mapOf(x to 2u, y to 1u) to Rational(2, 8), - mapOf(y to 2u) to Rational(19, 4), - mapOf(x to 1u, y to 2u) to Rational(15, 7), - mapOf(x to 2u, y to 2u) to Rational(-19, 4), - ), - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-11, 3), - mapOf(x to 1u) to Rational(5, 2), - mapOf(x to 2u) to Rational(13, 7), - mapOf(y to 1u) to Rational(16, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(6, 1), - mapOf(y to 2u) to Rational(-14, 3), - mapOf(x to 1u, y to 2u) to Rational(-2, 7), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - )), - "test 3'" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = s, y = (-9/2 + 2/7 s + 9/1 s^2) + (13/1 + -1/8 s + 2/8 s^2) t + (19/4 + 15/7 s + -19/4 s^2) t^2 - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(129, 4), - mapOf(x to 1u) to Rational(6817, 84), - mapOf(x to 2u) to Rational(-21445, 294), - mapOf(x to 3u) to Rational(-12151, 49), - mapOf(x to 4u) to Rational(-17789, 196), - mapOf(x to 5u) to Rational(1224, 7), - mapOf(x to 6u) to Rational(405, 2), - mapOf(y to 1u) to Rational(-156), - mapOf(x to 1u, y to 1u) to Rational(-2440, 7), - mapOf(x to 2u, y to 1u) to Rational(-1571, 112), - mapOf(x to 3u, y to 1u) to Rational(107515, 224), - mapOf(x to 4u, y to 1u) to Rational(64965, 112), - mapOf(x to 5u, y to 1u) to Rational(209, 56), - mapOf(x to 6u, y to 1u) to Rational(45, 4), - mapOf(y to 2u) to Rational(112), - mapOf(x to 1u, y to 2u) to Rational(1449, 8), - mapOf(x to 2u, y to 2u) to Rational(1306309, 3136), - mapOf(x to 3u, y to 2u) to Rational(483207, 1568), - mapOf(x to 4u, y to 2u) to Rational(1978437, 6272), - mapOf(x to 5u, y to 2u) to Rational(-18231, 224), - mapOf(x to 6u, y to 2u) to Rational(-6835, 32), - mapOf(y to 3u) to Rational(247, 2), - mapOf(x to 1u, y to 3u) to Rational(33771, 112), - mapOf(x to 2u, y to 3u) to Rational(2073, 7), - mapOf(x to 3u, y to 3u) to Rational(-23463, 224), - mapOf(x to 4u, y to 3u) to Rational(-33825, 112), - mapOf(x to 5u, y to 3u) to Rational(201, 224), - mapOf(x to 6u, y to 3u) to Rational(-95, 16), - mapOf(y to 4u) to Rational(361, 16), - mapOf(x to 1u, y to 4u) to Rational(3667, 56), - mapOf(x to 2u, y to 4u) to Rational(88729, 1568), - mapOf(x to 3u, y to 4u) to Rational(-2476, 49), - mapOf(x to 4u, y to 4u) to Rational(-23419, 196), - mapOf(x to 5u, y to 4u) to Rational(-323, 56), - mapOf(x to 6u, y to 4u) to Rational(1805, 32), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - y to LabeledPolynomialAsIs( - mapOf() to Rational(-9, 2), - mapOf(x to 1u) to Rational(2, 7), - mapOf(x to 2u) to Rational(9, 1), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-1, 8), - mapOf(x to 2u, y to 1u) to Rational(2, 8), - mapOf(y to 2u) to Rational(19, 4), - mapOf(x to 1u, y to 2u) to Rational(15, 7), - mapOf(x to 2u, y to 2u) to Rational(-19, 4), - ), - )), - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(129, 4), - mapOf(x to 1u) to Rational(6817, 84), - mapOf(x to 2u) to Rational(-21445, 294), - mapOf(x to 3u) to Rational(-12151, 49), - mapOf(x to 4u) to Rational(-17789, 196), - mapOf(x to 5u) to Rational(1224, 7), - mapOf(x to 6u) to Rational(405, 2), - mapOf(y to 1u) to Rational(-156), - mapOf(x to 1u, y to 1u) to Rational(-2440, 7), - mapOf(x to 2u, y to 1u) to Rational(-1571, 112), - mapOf(x to 3u, y to 1u) to Rational(107515, 224), - mapOf(x to 4u, y to 1u) to Rational(64965, 112), - mapOf(x to 5u, y to 1u) to Rational(209, 56), - mapOf(x to 6u, y to 1u) to Rational(45, 4), - mapOf(y to 2u) to Rational(112), - mapOf(x to 1u, y to 2u) to Rational(1449, 8), - mapOf(x to 2u, y to 2u) to Rational(1306309, 3136), - mapOf(x to 3u, y to 2u) to Rational(483207, 1568), - mapOf(x to 4u, y to 2u) to Rational(1978437, 6272), - mapOf(x to 5u, y to 2u) to Rational(-18231, 224), - mapOf(x to 6u, y to 2u) to Rational(-6835, 32), - mapOf(y to 3u) to Rational(247, 2), - mapOf(x to 1u, y to 3u) to Rational(33771, 112), - mapOf(x to 2u, y to 3u) to Rational(2073, 7), - mapOf(x to 3u, y to 3u) to Rational(-23463, 224), - mapOf(x to 4u, y to 3u) to Rational(-33825, 112), - mapOf(x to 5u, y to 3u) to Rational(201, 224), - mapOf(x to 6u, y to 3u) to Rational(-95, 16), - mapOf(y to 4u) to Rational(361, 16), - mapOf(x to 1u, y to 4u) to Rational(3667, 56), - mapOf(x to 2u, y to 4u) to Rational(88729, 1568), - mapOf(x to 3u, y to 4u) to Rational(-2476, 49), - mapOf(x to 4u, y to 4u) to Rational(-23419, 196), - mapOf(x to 5u, y to 4u) to Rational(-323, 56), - mapOf(x to 6u, y to 4u) to Rational(1805, 32), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - y to LabeledPolynomialAsIs( - mapOf() to Rational(-9, 2), - mapOf(x to 1u) to Rational(2, 7), - mapOf(x to 2u) to Rational(9, 1), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-1, 8), - mapOf(x to 2u, y to 1u) to Rational(2, 8), - mapOf(y to 2u) to Rational(19, 4), - mapOf(x to 1u, y to 2u) to Rational(15, 7), - mapOf(x to 2u, y to 2u) to Rational(-19, 4), - ), - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-11, 3), - mapOf(x to 1u) to Rational(5, 2), - mapOf(x to 2u) to Rational(13, 7), - mapOf(y to 1u) to Rational(16, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(6, 1), - mapOf(y to 2u) to Rational(-14, 3), - mapOf(x to 1u, y to 2u) to Rational(-2, 7), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - )), - "test 4'" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = (0/6 + 14/8 s + -14/2 s^2) + (-3/5 + 11/1 s + 3/7 s^2) t + (-3/7 + -18/5 s + -9/1 s^2) t^2, y = t - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(7, 3), - mapOf(x to 2u) to Rational(-35, 16), - mapOf(x to 3u) to Rational(-343, 6), - mapOf(x to 4u) to Rational(343, 3), - mapOf(y to 1u) to Rational(-19, 5), - mapOf(x to 1u, y to 1u) to Rational(-823, 120), - mapOf(x to 2u, y to 1u) to Rational(1232417, 6720), - mapOf(x to 3u, y to 1u) to Rational(-9863, 24), - mapOf(x to 4u, y to 1u) to Rational(385, 4), - mapOf(y to 2u) to Rational(2439, 350), - mapOf(x to 1u, y to 2u) to Rational(-5793, 40), - mapOf(x to 2u, y to 2u) to Rational(1172113, 3360), - mapOf(x to 3u, y to 2u) to Rational(-13531, 40), - mapOf(x to 4u, y to 2u) to Rational(2824, 7), - mapOf(y to 3u) to Rational(3417, 700), - mapOf(x to 1u, y to 3u) to Rational(1191, 200), - mapOf(x to 2u, y to 3u) to Rational(8383, 28), - mapOf(x to 3u, y to 3u) to Rational(-220279, 280), - mapOf(x to 4u, y to 3u) to Rational(49179, 196), - mapOf(y to 4u) to Rational(57, 35), - mapOf(x to 1u, y to 4u) to Rational(-33771, 700), - mapOf(x to 2u, y to 4u) to Rational(196279, 1225), - mapOf(x to 3u, y to 4u) to Rational(-32259, 140), - mapOf(x to 4u, y to 4u) to Rational(23868, 49), - mapOf(y to 5u) to Rational(333, 196), - mapOf(x to 1u, y to 5u) to Rational(-204, 35), - mapOf(x to 2u, y to 5u) to Rational(-307233, 2450), - mapOf(x to 3u, y to 5u) to Rational(-12492, 35), - mapOf(x to 4u, y to 5u) to Rational(4563, 28), - mapOf(y to 6u) to Rational(45, 98), - mapOf(x to 1u, y to 6u) to Rational(54, 7), - mapOf(x to 2u, y to 6u) to Rational(1809, 35), - mapOf(x to 3u, y to 6u) to Rational(162), - mapOf(x to 4u, y to 6u) to Rational(405, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(0, 6), - mapOf(x to 1u) to Rational(14, 8), - mapOf(x to 2u) to Rational(-14, 2), - mapOf(y to 1u) to Rational(-3, 5), - mapOf(x to 1u, y to 1u) to Rational(11, 1), - mapOf(x to 2u, y to 1u) to Rational(3, 7), - mapOf(y to 2u) to Rational(-3, 7), - mapOf(x to 1u, y to 2u) to Rational(-18, 5), - mapOf(x to 2u, y to 2u) to Rational(-9, 1), - ), - )), - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(7, 3), - mapOf(x to 2u) to Rational(-35, 16), - mapOf(x to 3u) to Rational(-343, 6), - mapOf(x to 4u) to Rational(343, 3), - mapOf(y to 1u) to Rational(-19, 5), - mapOf(x to 1u, y to 1u) to Rational(-823, 120), - mapOf(x to 2u, y to 1u) to Rational(1232417, 6720), - mapOf(x to 3u, y to 1u) to Rational(-9863, 24), - mapOf(x to 4u, y to 1u) to Rational(385, 4), - mapOf(y to 2u) to Rational(2439, 350), - mapOf(x to 1u, y to 2u) to Rational(-5793, 40), - mapOf(x to 2u, y to 2u) to Rational(1172113, 3360), - mapOf(x to 3u, y to 2u) to Rational(-13531, 40), - mapOf(x to 4u, y to 2u) to Rational(2824, 7), - mapOf(y to 3u) to Rational(3417, 700), - mapOf(x to 1u, y to 3u) to Rational(1191, 200), - mapOf(x to 2u, y to 3u) to Rational(8383, 28), - mapOf(x to 3u, y to 3u) to Rational(-220279, 280), - mapOf(x to 4u, y to 3u) to Rational(49179, 196), - mapOf(y to 4u) to Rational(57, 35), - mapOf(x to 1u, y to 4u) to Rational(-33771, 700), - mapOf(x to 2u, y to 4u) to Rational(196279, 1225), - mapOf(x to 3u, y to 4u) to Rational(-32259, 140), - mapOf(x to 4u, y to 4u) to Rational(23868, 49), - mapOf(y to 5u) to Rational(333, 196), - mapOf(x to 1u, y to 5u) to Rational(-204, 35), - mapOf(x to 2u, y to 5u) to Rational(-307233, 2450), - mapOf(x to 3u, y to 5u) to Rational(-12492, 35), - mapOf(x to 4u, y to 5u) to Rational(4563, 28), - mapOf(y to 6u) to Rational(45, 98), - mapOf(x to 1u, y to 6u) to Rational(54, 7), - mapOf(x to 2u, y to 6u) to Rational(1809, 35), - mapOf(x to 3u, y to 6u) to Rational(162), - mapOf(x to 4u, y to 6u) to Rational(405, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(0, 6), - mapOf(x to 1u) to Rational(14, 8), - mapOf(x to 2u) to Rational(-14, 2), - mapOf(y to 1u) to Rational(-3, 5), - mapOf(x to 1u, y to 1u) to Rational(11, 1), - mapOf(x to 2u, y to 1u) to Rational(3, 7), - mapOf(y to 2u) to Rational(-3, 7), - mapOf(x to 1u, y to 2u) to Rational(-18, 5), - mapOf(x to 2u, y to 2u) to Rational(-9, 1), - ), - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-11, 3), - mapOf(x to 1u) to Rational(5, 2), - mapOf(x to 2u) to Rational(13, 7), - mapOf(y to 1u) to Rational(16, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(6, 1), - mapOf(y to 2u) to Rational(-14, 3), - mapOf(x to 1u, y to 2u) to Rational(-2, 7), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - )), - "test 5'" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 2), - mapOf(x to 1u) to Rational(8, 6), - mapOf(x to 2u) to Rational(14, 6), - mapOf(y to 1u) to Rational(-3, 1), - mapOf(x to 1u, y to 1u) to Rational(-19, 2), - mapOf(x to 2u, y to 1u) to Rational(9, 4), - mapOf(y to 2u) to Rational(5, 5), - mapOf(x to 1u, y to 2u) to Rational(18, 9), - mapOf(x to 2u, y to 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-11, 3), - mapOf(x to 1u) to Rational(5, 2), - mapOf(x to 2u) to Rational(13, 7), - mapOf(y to 1u) to Rational(16, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(6, 1), - mapOf(y to 2u) to Rational(-14, 3), - mapOf(x to 1u, y to 2u) to Rational(-2, 7), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - )), - "test 6'" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_Polynomial_substitute_RationalFunction_Map() { - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(0) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1) - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ) - )), - "test 1" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf(x to 4u) to Rational(-194071, 4900), - mapOf(x to 3u, y to 1u) to Rational(394811, 225), - mapOf(x to 2u, y to 2u) to Rational(-444183161, 66150), - mapOf(x to 1u, y to 3u) to Rational(70537618, 59535), - mapOf(y to 4u) to Rational(9655504, 2835), - ), - LabeledPolynomialAsIs( - mapOf(x to 4u) to Rational(9, 1), - mapOf(x to 3u, y to 1u) to Rational(61, 1), - mapOf(x to 2u, y to 2u) to Rational(2137, 36), - mapOf(x to 1u, y to 3u) to Rational(-1342, 9), - mapOf(y to 4u) to Rational(484, 9), - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(17, 7), - mapOf(y to 1u) to Rational(-13, 1), - ), - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-18, 6), - mapOf(y to 1u) to Rational(11, 6), - ) - ), - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(18, 5), - mapOf(y to 1u) to Rational(-16, 3), - ), - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-1, 1), - mapOf(y to 1u) to Rational(-4, 1), - ) - ), - )), - "test 2" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-6443599, 10000), - mapOf(x to 1u) to Rational(166251223, 210000), - mapOf(x to 2u) to Rational(-4606805099, 3528000), - mapOf(x to 3u) to Rational(51204379, 19600), - mapOf(x to 4u) to Rational(-529045460659, 277830000), - mapOf(x to 5u) to Rational(2630836709, 1488375), - mapOf(x to 6u) to Rational(-42675691369, 25004700), - mapOf(x to 7u) to Rational(495825223, 1250235), - mapOf(x to 8u) to Rational(-22531756, 1750329), - mapOf(y to 1u) to Rational(-2526552797, 420000), - mapOf(x to 1u, y to 1u) to Rational(31108840471, 2520000), - mapOf(x to 2u, y to 1u) to Rational(-4789740847, 1102500), - mapOf(x to 3u, y to 1u) to Rational(186594307807, 11340000), - mapOf(x to 4u, y to 1u) to Rational(-11677815943, 1488375), - mapOf(x to 5u, y to 1u) to Rational(-181118486447, 27783000), - mapOf(x to 6u, y to 1u) to Rational(-16123292162, 14586075), - mapOf(x to 7u, y to 1u) to Rational(-140339343808, 26254935), - mapOf(x to 8u, y to 1u) to Rational(4570171616, 5250987), - mapOf(y to 2u) to Rational(-181436530573, 10080000), - mapOf(x to 1u, y to 2u) to Rational(6700437957491, 105840000), - mapOf(x to 2u, y to 2u) to Rational(-3527267461, 1417500), - mapOf(x to 3u, y to 2u) to Rational(-38084563451, 5556600), - mapOf(x to 4u, y to 2u) to Rational(-565662040631, 13891500), - mapOf(x to 5u, y to 2u) to Rational(-35479071126397, 583443000), - mapOf(x to 6u, y to 2u) to Rational(-11717559078469, 525098700), - mapOf(x to 7u, y to 2u) to Rational(-2043385293517, 225042300), - mapOf(x to 8u, y to 2u) to Rational(-3644439630451, 551353635), - mapOf(y to 3u) to Rational(-1760423269, 126000), - mapOf(x to 1u, y to 3u) to Rational(310176758299, 2352000), - mapOf(x to 2u, y to 3u) to Rational(-907229584837, 21168000), - mapOf(x to 3u, y to 3u) to Rational(-16717135885963, 95256000), - mapOf(x to 4u, y to 3u) to Rational(-43762928025353, 333396000), - mapOf(x to 5u, y to 3u) to Rational(-328427480571607, 3000564000), - mapOf(x to 6u, y to 3u) to Rational(-7722675917197, 210039480), - mapOf(x to 7u, y to 3u) to Rational(1713350137019, 1225230300), - mapOf(x to 8u, y to 3u) to Rational(156695935643, 31505922), - mapOf(y to 4u) to Rational(18362364269, 1008000), - mapOf(x to 1u, y to 4u) to Rational(955674858553, 10584000), - mapOf(x to 2u, y to 4u) to Rational(-71937470607371, 444528000), - mapOf(x to 3u, y to 4u) to Rational(-34097985615163, 95256000), - mapOf(x to 4u, y to 4u) to Rational(-340736178775883, 2000376000), - mapOf(x to 5u, y to 4u) to Rational(-511324523441897, 10501974000), - mapOf(x to 6u, y to 4u) to Rational(-125375649409151, 8821658160), - mapOf(x to 7u, y to 4u) to Rational(-2813518533421, 1575296100), - mapOf(x to 8u, y to 4u) to Rational(-17044089109, 5250987), - mapOf(y to 5u) to Rational(600086461, 20160), - mapOf(x to 1u, y to 5u) to Rational(-18959931367, 423360), - mapOf(x to 2u, y to 5u) to Rational(-9178804929607, 44452800), - mapOf(x to 3u, y to 5u) to Rational(-1460114275979, 5334336), - mapOf(x to 4u, y to 5u) to Rational(-342533479090169, 4200789600), - mapOf(x to 5u, y to 5u) to Rational(20335453022963, 4200789600), - mapOf(x to 6u, y to 5u) to Rational(-21649775090197, 6301184400), - mapOf(x to 7u, y to 5u) to Rational(-197301716069, 131274675), - mapOf(x to 8u, y to 5u) to Rational(18711357470, 15752961), - mapOf(y to 6u) to Rational(621417991, 100800), - mapOf(x to 1u, y to 6u) to Rational(-159236792977, 2116800), - mapOf(x to 2u, y to 6u) to Rational(-6602528890883, 66679200), - mapOf(x to 3u, y to 6u) to Rational(-1086091664047, 19051200), - mapOf(x to 4u, y to 6u) to Rational(3769375009003, 1680315840), - mapOf(x to 5u, y to 6u) to Rational(-12920385574769, 1050197400), - mapOf(x to 6u, y to 6u) to Rational(-90219591809287, 6301184400), - mapOf(x to 7u, y to 6u) to Rational(656361553391, 1575296100), - mapOf(x to 8u, y to 6u) to Rational(757900793, 2250423), - mapOf(y to 7u) to Rational(-100770017, 15120), - mapOf(x to 1u, y to 7u) to Rational(-316364851, 17640), - mapOf(x to 2u, y to 7u) to Rational(-85118560057, 6667920), - mapOf(x to 3u, y to 7u) to Rational(6286563719, 416745), - mapOf(x to 4u, y to 7u) to Rational(26803885301, 1714608), - mapOf(x to 5u, y to 7u) to Rational(-13767154393, 4286520), - mapOf(x to 6u, y to 7u) to Rational(-3875138933, 1224720), - mapOf(x to 7u, y to 7u) to Rational(65193755, 333396), - mapOf(x to 8u, y to 7u) to Rational(90974351, 2500470), - mapOf(y to 8u) to Rational(-3182197, 1260), - mapOf(x to 1u, y to 8u) to Rational(24899923, 8820), - mapOf(x to 2u, y to 8u) to Rational(-19999556, 19845), - mapOf(x to 3u, y to 8u) to Rational(3276587, 3969), - mapOf(x to 4u, y to 8u) to Rational(13719549239, 5000940), - mapOf(x to 5u, y to 8u) to Rational(-961839938, 1250235), - mapOf(x to 6u, y to 8u) to Rational(-198184871, 833490), - mapOf(x to 7u, y to 8u) to Rational(230659711, 5000940), - mapOf(x to 8u, y to 8u) to Rational(292447, 35721) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(9, 100), - mapOf(x to 1u) to Rational(-21, 50), - mapOf(x to 2u) to Rational(293, 700), - mapOf(x to 3u) to Rational(29, 210), - mapOf(x to 4u) to Rational(3233, 8820), - mapOf(x to 5u) to Rational(-289, 441), - mapOf(x to 6u) to Rational(-1, 9), - mapOf(x to 7u) to Rational(-20, 441), - mapOf(x to 8u) to Rational(100, 441), - mapOf(y to 1u) to Rational(-57, 80), - mapOf(x to 1u, y to 1u) to Rational(-121, 400), - mapOf(x to 2u, y to 1u) to Rational(37117, 8400), - mapOf(x to 3u, y to 1u) to Rational(-4853, 3150), - mapOf(x to 4u, y to 1u) to Rational(1166203, 132300), - mapOf(x to 5u, y to 1u) to Rational(-2708, 567), - mapOf(x to 6u, y to 1u) to Rational(-287159, 416745), - mapOf(x to 7u, y to 1u) to Rational(-478204, 83349), - mapOf(x to 8u, y to 1u) to Rational(176320, 83349), - mapOf(y to 2u) to Rational(-6239, 6400), - mapOf(x to 1u, y to 2u) to Rational(264211, 11200), - mapOf(x to 2u, y to 2u) to Rational(-1591999, 100800), - mapOf(x to 3u, y to 2u) to Rational(12450091, 529200), - mapOf(x to 4u, y to 2u) to Rational(9230759, 226800), - mapOf(x to 5u, y to 2u) to Rational(18995554, 2083725), - mapOf(x to 6u, y to 2u) to Rational(136706258, 6251175), - mapOf(x to 7u, y to 2u) to Rational(-120907496, 3750705), - mapOf(x to 8u, y to 2u) to Rational(117200176, 15752961), - mapOf(y to 3u) to Rational(5653, 320), - mapOf(x to 1u, y to 3u) to Rational(-130853, 8400), - mapOf(x to 2u, y to 3u) to Rational(-20939327, 151200), - mapOf(x to 3u, y to 3u) to Rational(2566691, 25200), - mapOf(x to 4u, y to 3u) to Rational(-68441519, 476280), - mapOf(x to 5u, y to 3u) to Rational(2462904247, 12502350), - mapOf(x to 6u, y to 3u) to Rational(353667161, 18753525), - mapOf(x to 7u, y to 3u) to Rational(-1689134372, 26254935), - mapOf(x to 8u, y to 3u) to Rational(35084104, 2250423), - mapOf(y to 4u) to Rational(-3587, 300), - mapOf(x to 1u, y to 4u) to Rational(-10513243, 33600), - mapOf(x to 2u, y to 4u) to Rational(30766733, 176400), - mapOf(x to 3u, y to 4u) to Rational(-65680021, 198450), - mapOf(x to 4u, y to 4u) to Rational(-8108910547, 20003760), - mapOf(x to 5u, y to 4u) to Rational(2922125159, 6251175), - mapOf(x to 6u, y to 4u) to Rational(-4245279943, 131274675), - mapOf(x to 7u, y to 4u) to Rational(-371946872, 3750705), - mapOf(x to 8u, y to 4u) to Rational(61286752, 2250423), - mapOf(y to 5u) to Rational(-20477, 160), - mapOf(x to 1u, y to 5u) to Rational(215741, 1120), - mapOf(x to 2u, y to 5u) to Rational(30785843, 31752), - mapOf(x to 3u, y to 5u) to Rational(-357495959, 317520), - mapOf(x to 4u, y to 5u) to Rational(-1611242993, 10001880), - mapOf(x to 5u, y to 5u) to Rational(345925495, 500094), - mapOf(x to 6u, y to 5u) to Rational(-755948411, 3750705), - mapOf(x to 7u, y to 5u) to Rational(-108643496, 1250235), - mapOf(x to 8u, y to 5u) to Rational(1122512, 35721), - mapOf(y to 6u) to Rational(358037, 2880), - mapOf(x to 1u, y to 6u) to Rational(3895837, 3360), - mapOf(x to 2u, y to 6u) to Rational(359419201, 1270080), - mapOf(x to 3u, y to 6u) to Rational(-158522587, 105840), - mapOf(x to 4u, y to 6u) to Rational(10909002599, 20003760), - mapOf(x to 5u, y to 6u) to Rational(76846972, 138915), - mapOf(x to 6u, y to 6u) to Rational(-327696553, 1250235), - mapOf(x to 7u, y to 6u) to Rational(-1687328, 35721), - mapOf(x to 8u, y to 6u) to Rational(1016836, 35721), - mapOf(y to 7u) to Rational(658, 3), - mapOf(x to 1u, y to 7u) to Rational(48035, 168), - mapOf(x to 2u, y to 7u) to Rational(-5777875, 5292), - mapOf(x to 3u, y to 7u) to Rational(-7893899, 10584), - mapOf(x to 4u, y to 7u) to Rational(10191652, 11907), - mapOf(x to 5u, y to 7u) to Rational(2920121, 23814), - mapOf(x to 6u, y to 7u) to Rational(-2699780, 11907), - mapOf(x to 7u, y to 7u) to Rational(4556, 441), - mapOf(x to 8u, y to 7u) to Rational(3440, 189), - mapOf(y to 8u) to Rational(64, 1), - mapOf(x to 1u, y to 8u) to Rational(-808, 7), - mapOf(x to 2u, y to 8u) to Rational(-360895, 1764), - mapOf(x to 3u, y to 8u) to Rational(257657, 882), - mapOf(x to 4u, y to 8u) to Rational(3779917, 15876), - mapOf(x to 5u, y to 8u) to Rational(-610279, 3969), - mapOf(x to 6u, y to 8u) to Rational(-25091, 441), - mapOf(x to 7u, y to 8u) to Rational(9560, 567), - mapOf(x to 8u, y to 8u) to Rational(400, 81) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(17, 5), - mapOf(x to 1u) to Rational(11, 6), - mapOf(x to 2u) to Rational(14, 3), - mapOf(y to 1u) to Rational(17, 1), - mapOf(x to 1u, y to 1u) to Rational(12, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 2), - mapOf(y to 2u) to Rational(17, 1), - mapOf(x to 1u, y to 2u) to Rational(-4, 3), - mapOf(x to 2u, y to 2u) to Rational(2, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(3, 5), - mapOf(x to 1u) to Rational(3, 5), - mapOf(x to 2u) to Rational(3, 7), - mapOf(y to 1u) to Rational(-3, 8), - mapOf(x to 1u, y to 1u) to Rational(-1, 1), - mapOf(x to 2u, y to 1u) to Rational(17, 9), - mapOf(y to 2u) to Rational(-8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 4), - mapOf(x to 2u, y to 2u) to Rational(10, 9), - ) - ), - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(18, 5), - mapOf(x to 1u) to Rational(-17, 5), - mapOf(x to 2u) to Rational(-2, 7), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(-5, 1), - mapOf(x to 2u, y to 1u) to Rational(-9, 1), - mapOf(y to 2u) to Rational(-8, 8), - mapOf(x to 1u, y to 2u) to Rational(2, 7), - mapOf(x to 2u, y to 2u) to Rational(-13, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-4, 8), - mapOf(x to 1u) to Rational(15, 9), - mapOf(x to 2u) to Rational(-10, 9), - mapOf(y to 1u) to Rational(5, 3), - mapOf(x to 1u, y to 1u) to Rational(4, 1), - mapOf(x to 2u, y to 1u) to Rational(-2, 7), - mapOf(y to 2u) to Rational(2, 2), - mapOf(x to 1u, y to 2u) to Rational(-5, 7), - mapOf(x to 2u, y to 2u) to Rational(-18, 9), - ) - ), - )), - "test 3" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-6443599, 10000), - mapOf(x to 1u) to Rational(166251223, 210000), - mapOf(x to 2u) to Rational(-4606805099, 3528000), - mapOf(x to 3u) to Rational(51204379, 19600), - mapOf(x to 4u) to Rational(-529045460659, 277830000), - mapOf(x to 5u) to Rational(2630836709, 1488375), - mapOf(x to 6u) to Rational(-42675691369, 25004700), - mapOf(x to 7u) to Rational(495825223, 1250235), - mapOf(x to 8u) to Rational(-22531756, 1750329), - mapOf(y to 1u) to Rational(-2526552797, 420000), - mapOf(x to 1u, y to 1u) to Rational(31108840471, 2520000), - mapOf(x to 2u, y to 1u) to Rational(-4789740847, 1102500), - mapOf(x to 3u, y to 1u) to Rational(186594307807, 11340000), - mapOf(x to 4u, y to 1u) to Rational(-11677815943, 1488375), - mapOf(x to 5u, y to 1u) to Rational(-181118486447, 27783000), - mapOf(x to 6u, y to 1u) to Rational(-16123292162, 14586075), - mapOf(x to 7u, y to 1u) to Rational(-140339343808, 26254935), - mapOf(x to 8u, y to 1u) to Rational(4570171616, 5250987), - mapOf(y to 2u) to Rational(-181436530573, 10080000), - mapOf(x to 1u, y to 2u) to Rational(6700437957491, 105840000), - mapOf(x to 2u, y to 2u) to Rational(-3527267461, 1417500), - mapOf(x to 3u, y to 2u) to Rational(-38084563451, 5556600), - mapOf(x to 4u, y to 2u) to Rational(-565662040631, 13891500), - mapOf(x to 5u, y to 2u) to Rational(-35479071126397, 583443000), - mapOf(x to 6u, y to 2u) to Rational(-11717559078469, 525098700), - mapOf(x to 7u, y to 2u) to Rational(-2043385293517, 225042300), - mapOf(x to 8u, y to 2u) to Rational(-3644439630451, 551353635), - mapOf(y to 3u) to Rational(-1760423269, 126000), - mapOf(x to 1u, y to 3u) to Rational(310176758299, 2352000), - mapOf(x to 2u, y to 3u) to Rational(-907229584837, 21168000), - mapOf(x to 3u, y to 3u) to Rational(-16717135885963, 95256000), - mapOf(x to 4u, y to 3u) to Rational(-43762928025353, 333396000), - mapOf(x to 5u, y to 3u) to Rational(-328427480571607, 3000564000), - mapOf(x to 6u, y to 3u) to Rational(-7722675917197, 210039480), - mapOf(x to 7u, y to 3u) to Rational(1713350137019, 1225230300), - mapOf(x to 8u, y to 3u) to Rational(156695935643, 31505922), - mapOf(y to 4u) to Rational(18362364269, 1008000), - mapOf(x to 1u, y to 4u) to Rational(955674858553, 10584000), - mapOf(x to 2u, y to 4u) to Rational(-71937470607371, 444528000), - mapOf(x to 3u, y to 4u) to Rational(-34097985615163, 95256000), - mapOf(x to 4u, y to 4u) to Rational(-340736178775883, 2000376000), - mapOf(x to 5u, y to 4u) to Rational(-511324523441897, 10501974000), - mapOf(x to 6u, y to 4u) to Rational(-125375649409151, 8821658160), - mapOf(x to 7u, y to 4u) to Rational(-2813518533421, 1575296100), - mapOf(x to 8u, y to 4u) to Rational(-17044089109, 5250987), - mapOf(y to 5u) to Rational(600086461, 20160), - mapOf(x to 1u, y to 5u) to Rational(-18959931367, 423360), - mapOf(x to 2u, y to 5u) to Rational(-9178804929607, 44452800), - mapOf(x to 3u, y to 5u) to Rational(-1460114275979, 5334336), - mapOf(x to 4u, y to 5u) to Rational(-342533479090169, 4200789600), - mapOf(x to 5u, y to 5u) to Rational(20335453022963, 4200789600), - mapOf(x to 6u, y to 5u) to Rational(-21649775090197, 6301184400), - mapOf(x to 7u, y to 5u) to Rational(-197301716069, 131274675), - mapOf(x to 8u, y to 5u) to Rational(18711357470, 15752961), - mapOf(y to 6u) to Rational(621417991, 100800), - mapOf(x to 1u, y to 6u) to Rational(-159236792977, 2116800), - mapOf(x to 2u, y to 6u) to Rational(-6602528890883, 66679200), - mapOf(x to 3u, y to 6u) to Rational(-1086091664047, 19051200), - mapOf(x to 4u, y to 6u) to Rational(3769375009003, 1680315840), - mapOf(x to 5u, y to 6u) to Rational(-12920385574769, 1050197400), - mapOf(x to 6u, y to 6u) to Rational(-90219591809287, 6301184400), - mapOf(x to 7u, y to 6u) to Rational(656361553391, 1575296100), - mapOf(x to 8u, y to 6u) to Rational(757900793, 2250423), - mapOf(y to 7u) to Rational(-100770017, 15120), - mapOf(x to 1u, y to 7u) to Rational(-316364851, 17640), - mapOf(x to 2u, y to 7u) to Rational(-85118560057, 6667920), - mapOf(x to 3u, y to 7u) to Rational(6286563719, 416745), - mapOf(x to 4u, y to 7u) to Rational(26803885301, 1714608), - mapOf(x to 5u, y to 7u) to Rational(-13767154393, 4286520), - mapOf(x to 6u, y to 7u) to Rational(-3875138933, 1224720), - mapOf(x to 7u, y to 7u) to Rational(65193755, 333396), - mapOf(x to 8u, y to 7u) to Rational(90974351, 2500470), - mapOf(y to 8u) to Rational(-3182197, 1260), - mapOf(x to 1u, y to 8u) to Rational(24899923, 8820), - mapOf(x to 2u, y to 8u) to Rational(-19999556, 19845), - mapOf(x to 3u, y to 8u) to Rational(3276587, 3969), - mapOf(x to 4u, y to 8u) to Rational(13719549239, 5000940), - mapOf(x to 5u, y to 8u) to Rational(-961839938, 1250235), - mapOf(x to 6u, y to 8u) to Rational(-198184871, 833490), - mapOf(x to 7u, y to 8u) to Rational(230659711, 5000940), - mapOf(x to 8u, y to 8u) to Rational(292447, 35721) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(9, 100), - mapOf(x to 1u) to Rational(-21, 50), - mapOf(x to 2u) to Rational(293, 700), - mapOf(x to 3u) to Rational(29, 210), - mapOf(x to 4u) to Rational(3233, 8820), - mapOf(x to 5u) to Rational(-289, 441), - mapOf(x to 6u) to Rational(-1, 9), - mapOf(x to 7u) to Rational(-20, 441), - mapOf(x to 8u) to Rational(100, 441), - mapOf(y to 1u) to Rational(-57, 80), - mapOf(x to 1u, y to 1u) to Rational(-121, 400), - mapOf(x to 2u, y to 1u) to Rational(37117, 8400), - mapOf(x to 3u, y to 1u) to Rational(-4853, 3150), - mapOf(x to 4u, y to 1u) to Rational(1166203, 132300), - mapOf(x to 5u, y to 1u) to Rational(-2708, 567), - mapOf(x to 6u, y to 1u) to Rational(-287159, 416745), - mapOf(x to 7u, y to 1u) to Rational(-478204, 83349), - mapOf(x to 8u, y to 1u) to Rational(176320, 83349), - mapOf(y to 2u) to Rational(-6239, 6400), - mapOf(x to 1u, y to 2u) to Rational(264211, 11200), - mapOf(x to 2u, y to 2u) to Rational(-1591999, 100800), - mapOf(x to 3u, y to 2u) to Rational(12450091, 529200), - mapOf(x to 4u, y to 2u) to Rational(9230759, 226800), - mapOf(x to 5u, y to 2u) to Rational(18995554, 2083725), - mapOf(x to 6u, y to 2u) to Rational(136706258, 6251175), - mapOf(x to 7u, y to 2u) to Rational(-120907496, 3750705), - mapOf(x to 8u, y to 2u) to Rational(117200176, 15752961), - mapOf(y to 3u) to Rational(5653, 320), - mapOf(x to 1u, y to 3u) to Rational(-130853, 8400), - mapOf(x to 2u, y to 3u) to Rational(-20939327, 151200), - mapOf(x to 3u, y to 3u) to Rational(2566691, 25200), - mapOf(x to 4u, y to 3u) to Rational(-68441519, 476280), - mapOf(x to 5u, y to 3u) to Rational(2462904247, 12502350), - mapOf(x to 6u, y to 3u) to Rational(353667161, 18753525), - mapOf(x to 7u, y to 3u) to Rational(-1689134372, 26254935), - mapOf(x to 8u, y to 3u) to Rational(35084104, 2250423), - mapOf(y to 4u) to Rational(-3587, 300), - mapOf(x to 1u, y to 4u) to Rational(-10513243, 33600), - mapOf(x to 2u, y to 4u) to Rational(30766733, 176400), - mapOf(x to 3u, y to 4u) to Rational(-65680021, 198450), - mapOf(x to 4u, y to 4u) to Rational(-8108910547, 20003760), - mapOf(x to 5u, y to 4u) to Rational(2922125159, 6251175), - mapOf(x to 6u, y to 4u) to Rational(-4245279943, 131274675), - mapOf(x to 7u, y to 4u) to Rational(-371946872, 3750705), - mapOf(x to 8u, y to 4u) to Rational(61286752, 2250423), - mapOf(y to 5u) to Rational(-20477, 160), - mapOf(x to 1u, y to 5u) to Rational(215741, 1120), - mapOf(x to 2u, y to 5u) to Rational(30785843, 31752), - mapOf(x to 3u, y to 5u) to Rational(-357495959, 317520), - mapOf(x to 4u, y to 5u) to Rational(-1611242993, 10001880), - mapOf(x to 5u, y to 5u) to Rational(345925495, 500094), - mapOf(x to 6u, y to 5u) to Rational(-755948411, 3750705), - mapOf(x to 7u, y to 5u) to Rational(-108643496, 1250235), - mapOf(x to 8u, y to 5u) to Rational(1122512, 35721), - mapOf(y to 6u) to Rational(358037, 2880), - mapOf(x to 1u, y to 6u) to Rational(3895837, 3360), - mapOf(x to 2u, y to 6u) to Rational(359419201, 1270080), - mapOf(x to 3u, y to 6u) to Rational(-158522587, 105840), - mapOf(x to 4u, y to 6u) to Rational(10909002599, 20003760), - mapOf(x to 5u, y to 6u) to Rational(76846972, 138915), - mapOf(x to 6u, y to 6u) to Rational(-327696553, 1250235), - mapOf(x to 7u, y to 6u) to Rational(-1687328, 35721), - mapOf(x to 8u, y to 6u) to Rational(1016836, 35721), - mapOf(y to 7u) to Rational(658, 3), - mapOf(x to 1u, y to 7u) to Rational(48035, 168), - mapOf(x to 2u, y to 7u) to Rational(-5777875, 5292), - mapOf(x to 3u, y to 7u) to Rational(-7893899, 10584), - mapOf(x to 4u, y to 7u) to Rational(10191652, 11907), - mapOf(x to 5u, y to 7u) to Rational(2920121, 23814), - mapOf(x to 6u, y to 7u) to Rational(-2699780, 11907), - mapOf(x to 7u, y to 7u) to Rational(4556, 441), - mapOf(x to 8u, y to 7u) to Rational(3440, 189), - mapOf(y to 8u) to Rational(64, 1), - mapOf(x to 1u, y to 8u) to Rational(-808, 7), - mapOf(x to 2u, y to 8u) to Rational(-360895, 1764), - mapOf(x to 3u, y to 8u) to Rational(257657, 882), - mapOf(x to 4u, y to 8u) to Rational(3779917, 15876), - mapOf(x to 5u, y to 8u) to Rational(-610279, 3969), - mapOf(x to 6u, y to 8u) to Rational(-25091, 441), - mapOf(x to 7u, y to 8u) to Rational(9560, 567), - mapOf(x to 8u, y to 8u) to Rational(400, 81) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(17, 5), - mapOf(x to 1u) to Rational(11, 6), - mapOf(x to 2u) to Rational(14, 3), - mapOf(y to 1u) to Rational(17, 1), - mapOf(x to 1u, y to 1u) to Rational(12, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 2), - mapOf(y to 2u) to Rational(17, 1), - mapOf(x to 1u, y to 2u) to Rational(-4, 3), - mapOf(x to 2u, y to 2u) to Rational(2, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(3, 5), - mapOf(x to 1u) to Rational(3, 5), - mapOf(x to 2u) to Rational(3, 7), - mapOf(y to 1u) to Rational(-3, 8), - mapOf(x to 1u, y to 1u) to Rational(-1, 1), - mapOf(x to 2u, y to 1u) to Rational(17, 9), - mapOf(y to 2u) to Rational(-8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 4), - mapOf(x to 2u, y to 2u) to Rational(10, 9), - ) - ), - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(18, 5), - mapOf(x to 1u) to Rational(-17, 5), - mapOf(x to 2u) to Rational(-2, 7), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(-5, 1), - mapOf(x to 2u, y to 1u) to Rational(-9, 1), - mapOf(y to 2u) to Rational(-8, 8), - mapOf(x to 1u, y to 2u) to Rational(2, 7), - mapOf(x to 2u, y to 2u) to Rational(-13, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-4, 8), - mapOf(x to 1u) to Rational(15, 9), - mapOf(x to 2u) to Rational(-10, 9), - mapOf(y to 1u) to Rational(5, 3), - mapOf(x to 1u, y to 1u) to Rational(4, 1), - mapOf(x to 2u, y to 1u) to Rational(-2, 7), - mapOf(y to 2u) to Rational(2, 2), - mapOf(x to 1u, y to 2u) to Rational(-5, 7), - mapOf(x to 2u, y to 2u) to Rational(-18, 9), - ) - ), - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-2, 9), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(10, 9), - mapOf(y to 1u) to Rational(13, 3), - mapOf(x to 1u, y to 1u) to Rational(-12, 4), - mapOf(x to 2u, y to 1u) to Rational(3, 6), - mapOf(y to 2u) to Rational(2, 9), - mapOf(x to 1u, y to 2u) to Rational(7, 3), - mapOf(x to 2u, y to 2u) to Rational(16, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 2), - mapOf(x to 1u) to Rational(6, 2), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 5), - mapOf(y to 2u) to Rational(8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(17, 4), - ) - ) - )), - "test 3'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-66677, 3500), - mapOf(x to 1u) to Rational(-206281, 10500), - mapOf(x to 2u) to Rational(-412567, 7056), - mapOf(x to 3u) to Rational(-310081, 11025), - mapOf(x to 4u) to Rational(-575996, 15435), - mapOf(y to 1u) to Rational(-573701, 4200), - mapOf(x to 1u, y to 1u) to Rational(-2239001, 25200), - mapOf(x to 2u, y to 1u) to Rational(-8817889, 132300), - mapOf(x to 3u, y to 1u) to Rational(2317919, 44100), - mapOf(x to 4u, y to 1u) to Rational(1169471, 6615), - mapOf(y to 2u) to Rational(-4057819, 33600), - mapOf(x to 1u, y to 2u) to Rational(1373311, 12600), - mapOf(x to 2u, y to 2u) to Rational(32433493, 52920), - mapOf(x to 3u, y to 2u) to Rational(4998053, 33075), - mapOf(x to 4u, y to 2u) to Rational(-2147779, 8820), - mapOf(y to 3u) to Rational(2018481, 2240), - mapOf(x to 1u, y to 3u) to Rational(941713, 1440), - mapOf(x to 2u, y to 3u) to Rational(183749, 6615), - mapOf(x to 3u, y to 3u) to Rational(-4631023, 15876), - mapOf(x to 4u, y to 3u) to Rational(25609336, 178605), - mapOf(y to 4u) to Rational(11886431, 6720), - mapOf(x to 1u, y to 4u) to Rational(18433, 504), - mapOf(x to 2u, y to 4u) to Rational(-39613331, 45360), - mapOf(x to 3u, y to 4u) to Rational(681619, 5670), - mapOf(x to 4u, y to 4u) to Rational(-864841, 20412), - mapOf(y to 5u) to Rational(343535, 1008), - mapOf(x to 1u, y to 5u) to Rational(-33583, 72), - mapOf(x to 2u, y to 5u) to Rational(1194625, 9072), - mapOf(x to 3u, y to 5u) to Rational(-62917, 2268), - mapOf(x to 4u, y to 5u) to Rational(157645, 10206), - mapOf(y to 6u) to Rational(-1381, 3), - mapOf(x to 1u, y to 6u) to Rational(919, 36), - mapOf(x to 2u, y to 6u) to Rational(-3053, 36), - mapOf(x to 3u, y to 6u) to Rational(2125, 324), - mapOf(x to 4u, y to 6u) to Rational(-236, 243) - ), - LabeledPolynomialAsIs(mapOf() to Rational(0, 1), - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-5, 3), - mapOf(x to 2u) to Rational(35, 9), - mapOf(x to 3u) to Rational(-100, 27), - mapOf(x to 4u) to Rational(100, 81), - mapOf(y to 1u) to Rational(-5, 3), - mapOf(x to 1u, y to 1u) to Rational(14, 9), - mapOf(x to 2u, y to 1u) to Rational(1874, 189), - mapOf(x to 3u, y to 1u) to Rational(-620, 63), - mapOf(x to 4u, y to 1u) to Rational(40, 63), - mapOf(y to 2u) to Rational(16, 9), - mapOf(x to 1u, y to 2u) to Rational(365, 21), - mapOf(x to 2u, y to 2u) to Rational(112, 9), - mapOf(x to 3u, y to 2u) to Rational(-464, 63), - mapOf(x to 4u, y to 2u) to Rational(1996, 441), - mapOf(y to 3u) to Rational(10, 3), - mapOf(x to 1u, y to 3u) to Rational(118, 21), - mapOf(x to 2u, y to 3u) to Rational(-272, 21), - mapOf(x to 3u, y to 3u) to Rational(-764, 49), - mapOf(x to 4u, y to 3u) to Rational(8, 7), - mapOf(y to 4u) to Rational(1, 1), - mapOf(x to 1u, y to 4u) to Rational(-10, 7), - mapOf(x to 2u, y to 4u) to Rational(-171, 49), - mapOf(x to 3u, y to 4u) to Rational(20, 7), - mapOf(x to 4u, y to 4u) to Rational(4, 1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(17, 5), - mapOf(x to 1u) to Rational(11, 6), - mapOf(x to 2u) to Rational(14, 3), - mapOf(y to 1u) to Rational(17, 1), - mapOf(x to 1u, y to 1u) to Rational(12, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 2), - mapOf(y to 2u) to Rational(17, 1), - mapOf(x to 1u, y to 2u) to Rational(-4, 3), - mapOf(x to 2u, y to 2u) to Rational(2, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(3, 5), - mapOf(x to 1u) to Rational(3, 5), - mapOf(x to 2u) to Rational(3, 7), - mapOf(y to 1u) to Rational(-3, 8), - mapOf(x to 1u, y to 1u) to Rational(-1, 1), - mapOf(x to 2u, y to 1u) to Rational(17, 9), - mapOf(y to 2u) to Rational(-8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 4), - mapOf(x to 2u, y to 2u) to Rational(10, 9), - ) - ), - )), - "test 4" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-66677, 3500), - mapOf(x to 1u) to Rational(-206281, 10500), - mapOf(x to 2u) to Rational(-412567, 7056), - mapOf(x to 3u) to Rational(-310081, 11025), - mapOf(x to 4u) to Rational(-575996, 15435), - mapOf(y to 1u) to Rational(-573701, 4200), - mapOf(x to 1u, y to 1u) to Rational(-2239001, 25200), - mapOf(x to 2u, y to 1u) to Rational(-8817889, 132300), - mapOf(x to 3u, y to 1u) to Rational(2317919, 44100), - mapOf(x to 4u, y to 1u) to Rational(1169471, 6615), - mapOf(y to 2u) to Rational(-4057819, 33600), - mapOf(x to 1u, y to 2u) to Rational(1373311, 12600), - mapOf(x to 2u, y to 2u) to Rational(32433493, 52920), - mapOf(x to 3u, y to 2u) to Rational(4998053, 33075), - mapOf(x to 4u, y to 2u) to Rational(-2147779, 8820), - mapOf(y to 3u) to Rational(2018481, 2240), - mapOf(x to 1u, y to 3u) to Rational(941713, 1440), - mapOf(x to 2u, y to 3u) to Rational(183749, 6615), - mapOf(x to 3u, y to 3u) to Rational(-4631023, 15876), - mapOf(x to 4u, y to 3u) to Rational(25609336, 178605), - mapOf(y to 4u) to Rational(11886431, 6720), - mapOf(x to 1u, y to 4u) to Rational(18433, 504), - mapOf(x to 2u, y to 4u) to Rational(-39613331, 45360), - mapOf(x to 3u, y to 4u) to Rational(681619, 5670), - mapOf(x to 4u, y to 4u) to Rational(-864841, 20412), - mapOf(y to 5u) to Rational(343535, 1008), - mapOf(x to 1u, y to 5u) to Rational(-33583, 72), - mapOf(x to 2u, y to 5u) to Rational(1194625, 9072), - mapOf(x to 3u, y to 5u) to Rational(-62917, 2268), - mapOf(x to 4u, y to 5u) to Rational(157645, 10206), - mapOf(y to 6u) to Rational(-1381, 3), - mapOf(x to 1u, y to 6u) to Rational(919, 36), - mapOf(x to 2u, y to 6u) to Rational(-3053, 36), - mapOf(x to 3u, y to 6u) to Rational(2125, 324), - mapOf(x to 4u, y to 6u) to Rational(-236, 243) - ), - LabeledPolynomialAsIs(mapOf() to Rational(0, 1), - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-5, 3), - mapOf(x to 2u) to Rational(35, 9), - mapOf(x to 3u) to Rational(-100, 27), - mapOf(x to 4u) to Rational(100, 81), - mapOf(y to 1u) to Rational(-5, 3), - mapOf(x to 1u, y to 1u) to Rational(14, 9), - mapOf(x to 2u, y to 1u) to Rational(1874, 189), - mapOf(x to 3u, y to 1u) to Rational(-620, 63), - mapOf(x to 4u, y to 1u) to Rational(40, 63), - mapOf(y to 2u) to Rational(16, 9), - mapOf(x to 1u, y to 2u) to Rational(365, 21), - mapOf(x to 2u, y to 2u) to Rational(112, 9), - mapOf(x to 3u, y to 2u) to Rational(-464, 63), - mapOf(x to 4u, y to 2u) to Rational(1996, 441), - mapOf(y to 3u) to Rational(10, 3), - mapOf(x to 1u, y to 3u) to Rational(118, 21), - mapOf(x to 2u, y to 3u) to Rational(-272, 21), - mapOf(x to 3u, y to 3u) to Rational(-764, 49), - mapOf(x to 4u, y to 3u) to Rational(8, 7), - mapOf(y to 4u) to Rational(1, 1), - mapOf(x to 1u, y to 4u) to Rational(-10, 7), - mapOf(x to 2u, y to 4u) to Rational(-171, 49), - mapOf(x to 3u, y to 4u) to Rational(20, 7), - mapOf(x to 4u, y to 4u) to Rational(4, 1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(17, 5), - mapOf(x to 1u) to Rational(11, 6), - mapOf(x to 2u) to Rational(14, 3), - mapOf(y to 1u) to Rational(17, 1), - mapOf(x to 1u, y to 1u) to Rational(12, 3), - mapOf(x to 2u, y to 1u) to Rational(-6, 2), - mapOf(y to 2u) to Rational(17, 1), - mapOf(x to 1u, y to 2u) to Rational(-4, 3), - mapOf(x to 2u, y to 2u) to Rational(2, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(3, 5), - mapOf(x to 1u) to Rational(3, 5), - mapOf(x to 2u) to Rational(3, 7), - mapOf(y to 1u) to Rational(-3, 8), - mapOf(x to 1u, y to 1u) to Rational(-1, 1), - mapOf(x to 2u, y to 1u) to Rational(17, 9), - mapOf(y to 2u) to Rational(-8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 4), - mapOf(x to 2u, y to 2u) to Rational(10, 9), - ) - ), - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-2, 9), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(10, 9), - mapOf(y to 1u) to Rational(13, 3), - mapOf(x to 1u, y to 1u) to Rational(-12, 4), - mapOf(x to 2u, y to 1u) to Rational(3, 6), - mapOf(y to 2u) to Rational(2, 9), - mapOf(x to 1u, y to 2u) to Rational(7, 3), - mapOf(x to 2u, y to 2u) to Rational(16, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 2), - mapOf(x to 1u) to Rational(6, 2), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 5), - mapOf(y to 2u) to Rational(8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(17, 4), - ) - ) - )), - "test 4'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(3539, 700), - mapOf(x to 1u) to Rational(-307079, 6300), - mapOf(x to 2u) to Rational(451609, 15120), - mapOf(x to 3u) to Rational(35287733, 396900), - mapOf(x to 4u) to Rational(-37242617, 396900), - mapOf(x to 5u) to Rational(382747, 19845), - mapOf(x to 6u) to Rational(-2407, 3969), - mapOf(y to 1u) to Rational(-226, 175), - mapOf(x to 1u, y to 1u) to Rational(-74113, 1890), - mapOf(x to 2u, y to 1u) to Rational(250931, 1764), - mapOf(x to 3u, y to 1u) to Rational(30071473, 99225), - mapOf(x to 4u, y to 1u) to Rational(-286466, 1323), - mapOf(x to 5u, y to 1u) to Rational(-2285282, 9261), - mapOf(x to 6u, y to 1u) to Rational(17900, 441), - mapOf(y to 2u) to Rational(3817, 3150), - mapOf(x to 1u, y to 2u) to Rational(577568, 11025), - mapOf(x to 2u, y to 2u) to Rational(9073553, 99225), - mapOf(x to 3u, y to 2u) to Rational(-1415849, 79380), - mapOf(x to 4u, y to 2u) to Rational(-124715629, 277830), - mapOf(x to 5u, y to 2u) to Rational(-1328953, 1890), - mapOf(x to 6u, y to 2u) to Rational(-297148, 1323), - mapOf(y to 3u) to Rational(6043, 945), - mapOf(x to 1u, y to 3u) to Rational(160381, 6615), - mapOf(x to 2u, y to 3u) to Rational(-673249, 13230), - mapOf(x to 3u, y to 3u) to Rational(-319255, 2058), - mapOf(x to 4u, y to 3u) to Rational(-98144, 1029), - mapOf(x to 5u, y to 3u) to Rational(-320239, 5145), - mapOf(x to 6u, y to 3u) to Rational(400, 147), - mapOf(y to 4u) to Rational(163, 63), - mapOf(x to 1u, y to 4u) to Rational(-25183, 4410), - mapOf(x to 2u, y to 4u) to Rational(-21369, 1372), - mapOf(x to 3u, y to 4u) to Rational(127499, 30870), - mapOf(x to 4u, y to 4u) to Rational(86971, 12348), - mapOf(x to 5u, y to 4u) to Rational(-11129, 1470), - mapOf(x to 6u, y to 4u) to Rational(544, 147) - ), - LabeledPolynomialAsIs(mapOf() to Rational(0, 1), - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-5, 3), - mapOf(x to 2u) to Rational(35, 9), - mapOf(x to 3u) to Rational(-100, 27), - mapOf(x to 4u) to Rational(100, 81), - mapOf(y to 1u) to Rational(-5, 3), - mapOf(x to 1u, y to 1u) to Rational(14, 9), - mapOf(x to 2u, y to 1u) to Rational(1874, 189), - mapOf(x to 3u, y to 1u) to Rational(-620, 63), - mapOf(x to 4u, y to 1u) to Rational(40, 63), - mapOf(y to 2u) to Rational(16, 9), - mapOf(x to 1u, y to 2u) to Rational(365, 21), - mapOf(x to 2u, y to 2u) to Rational(112, 9), - mapOf(x to 3u, y to 2u) to Rational(-464, 63), - mapOf(x to 4u, y to 2u) to Rational(1996, 441), - mapOf(y to 3u) to Rational(10, 3), - mapOf(x to 1u, y to 3u) to Rational(118, 21), - mapOf(x to 2u, y to 3u) to Rational(-272, 21), - mapOf(x to 3u, y to 3u) to Rational(-764, 49), - mapOf(x to 4u, y to 3u) to Rational(8, 7), - mapOf(y to 4u) to Rational(1, 1), - mapOf(x to 1u, y to 4u) to Rational(-10, 7), - mapOf(x to 2u, y to 4u) to Rational(-171, 49), - mapOf(x to 3u, y to 4u) to Rational(20, 7), - mapOf(x to 4u, y to 4u) to Rational(4, 1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(18, 5), - mapOf(x to 1u) to Rational(-17, 5), - mapOf(x to 2u) to Rational(-2, 7), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(-5, 1), - mapOf(x to 2u, y to 1u) to Rational(-9, 1), - mapOf(y to 2u) to Rational(-8, 8), - mapOf(x to 1u, y to 2u) to Rational(2, 7), - mapOf(x to 2u, y to 2u) to Rational(-13, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-4, 8), - mapOf(x to 1u) to Rational(15, 9), - mapOf(x to 2u) to Rational(-10, 9), - mapOf(y to 1u) to Rational(5, 3), - mapOf(x to 1u, y to 1u) to Rational(4, 1), - mapOf(x to 2u, y to 1u) to Rational(-2, 7), - mapOf(y to 2u) to Rational(2, 2), - mapOf(x to 1u, y to 2u) to Rational(-5, 7), - mapOf(x to 2u, y to 2u) to Rational(-18, 9), - ) - ), - )), - "test 5" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(3539, 700), - mapOf(x to 1u) to Rational(-307079, 6300), - mapOf(x to 2u) to Rational(451609, 15120), - mapOf(x to 3u) to Rational(35287733, 396900), - mapOf(x to 4u) to Rational(-37242617, 396900), - mapOf(x to 5u) to Rational(382747, 19845), - mapOf(x to 6u) to Rational(-2407, 3969), - mapOf(y to 1u) to Rational(-226, 175), - mapOf(x to 1u, y to 1u) to Rational(-74113, 1890), - mapOf(x to 2u, y to 1u) to Rational(250931, 1764), - mapOf(x to 3u, y to 1u) to Rational(30071473, 99225), - mapOf(x to 4u, y to 1u) to Rational(-286466, 1323), - mapOf(x to 5u, y to 1u) to Rational(-2285282, 9261), - mapOf(x to 6u, y to 1u) to Rational(17900, 441), - mapOf(y to 2u) to Rational(3817, 3150), - mapOf(x to 1u, y to 2u) to Rational(577568, 11025), - mapOf(x to 2u, y to 2u) to Rational(9073553, 99225), - mapOf(x to 3u, y to 2u) to Rational(-1415849, 79380), - mapOf(x to 4u, y to 2u) to Rational(-124715629, 277830), - mapOf(x to 5u, y to 2u) to Rational(-1328953, 1890), - mapOf(x to 6u, y to 2u) to Rational(-297148, 1323), - mapOf(y to 3u) to Rational(6043, 945), - mapOf(x to 1u, y to 3u) to Rational(160381, 6615), - mapOf(x to 2u, y to 3u) to Rational(-673249, 13230), - mapOf(x to 3u, y to 3u) to Rational(-319255, 2058), - mapOf(x to 4u, y to 3u) to Rational(-98144, 1029), - mapOf(x to 5u, y to 3u) to Rational(-320239, 5145), - mapOf(x to 6u, y to 3u) to Rational(400, 147), - mapOf(y to 4u) to Rational(163, 63), - mapOf(x to 1u, y to 4u) to Rational(-25183, 4410), - mapOf(x to 2u, y to 4u) to Rational(-21369, 1372), - mapOf(x to 3u, y to 4u) to Rational(127499, 30870), - mapOf(x to 4u, y to 4u) to Rational(86971, 12348), - mapOf(x to 5u, y to 4u) to Rational(-11129, 1470), - mapOf(x to 6u, y to 4u) to Rational(544, 147) - ), - LabeledPolynomialAsIs(mapOf() to Rational(0, 1), - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-5, 3), - mapOf(x to 2u) to Rational(35, 9), - mapOf(x to 3u) to Rational(-100, 27), - mapOf(x to 4u) to Rational(100, 81), - mapOf(y to 1u) to Rational(-5, 3), - mapOf(x to 1u, y to 1u) to Rational(14, 9), - mapOf(x to 2u, y to 1u) to Rational(1874, 189), - mapOf(x to 3u, y to 1u) to Rational(-620, 63), - mapOf(x to 4u, y to 1u) to Rational(40, 63), - mapOf(y to 2u) to Rational(16, 9), - mapOf(x to 1u, y to 2u) to Rational(365, 21), - mapOf(x to 2u, y to 2u) to Rational(112, 9), - mapOf(x to 3u, y to 2u) to Rational(-464, 63), - mapOf(x to 4u, y to 2u) to Rational(1996, 441), - mapOf(y to 3u) to Rational(10, 3), - mapOf(x to 1u, y to 3u) to Rational(118, 21), - mapOf(x to 2u, y to 3u) to Rational(-272, 21), - mapOf(x to 3u, y to 3u) to Rational(-764, 49), - mapOf(x to 4u, y to 3u) to Rational(8, 7), - mapOf(y to 4u) to Rational(1, 1), - mapOf(x to 1u, y to 4u) to Rational(-10, 7), - mapOf(x to 2u, y to 4u) to Rational(-171, 49), - mapOf(x to 3u, y to 4u) to Rational(20, 7), - mapOf(x to 4u, y to 4u) to Rational(4, 1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(18, 5), - mapOf(x to 1u) to Rational(-17, 5), - mapOf(x to 2u) to Rational(-2, 7), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(-5, 1), - mapOf(x to 2u, y to 1u) to Rational(-9, 1), - mapOf(y to 2u) to Rational(-8, 8), - mapOf(x to 1u, y to 2u) to Rational(2, 7), - mapOf(x to 2u, y to 2u) to Rational(-13, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-4, 8), - mapOf(x to 1u) to Rational(15, 9), - mapOf(x to 2u) to Rational(-10, 9), - mapOf(y to 1u) to Rational(5, 3), - mapOf(x to 1u, y to 1u) to Rational(4, 1), - mapOf(x to 2u, y to 1u) to Rational(-2, 7), - mapOf(y to 2u) to Rational(2, 2), - mapOf(x to 1u, y to 2u) to Rational(-5, 7), - mapOf(x to 2u, y to 2u) to Rational(-18, 9), - ) - ), - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-2, 9), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(10, 9), - mapOf(y to 1u) to Rational(13, 3), - mapOf(x to 1u, y to 1u) to Rational(-12, 4), - mapOf(x to 2u, y to 1u) to Rational(3, 6), - mapOf(y to 2u) to Rational(2, 9), - mapOf(x to 1u, y to 2u) to Rational(7, 3), - mapOf(x to 2u, y to 2u) to Rational(16, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 2), - mapOf(x to 1u) to Rational(6, 2), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 5), - mapOf(y to 2u) to Rational(8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(17, 4), - ) - ) - )), - "test 5'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ), - LabeledPolynomialAsIs(mapOf() to Rational(0, 1), - mapOf() to Rational(0, 1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ), - LabeledPolynomialAsIs(mapOf() to Rational(0, 1), - mapOf() to Rational(0, 1) - ) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(15, 7), - mapOf(x to 1u) to Rational(1, 5), - mapOf(x to 2u) to Rational(-7, 4), - mapOf(y to 1u) to Rational(-1, 9), - mapOf(x to 1u, y to 1u) to Rational(-2, 7), - mapOf(x to 2u, y to 1u) to Rational(17, 3), - mapOf(y to 2u) to Rational(2, 6), - mapOf(x to 1u, y to 2u) to Rational(-17, 6), - mapOf(x to 2u, y to 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-2, 9), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(10, 9), - mapOf(y to 1u) to Rational(13, 3), - mapOf(x to 1u, y to 1u) to Rational(-12, 4), - mapOf(x to 2u, y to 1u) to Rational(3, 6), - mapOf(y to 2u) to Rational(2, 9), - mapOf(x to 1u, y to 2u) to Rational(7, 3), - mapOf(x to 2u, y to 2u) to Rational(16, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 2), - mapOf(x to 1u) to Rational(6, 2), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 5), - mapOf(y to 2u) to Rational(8, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(17, 4), - ) - ) - )), - "test 6'" - ) - } - @Test - fun test_RationalFunction_substitute_Double_Map() { - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs(emptyMap() to 0.0), - LabeledPolynomialAsIs(emptyMap() to 1.0), - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 1.0, - mapOf(x to 1u) to -2.0, - mapOf(x to 2u) to 1.0, - ), - LabeledPolynomialAsIs( - mapOf() to 1.0, - ) - ).substitute(mapOf( - x to 1.0 - )), - 0.001, - "test 1" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf()), - 0.001, - "test 2" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - iota to 0.9211194782050933 - )), - 0.001, - "test 2'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 151.1502229133916, - mapOf(y to 1u) to -262.3790170577034, - mapOf(y to 2u) to 102.5097937392923, - ), - LabeledPolynomialAsIs( - mapOf() to -367.9969733169944, - mapOf(y to 1u) to 112.4911133334554, - mapOf(y to 2u) to -469.755906895345, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - x to -8.11707689492641, - )), - 0.001, - "test 3" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 151.1502229133916, - mapOf(y to 1u) to -262.3790170577034, - mapOf(y to 2u) to 102.5097937392923, - ), - LabeledPolynomialAsIs( - mapOf() to -367.9969733169944, - mapOf(y to 1u) to 112.4911133334554, - mapOf(y to 2u) to -469.755906895345, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - x to -8.11707689492641, - iota to 0.9211194782050933 - )), - 0.001, - "test 3'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 14.24074356896978, - mapOf(x to 1u) to -17.71987055153461, - mapOf(x to 2u) to -2.288056483312383, - ), - LabeledPolynomialAsIs( - mapOf() to 7.480604285873397, - mapOf(x to 1u) to -8.43478016688617, - mapOf(x to 2u) to -9.88934943900592, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - y to 0.795265651276015, - )), - 0.001, - "test 4" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 14.24074356896978, - mapOf(x to 1u) to -17.71987055153461, - mapOf(x to 2u) to -2.288056483312383, - ), - LabeledPolynomialAsIs( - mapOf() to 7.480604285873397, - mapOf(x to 1u) to -8.43478016688617, - mapOf(x to 2u) to -9.88934943900592, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - y to 0.795265651276015, - iota to 0.9211194782050933 - )), - 0.001, - "test 4'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 7.321261307532708, - ), - LabeledPolynomialAsIs( - mapOf() to -575.6325831127576, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - x to -8.11707689492641, - y to 0.795265651276015, - )), - 0.001, - "test 5" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 7.321261307532708, - ), - LabeledPolynomialAsIs( - mapOf() to -575.6325831127576, - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to 6.593754860231304, - mapOf(x to 1u) to -7.853302571550634, - mapOf(x to 2u) to 1.2265042281530025, - mapOf(y to 1u) to 3.762648877294904, - mapOf(x to 1u, y to 1u) to -8.945144619305292, - mapOf(x to 2u, y to 1u) to -5.141384718042281, - mapOf(y to 2u) to 7.359794483988782, - mapOf(x to 1u, y to 2u) to -4.3526172680518815, - mapOf(x to 2u, y to 2u) to 0.907910924854372, - ), - LabeledPolynomialAsIs( - mapOf() to 9.533292132172562, - mapOf(x to 1u) to -1.982814534018857, - mapOf(x to 2u) to -5.974248303415283, - mapOf(y to 1u) to 1.5876716499288879, - mapOf(x to 1u, y to 1u) to -7.535152566659664, - mapOf(x to 2u, y to 1u) to 0.7549300500153517, - mapOf(y to 2u) to -5.242030058021028, - mapOf(x to 1u, y to 2u) to -0.7265704289690582, - mapOf(x to 2u, y to 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - x to -8.11707689492641, - y to 0.795265651276015, - iota to 0.9211194782050933 - )), - 0.001, - "test 5'" - ) - } - @Test - fun test_RationalFunction_substitute_Constant_Map() { - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(0) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ).substitute(RationalField, mapOf( - x to Rational(1) - )), - "test 1" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(22047, 2450), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-2204953, 147000), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - x to Rational(7, 5), - y to Rational(-13, 7), - )), - "test 2" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(22047, 2450), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-2204953, 147000), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - x to Rational(7, 5), - y to Rational(-13, 7), - iota to Rational(-16, 4), - )), - "test 2'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(4191, 490), - mapOf(x to 1u) to Rational(14975, 1176), - mapOf(x to 2u) to Rational(-10429, 1176) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-775, 147), - mapOf(x to 1u) to Rational(-155, 49), - mapOf(x to 2u) to Rational(-757, 280) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - y to Rational(-13, 7), - )), - "test 3" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(4191, 490), - mapOf(x to 1u) to Rational(14975, 1176), - mapOf(x to 2u) to Rational(-10429, 1176) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-775, 147), - mapOf(x to 1u) to Rational(-155, 49), - mapOf(x to 2u) to Rational(-757, 280) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - y to Rational(-13, 7), - iota to Rational(-16, 4), - )), - "test 3'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-939, 200), - mapOf(y to 1u) to Rational(123, 50), - mapOf(y to 2u) to Rational(1059, 200) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(121, 25), - mapOf(y to 1u) to Rational(-949, 375), - mapOf(y to 2u) to Rational(-1423, 200) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - x to Rational(7, 5), - )), - "test 4" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-939, 200), - mapOf(y to 1u) to Rational(123, 50), - mapOf(y to 2u) to Rational(1059, 200) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(121, 25), - mapOf(y to 1u) to Rational(-949, 375), - mapOf(y to 2u) to Rational(-1423, 200) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - x to Rational(7, 5), - iota to Rational(-16, 4), - )), - "test 4'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf()), - "test 5" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-3, 5), - mapOf(x to 1u) to Rational(-18, 4), - mapOf(x to 2u) to Rational(9, 8), - mapOf(y to 1u) to Rational(-11, 6), - mapOf(x to 1u, y to 1u) to Rational(-16, 3), - mapOf(x to 2u, y to 1u) to Rational(12, 2), - mapOf(y to 2u) to Rational(5, 3), - mapOf(x to 1u, y to 2u) to Rational(17, 8), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(11, 1), - mapOf(x to 1u) to Rational(4, 1), - mapOf(x to 2u) to Rational(-18, 3), - mapOf(y to 1u) to Rational(12, 9), - mapOf(x to 1u, y to 1u) to Rational(14, 7), - mapOf(x to 2u, y to 1u) to Rational(-17, 5), - mapOf(y to 2u) to Rational(-4, 1), - mapOf(x to 1u, y to 2u) to Rational(-5, 5), - mapOf(x to 2u, y to 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - iota to Rational(-16, 4), - )), - "test 5'" - ) - } - @Test - fun test_RationalFunction_substitute_Polynomial_Map() { - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(0) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - )), - "test 1" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(211, 4), - mapOf(x to 2u) to Rational(88, 3), - mapOf(x to 3u) to Rational(-63, 8), - mapOf(x to 4u) to Rational(441, 16), - mapOf(y to 1u) to Rational(-671, 15), - mapOf(x to 1u, y to 1u) to Rational(-551, 21), - mapOf(x to 2u, y to 1u) to Rational(279, 25), - mapOf(x to 3u, y to 1u) to Rational(231, 20), - mapOf(y to 2u) to Rational(-1436, 1575), - mapOf(x to 1u, y to 2u) to Rational(2471, 250), - mapOf(x to 2u, y to 2u) to Rational(-4919, 100), - mapOf(y to 3u) to Rational(-1464, 125), - mapOf(x to 1u, y to 3u) to Rational(-264, 25), - mapOf(y to 4u) to Rational(576, 25), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(-9, 4), - mapOf(x to 2u) to Rational(943, 8), - mapOf(x to 3u) to Rational(117, 8), - mapOf(x to 4u) to Rational(147, 16), - mapOf(y to 1u) to Rational(289, 90), - mapOf(x to 1u, y to 1u) to Rational(-2692, 15), - mapOf(x to 2u, y to 1u) to Rational(-1629, 140), - mapOf(x to 3u, y to 1u) to Rational(77, 20), - mapOf(y to 2u) to Rational(6187, 75), - mapOf(x to 1u, y to 2u) to Rational(-2879, 175), - mapOf(x to 2u, y to 2u) to Rational(-4919, 300), - mapOf(y to 3u) to Rational(336, 25), - mapOf(x to 1u, y to 3u) to Rational(-88, 25), - mapOf(y to 4u) to Rational(192, 25), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(3, 2), - mapOf(y to 1u) to Rational(8, 5), - ), - y to LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(7, 2), - mapOf(y to 1u) to Rational(-3, 1), - ) - )), - "test 2" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1202861, 210), - mapOf(x to 1u) to Rational(-215117, 45), - mapOf(x to 2u) to Rational(10889651, 19845), - mapOf(x to 3u) to Rational(-3503956, 6615), - mapOf(x to 4u) to Rational(809066, 2205), - mapOf(x to 5u) to Rational(-9056, 735), - mapOf(x to 6u) to Rational(5396, 315), - mapOf(x to 7u) to Rational(-752, 147), - mapOf(x to 8u) to Rational(16, 49), - mapOf(y to 1u) to Rational(1738469, 1470), - mapOf(x to 1u, y to 1u) to Rational(-926238703, 52920), - mapOf(x to 2u, y to 1u) to Rational(-44113982, 6615), - mapOf(x to 3u, y to 1u) to Rational(10423519, 5292), - mapOf(x to 4u, y to 1u) to Rational(3769712, 2205), - mapOf(x to 5u, y to 1u) to Rational(8905046, 6615), - mapOf(x to 6u, y to 1u) to Rational(1186972, 6615), - mapOf(x to 7u, y to 1u) to Rational(22124, 441), - mapOf(x to 8u, y to 1u) to Rational(-1504, 147), - mapOf(y to 2u) to Rational(-54723628, 2205), - mapOf(x to 1u, y to 2u) to Rational(70109407, 1323), - mapOf(x to 2u, y to 2u) to Rational(151072591, 17640), - mapOf(x to 3u, y to 2u) to Rational(1216428107, 52920), - mapOf(x to 4u, y to 2u) to Rational(2587873193, 317520), - mapOf(x to 5u, y to 2u) to Rational(393536369, 79380), - mapOf(x to 6u, y to 2u) to Rational(137614937, 79380), - mapOf(x to 7u, y to 2u) to Rational(566866, 1323), - mapOf(x to 8u, y to 2u) to Rational(41848, 441), - mapOf(y to 3u) to Rational(-19470406, 2205), - mapOf(x to 1u, y to 3u) to Rational(72514195, 882), - mapOf(x to 2u, y to 3u) to Rational(-78090707, 1764), - mapOf(x to 3u, y to 3u) to Rational(-1988237707, 26460), - mapOf(x to 4u, y to 3u) to Rational(-802137919, 17640), - mapOf(x to 5u, y to 3u) to Rational(-139989463, 5880), - mapOf(x to 6u, y to 3u) to Rational(-26066641, 3780), - mapOf(x to 7u, y to 3u) to Rational(-2363369, 1323), - mapOf(x to 8u, y to 3u) to Rational(-108280, 441), - mapOf(y to 4u) to Rational(14878516, 441), - mapOf(x to 1u, y to 4u) to Rational(-253416724, 2205), - mapOf(x to 2u, y to 4u) to Rational(16699157, 840), - mapOf(x to 3u, y to 4u) to Rational(-105220979, 13230), - mapOf(x to 4u, y to 4u) to Rational(208266383, 5880), - mapOf(x to 5u, y to 4u) to Rational(650135309, 26460), - mapOf(x to 6u, y to 4u) to Rational(123808663, 11760), - mapOf(x to 7u, y to 4u) to Rational(8563385, 2646), - mapOf(x to 8u, y to 4u) to Rational(19721, 49), - mapOf(y to 5u) to Rational(675645, 49), - mapOf(x to 1u, y to 5u) to Rational(-70554077, 588), - mapOf(x to 2u, y to 5u) to Rational(157884029, 980), - mapOf(x to 3u, y to 5u) to Rational(489548623, 4410), - mapOf(x to 4u, y to 5u) to Rational(148540519, 17640), - mapOf(x to 5u, y to 5u) to Rational(-5559551, 392), - mapOf(x to 6u, y to 5u) to Rational(-18335711, 1470), - mapOf(x to 7u, y to 5u) to Rational(-38437, 9), - mapOf(x to 8u, y to 5u) to Rational(-29620, 63), - mapOf(y to 6u) to Rational(-727625, 49), - mapOf(x to 1u, y to 6u) to Rational(7046685, 98), - mapOf(x to 2u, y to 6u) to Rational(-334814231, 7056), - mapOf(x to 3u, y to 6u) to Rational(-243971737, 17640), - mapOf(x to 4u, y to 6u) to Rational(-571116659, 35280), - mapOf(x to 5u, y to 6u) to Rational(567538, 315), - mapOf(x to 6u, y to 6u) to Rational(3199768, 315), - mapOf(x to 7u, y to 6u) to Rational(227744, 63), - mapOf(x to 8u, y to 6u) to Rational(23116, 63), - mapOf(y to 7u) to Rational(-27500, 7), - mapOf(x to 1u, y to 7u) to Rational(120125, 3), - mapOf(x to 2u, y to 7u) to Rational(-279200, 3), - mapOf(x to 3u, y to 7u) to Rational(-100160, 7), - mapOf(x to 4u, y to 7u) to Rational(920452, 21), - mapOf(x to 5u, y to 7u) to Rational(226481, 21), - mapOf(x to 6u, y to 7u) to Rational(-34428, 7), - mapOf(x to 7u, y to 7u) to Rational(-6232, 3), - mapOf(x to 8u, y to 7u) to Rational(-608, 3), - mapOf(y to 8u) to Rational(2500, 1), - mapOf(x to 1u, y to 8u) to Rational(-19000, 1), - mapOf(x to 2u, y to 8u) to Rational(37900, 1), - mapOf(x to 3u, y to 8u) to Rational(-1840, 1), - mapOf(x to 4u, y to 8u) to Rational(-17876, 1), - mapOf(x to 5u, y to 8u) to Rational(-1240, 1), - mapOf(x to 6u, y to 8u) to Rational(2788, 1), - mapOf(x to 7u, y to 8u) to Rational(800, 1), - mapOf(x to 8u, y to 8u) to Rational(64, 1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(162487, 63), - mapOf(x to 1u) to Rational(-92713, 54), - mapOf(x to 2u) to Rational(802436, 1323), - mapOf(x to 3u) to Rational(-55088, 441), - mapOf(x to 4u) to Rational(1404034, 9261), - mapOf(x to 5u) to Rational(-5804, 1029), - mapOf(x to 6u) to Rational(51556, 9261), - mapOf(x to 7u) to Rational(-752, 441), - mapOf(x to 8u) to Rational(16, 147), - mapOf(y to 1u) to Rational(296071, 441), - mapOf(x to 1u, y to 1u) to Rational(-4991281, 882), - mapOf(x to 2u, y to 1u) to Rational(-18702811, 9261), - mapOf(x to 3u, y to 1u) to Rational(40759043, 27783), - mapOf(x to 4u, y to 1u) to Rational(19768501, 27783), - mapOf(x to 5u, y to 1u) to Rational(14307337, 27783), - mapOf(x to 6u, y to 1u) to Rational(1655684, 27783), - mapOf(x to 7u, y to 1u) to Rational(22124, 1323), - mapOf(x to 8u, y to 1u) to Rational(-1504, 441), - mapOf(y to 2u) to Rational(-27667474, 3087), - mapOf(x to 1u, y to 2u) to Rational(265605901, 12348), - mapOf(x to 2u, y to 2u) to Rational(160360775, 98784), - mapOf(x to 3u, y to 2u) to Rational(1169992093, 148176), - mapOf(x to 4u, y to 2u) to Rational(3978014077, 1333584), - mapOf(x to 5u, y to 2u) to Rational(567058123, 333396), - mapOf(x to 6u, y to 2u) to Rational(205132579, 333396), - mapOf(x to 7u, y to 2u) to Rational(566866, 3969), - mapOf(x to 8u, y to 2u) to Rational(41848, 1323), - mapOf(y to 3u) to Rational(-2228822, 1029), - mapOf(x to 1u, y to 3u) to Rational(80179390, 3087), - mapOf(x to 2u, y to 3u) to Rational(-1378630487, 74088), - mapOf(x to 3u, y to 3u) to Rational(-3385811693, 111132), - mapOf(x to 4u, y to 3u) to Rational(-820686977, 49392), - mapOf(x to 5u, y to 3u) to Rational(-89101027, 10584), - mapOf(x to 6u, y to 3u) to Rational(-37847387, 15876), - mapOf(x to 7u, y to 3u) to Rational(-2363369, 3969), - mapOf(x to 8u, y to 3u) to Rational(-108280, 1323), - mapOf(y to 4u) to Rational(12619982, 1029), - mapOf(x to 1u, y to 4u) to Rational(-277723177, 6174), - mapOf(x to 2u, y to 4u) to Rational(649414169, 49392), - mapOf(x to 3u, y to 4u) to Rational(14457595, 63504), - mapOf(x to 4u, y to 4u) to Rational(139270339, 10584), - mapOf(x to 5u, y to 4u) to Rational(140367961, 15876), - mapOf(x to 6u, y to 4u) to Rational(25467083, 7056), - mapOf(x to 7u, y to 4u) to Rational(8563385, 7938), - mapOf(x to 8u, y to 4u) to Rational(19721, 147), - mapOf(y to 5u) to Rational(643850, 147), - mapOf(x to 1u, y to 5u) to Rational(-11818025, 294), - mapOf(x to 2u, y to 5u) to Rational(33963203, 588), - mapOf(x to 3u, y to 5u) to Rational(207216235, 5292), - mapOf(x to 4u, y to 5u) to Rational(2861021, 1512), - mapOf(x to 5u, y to 5u) to Rational(-6302335, 1176), - mapOf(x to 6u, y to 5u) to Rational(-3738587, 882), - mapOf(x to 7u, y to 5u) to Rational(-38437, 27), - mapOf(x to 8u, y to 5u) to Rational(-29620, 189), - mapOf(y to 6u) to Rational(-248725, 49), - mapOf(x to 1u, y to 6u) to Rational(2478535, 98), - mapOf(x to 2u, y to 6u) to Rational(-399721367, 21168), - mapOf(x to 3u, y to 6u) to Rational(-54309317, 10584), - mapOf(x to 4u, y to 6u) to Rational(-95398327, 21168), - mapOf(x to 5u, y to 6u) to Rational(173750, 189), - mapOf(x to 6u, y to 6u) to Rational(92216, 27), - mapOf(x to 7u, y to 6u) to Rational(227744, 189), - mapOf(x to 8u, y to 6u) to Rational(23116, 189), - mapOf(y to 7u) to Rational(-27500, 21), - mapOf(x to 1u, y to 7u) to Rational(120125, 9), - mapOf(x to 2u, y to 7u) to Rational(-279200, 9), - mapOf(x to 3u, y to 7u) to Rational(-100160, 21), - mapOf(x to 4u, y to 7u) to Rational(920452, 63), - mapOf(x to 5u, y to 7u) to Rational(226481, 63), - mapOf(x to 6u, y to 7u) to Rational(-11476, 7), - mapOf(x to 7u, y to 7u) to Rational(-6232, 9), - mapOf(x to 8u, y to 7u) to Rational(-608, 9), - mapOf(y to 8u) to Rational(2500, 3), - mapOf(x to 1u, y to 8u) to Rational(-19000, 3), - mapOf(x to 2u, y to 8u) to Rational(37900, 3), - mapOf(x to 3u, y to 8u) to Rational(-1840, 3), - mapOf(x to 4u, y to 8u) to Rational(-17876, 3), - mapOf(x to 5u, y to 8u) to Rational(-1240, 3), - mapOf(x to 6u, y to 8u) to Rational(2788, 3), - mapOf(x to 7u, y to 8u) to Rational(800, 3), - mapOf(x to 8u, y to 8u) to Rational(64, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(18, 1), - mapOf(x to 1u) to Rational(16, 3), - mapOf(x to 2u) to Rational(12, 6), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 4), - mapOf(x to 2u, y to 1u) to Rational(-1, 1), - mapOf(y to 2u) to Rational(-10, 1), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - y to LabeledPolynomialAsIs( - mapOf() to Rational(8, 2), - mapOf(x to 1u) to Rational(-15, 5), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 7), - mapOf(x to 1u, y to 1u) to Rational(-16, 6), - mapOf(x to 2u, y to 1u) to Rational(-13, 3), - mapOf(y to 2u) to Rational(-5, 1), - mapOf(x to 1u, y to 2u) to Rational(17, 1), - mapOf(x to 2u, y to 2u) to Rational(8, 2), - ), - )), - "test 3" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1202861, 210), - mapOf(x to 1u) to Rational(-215117, 45), - mapOf(x to 2u) to Rational(10889651, 19845), - mapOf(x to 3u) to Rational(-3503956, 6615), - mapOf(x to 4u) to Rational(809066, 2205), - mapOf(x to 5u) to Rational(-9056, 735), - mapOf(x to 6u) to Rational(5396, 315), - mapOf(x to 7u) to Rational(-752, 147), - mapOf(x to 8u) to Rational(16, 49), - mapOf(y to 1u) to Rational(1738469, 1470), - mapOf(x to 1u, y to 1u) to Rational(-926238703, 52920), - mapOf(x to 2u, y to 1u) to Rational(-44113982, 6615), - mapOf(x to 3u, y to 1u) to Rational(10423519, 5292), - mapOf(x to 4u, y to 1u) to Rational(3769712, 2205), - mapOf(x to 5u, y to 1u) to Rational(8905046, 6615), - mapOf(x to 6u, y to 1u) to Rational(1186972, 6615), - mapOf(x to 7u, y to 1u) to Rational(22124, 441), - mapOf(x to 8u, y to 1u) to Rational(-1504, 147), - mapOf(y to 2u) to Rational(-54723628, 2205), - mapOf(x to 1u, y to 2u) to Rational(70109407, 1323), - mapOf(x to 2u, y to 2u) to Rational(151072591, 17640), - mapOf(x to 3u, y to 2u) to Rational(1216428107, 52920), - mapOf(x to 4u, y to 2u) to Rational(2587873193, 317520), - mapOf(x to 5u, y to 2u) to Rational(393536369, 79380), - mapOf(x to 6u, y to 2u) to Rational(137614937, 79380), - mapOf(x to 7u, y to 2u) to Rational(566866, 1323), - mapOf(x to 8u, y to 2u) to Rational(41848, 441), - mapOf(y to 3u) to Rational(-19470406, 2205), - mapOf(x to 1u, y to 3u) to Rational(72514195, 882), - mapOf(x to 2u, y to 3u) to Rational(-78090707, 1764), - mapOf(x to 3u, y to 3u) to Rational(-1988237707, 26460), - mapOf(x to 4u, y to 3u) to Rational(-802137919, 17640), - mapOf(x to 5u, y to 3u) to Rational(-139989463, 5880), - mapOf(x to 6u, y to 3u) to Rational(-26066641, 3780), - mapOf(x to 7u, y to 3u) to Rational(-2363369, 1323), - mapOf(x to 8u, y to 3u) to Rational(-108280, 441), - mapOf(y to 4u) to Rational(14878516, 441), - mapOf(x to 1u, y to 4u) to Rational(-253416724, 2205), - mapOf(x to 2u, y to 4u) to Rational(16699157, 840), - mapOf(x to 3u, y to 4u) to Rational(-105220979, 13230), - mapOf(x to 4u, y to 4u) to Rational(208266383, 5880), - mapOf(x to 5u, y to 4u) to Rational(650135309, 26460), - mapOf(x to 6u, y to 4u) to Rational(123808663, 11760), - mapOf(x to 7u, y to 4u) to Rational(8563385, 2646), - mapOf(x to 8u, y to 4u) to Rational(19721, 49), - mapOf(y to 5u) to Rational(675645, 49), - mapOf(x to 1u, y to 5u) to Rational(-70554077, 588), - mapOf(x to 2u, y to 5u) to Rational(157884029, 980), - mapOf(x to 3u, y to 5u) to Rational(489548623, 4410), - mapOf(x to 4u, y to 5u) to Rational(148540519, 17640), - mapOf(x to 5u, y to 5u) to Rational(-5559551, 392), - mapOf(x to 6u, y to 5u) to Rational(-18335711, 1470), - mapOf(x to 7u, y to 5u) to Rational(-38437, 9), - mapOf(x to 8u, y to 5u) to Rational(-29620, 63), - mapOf(y to 6u) to Rational(-727625, 49), - mapOf(x to 1u, y to 6u) to Rational(7046685, 98), - mapOf(x to 2u, y to 6u) to Rational(-334814231, 7056), - mapOf(x to 3u, y to 6u) to Rational(-243971737, 17640), - mapOf(x to 4u, y to 6u) to Rational(-571116659, 35280), - mapOf(x to 5u, y to 6u) to Rational(567538, 315), - mapOf(x to 6u, y to 6u) to Rational(3199768, 315), - mapOf(x to 7u, y to 6u) to Rational(227744, 63), - mapOf(x to 8u, y to 6u) to Rational(23116, 63), - mapOf(y to 7u) to Rational(-27500, 7), - mapOf(x to 1u, y to 7u) to Rational(120125, 3), - mapOf(x to 2u, y to 7u) to Rational(-279200, 3), - mapOf(x to 3u, y to 7u) to Rational(-100160, 7), - mapOf(x to 4u, y to 7u) to Rational(920452, 21), - mapOf(x to 5u, y to 7u) to Rational(226481, 21), - mapOf(x to 6u, y to 7u) to Rational(-34428, 7), - mapOf(x to 7u, y to 7u) to Rational(-6232, 3), - mapOf(x to 8u, y to 7u) to Rational(-608, 3), - mapOf(y to 8u) to Rational(2500, 1), - mapOf(x to 1u, y to 8u) to Rational(-19000, 1), - mapOf(x to 2u, y to 8u) to Rational(37900, 1), - mapOf(x to 3u, y to 8u) to Rational(-1840, 1), - mapOf(x to 4u, y to 8u) to Rational(-17876, 1), - mapOf(x to 5u, y to 8u) to Rational(-1240, 1), - mapOf(x to 6u, y to 8u) to Rational(2788, 1), - mapOf(x to 7u, y to 8u) to Rational(800, 1), - mapOf(x to 8u, y to 8u) to Rational(64, 1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(162487, 63), - mapOf(x to 1u) to Rational(-92713, 54), - mapOf(x to 2u) to Rational(802436, 1323), - mapOf(x to 3u) to Rational(-55088, 441), - mapOf(x to 4u) to Rational(1404034, 9261), - mapOf(x to 5u) to Rational(-5804, 1029), - mapOf(x to 6u) to Rational(51556, 9261), - mapOf(x to 7u) to Rational(-752, 441), - mapOf(x to 8u) to Rational(16, 147), - mapOf(y to 1u) to Rational(296071, 441), - mapOf(x to 1u, y to 1u) to Rational(-4991281, 882), - mapOf(x to 2u, y to 1u) to Rational(-18702811, 9261), - mapOf(x to 3u, y to 1u) to Rational(40759043, 27783), - mapOf(x to 4u, y to 1u) to Rational(19768501, 27783), - mapOf(x to 5u, y to 1u) to Rational(14307337, 27783), - mapOf(x to 6u, y to 1u) to Rational(1655684, 27783), - mapOf(x to 7u, y to 1u) to Rational(22124, 1323), - mapOf(x to 8u, y to 1u) to Rational(-1504, 441), - mapOf(y to 2u) to Rational(-27667474, 3087), - mapOf(x to 1u, y to 2u) to Rational(265605901, 12348), - mapOf(x to 2u, y to 2u) to Rational(160360775, 98784), - mapOf(x to 3u, y to 2u) to Rational(1169992093, 148176), - mapOf(x to 4u, y to 2u) to Rational(3978014077, 1333584), - mapOf(x to 5u, y to 2u) to Rational(567058123, 333396), - mapOf(x to 6u, y to 2u) to Rational(205132579, 333396), - mapOf(x to 7u, y to 2u) to Rational(566866, 3969), - mapOf(x to 8u, y to 2u) to Rational(41848, 1323), - mapOf(y to 3u) to Rational(-2228822, 1029), - mapOf(x to 1u, y to 3u) to Rational(80179390, 3087), - mapOf(x to 2u, y to 3u) to Rational(-1378630487, 74088), - mapOf(x to 3u, y to 3u) to Rational(-3385811693, 111132), - mapOf(x to 4u, y to 3u) to Rational(-820686977, 49392), - mapOf(x to 5u, y to 3u) to Rational(-89101027, 10584), - mapOf(x to 6u, y to 3u) to Rational(-37847387, 15876), - mapOf(x to 7u, y to 3u) to Rational(-2363369, 3969), - mapOf(x to 8u, y to 3u) to Rational(-108280, 1323), - mapOf(y to 4u) to Rational(12619982, 1029), - mapOf(x to 1u, y to 4u) to Rational(-277723177, 6174), - mapOf(x to 2u, y to 4u) to Rational(649414169, 49392), - mapOf(x to 3u, y to 4u) to Rational(14457595, 63504), - mapOf(x to 4u, y to 4u) to Rational(139270339, 10584), - mapOf(x to 5u, y to 4u) to Rational(140367961, 15876), - mapOf(x to 6u, y to 4u) to Rational(25467083, 7056), - mapOf(x to 7u, y to 4u) to Rational(8563385, 7938), - mapOf(x to 8u, y to 4u) to Rational(19721, 147), - mapOf(y to 5u) to Rational(643850, 147), - mapOf(x to 1u, y to 5u) to Rational(-11818025, 294), - mapOf(x to 2u, y to 5u) to Rational(33963203, 588), - mapOf(x to 3u, y to 5u) to Rational(207216235, 5292), - mapOf(x to 4u, y to 5u) to Rational(2861021, 1512), - mapOf(x to 5u, y to 5u) to Rational(-6302335, 1176), - mapOf(x to 6u, y to 5u) to Rational(-3738587, 882), - mapOf(x to 7u, y to 5u) to Rational(-38437, 27), - mapOf(x to 8u, y to 5u) to Rational(-29620, 189), - mapOf(y to 6u) to Rational(-248725, 49), - mapOf(x to 1u, y to 6u) to Rational(2478535, 98), - mapOf(x to 2u, y to 6u) to Rational(-399721367, 21168), - mapOf(x to 3u, y to 6u) to Rational(-54309317, 10584), - mapOf(x to 4u, y to 6u) to Rational(-95398327, 21168), - mapOf(x to 5u, y to 6u) to Rational(173750, 189), - mapOf(x to 6u, y to 6u) to Rational(92216, 27), - mapOf(x to 7u, y to 6u) to Rational(227744, 189), - mapOf(x to 8u, y to 6u) to Rational(23116, 189), - mapOf(y to 7u) to Rational(-27500, 21), - mapOf(x to 1u, y to 7u) to Rational(120125, 9), - mapOf(x to 2u, y to 7u) to Rational(-279200, 9), - mapOf(x to 3u, y to 7u) to Rational(-100160, 21), - mapOf(x to 4u, y to 7u) to Rational(920452, 63), - mapOf(x to 5u, y to 7u) to Rational(226481, 63), - mapOf(x to 6u, y to 7u) to Rational(-11476, 7), - mapOf(x to 7u, y to 7u) to Rational(-6232, 9), - mapOf(x to 8u, y to 7u) to Rational(-608, 9), - mapOf(y to 8u) to Rational(2500, 3), - mapOf(x to 1u, y to 8u) to Rational(-19000, 3), - mapOf(x to 2u, y to 8u) to Rational(37900, 3), - mapOf(x to 3u, y to 8u) to Rational(-1840, 3), - mapOf(x to 4u, y to 8u) to Rational(-17876, 3), - mapOf(x to 5u, y to 8u) to Rational(-1240, 3), - mapOf(x to 6u, y to 8u) to Rational(2788, 3), - mapOf(x to 7u, y to 8u) to Rational(800, 3), - mapOf(x to 8u, y to 8u) to Rational(64, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(18, 1), - mapOf(x to 1u) to Rational(16, 3), - mapOf(x to 2u) to Rational(12, 6), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 4), - mapOf(x to 2u, y to 1u) to Rational(-1, 1), - mapOf(y to 2u) to Rational(-10, 1), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - y to LabeledPolynomialAsIs( - mapOf() to Rational(8, 2), - mapOf(x to 1u) to Rational(-15, 5), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 7), - mapOf(x to 1u, y to 1u) to Rational(-16, 6), - mapOf(x to 2u, y to 1u) to Rational(-13, 3), - mapOf(y to 2u) to Rational(-5, 1), - mapOf(x to 1u, y to 2u) to Rational(17, 1), - mapOf(x to 2u, y to 2u) to Rational(8, 2), - ), - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-6, 1), - mapOf(x to 1u) to Rational(-9, 8), - mapOf(x to 2u) to Rational(17, 5), - mapOf(y to 1u) to Rational(-2, 3), - mapOf(x to 1u, y to 1u) to Rational(1, 5), - mapOf(x to 2u, y to 1u) to Rational(-11, 7), - mapOf(y to 2u) to Rational(13, 6), - mapOf(x to 1u, y to 2u) to Rational(-15, 2), - mapOf(x to 2u, y to 2u) to Rational(-14, 4), - ) - )), - "test 3'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(493, 6), - mapOf(x to 1u) to Rational(-15991, 210), - mapOf(x to 2u) to Rational(2734, 63), - mapOf(x to 3u) to Rational(-8213, 245), - mapOf(x to 4u) to Rational(1843, 147), - mapOf(x to 5u) to Rational(-432, 245), - mapOf(x to 6u) to Rational(4, 49), - mapOf(y to 1u) to Rational(-66, 1), - mapOf(x to 1u, y to 1u) to Rational(-92924, 2205), - mapOf(x to 2u, y to 1u) to Rational(-257461, 2205), - mapOf(x to 3u, y to 1u) to Rational(58658, 2205), - mapOf(x to 4u, y to 1u) to Rational(-87884, 2205), - mapOf(x to 5u, y to 1u) to Rational(2726, 105), - mapOf(x to 6u, y to 1u) to Rational(-52, 21), - mapOf(y to 2u) to Rational(-17569, 147), - mapOf(x to 1u, y to 2u) to Rational(368819, 735), - mapOf(x to 2u, y to 2u) to Rational(-644626, 6615), - mapOf(x to 3u, y to 2u) to Rational(221738, 945), - mapOf(x to 4u, y to 2u) to Rational(-18022, 945), - mapOf(x to 5u, y to 2u) to Rational(-1201, 315), - mapOf(x to 6u, y to 2u) to Rational(1327, 63), - mapOf(y to 3u) to Rational(240, 7), - mapOf(x to 1u, y to 3u) to Rational(-868, 9), - mapOf(x to 2u, y to 3u) to Rational(-8936, 315), - mapOf(x to 3u, y to 3u) to Rational(-77146, 315), - mapOf(x to 4u, y to 3u) to Rational(-4072, 315), - mapOf(x to 5u, y to 3u) to Rational(-2218, 15), - mapOf(x to 6u, y to 3u) to Rational(-104, 3), - mapOf(y to 4u) to Rational(100, 3), - mapOf(x to 1u, y to 4u) to Rational(-725, 3), - mapOf(x to 2u, y to 4u) to Rational(459, 1), - mapOf(x to 3u, y to 4u) to Rational(-2071, 15), - mapOf(x to 4u, y to 4u) to Rational(2831, 15), - mapOf(x to 5u, y to 4u) to Rational(632, 5), - mapOf(x to 6u, y to 4u) to Rational(16, 1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1255, 9), - mapOf(x to 1u) to Rational(-24781, 126), - mapOf(x to 2u) to Rational(1195, 14), - mapOf(x to 3u) to Rational(-1931, 147), - mapOf(x to 4u) to Rational(439, 147), - mapOf(x to 5u) to Rational(-172, 343), - mapOf(x to 6u) to Rational(4, 147), - mapOf(y to 1u) to Rational(-183, 1), - mapOf(x to 1u, y to 1u) to Rational(-30988, 441), - mapOf(x to 2u, y to 1u) to Rational(-56137, 294), - mapOf(x to 3u, y to 1u) to Rational(204308, 1029), - mapOf(x to 4u, y to 1u) to Rational(-3263, 441), - mapOf(x to 5u, y to 1u) to Rational(2662, 441), - mapOf(x to 6u, y to 1u) to Rational(-52, 63), - mapOf(y to 2u) to Rational(-87119, 294), - mapOf(x to 1u, y to 2u) to Rational(1077919, 686), - mapOf(x to 2u, y to 2u) to Rational(-35209, 147), - mapOf(x to 3u, y to 2u) to Rational(15041, 147), - mapOf(x to 4u, y to 2u) to Rational(240889, 1323), - mapOf(x to 5u, y to 2u) to Rational(27778, 1323), - mapOf(x to 6u, y to 2u) to Rational(1327, 189), - mapOf(y to 3u) to Rational(1620, 7), - mapOf(x to 1u, y to 3u) to Rational(-25716, 49), - mapOf(x to 2u, y to 3u) to Rational(-32078, 49), - mapOf(x to 3u, y to 3u) to Rational(-704038, 441), - mapOf(x to 4u, y to 3u) to Rational(-30190, 63), - mapOf(x to 5u, y to 3u) to Rational(-5414, 63), - mapOf(x to 6u, y to 3u) to Rational(-104, 9), - mapOf(y to 4u) to Rational(225, 1), - mapOf(x to 1u, y to 4u) to Rational(-10560, 7), - mapOf(x to 2u, y to 4u) to Rational(44176, 21), - mapOf(x to 3u, y to 4u) to Rational(28996, 21), - mapOf(x to 4u, y to 4u) to Rational(2405, 7), - mapOf(x to 5u, y to 4u) to Rational(1240, 21), - mapOf(x to 6u, y to 4u) to Rational(16, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - y to LabeledPolynomialAsIs( - mapOf() to Rational(8, 2), - mapOf(x to 1u) to Rational(-15, 5), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 7), - mapOf(x to 1u, y to 1u) to Rational(-16, 6), - mapOf(x to 2u, y to 1u) to Rational(-13, 3), - mapOf(y to 2u) to Rational(-5, 1), - mapOf(x to 1u, y to 2u) to Rational(17, 1), - mapOf(x to 2u, y to 2u) to Rational(8, 2), - ), - )), - "test 4" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(493, 6), - mapOf(x to 1u) to Rational(-15991, 210), - mapOf(x to 2u) to Rational(2734, 63), - mapOf(x to 3u) to Rational(-8213, 245), - mapOf(x to 4u) to Rational(1843, 147), - mapOf(x to 5u) to Rational(-432, 245), - mapOf(x to 6u) to Rational(4, 49), - mapOf(y to 1u) to Rational(-66, 1), - mapOf(x to 1u, y to 1u) to Rational(-92924, 2205), - mapOf(x to 2u, y to 1u) to Rational(-257461, 2205), - mapOf(x to 3u, y to 1u) to Rational(58658, 2205), - mapOf(x to 4u, y to 1u) to Rational(-87884, 2205), - mapOf(x to 5u, y to 1u) to Rational(2726, 105), - mapOf(x to 6u, y to 1u) to Rational(-52, 21), - mapOf(y to 2u) to Rational(-17569, 147), - mapOf(x to 1u, y to 2u) to Rational(368819, 735), - mapOf(x to 2u, y to 2u) to Rational(-644626, 6615), - mapOf(x to 3u, y to 2u) to Rational(221738, 945), - mapOf(x to 4u, y to 2u) to Rational(-18022, 945), - mapOf(x to 5u, y to 2u) to Rational(-1201, 315), - mapOf(x to 6u, y to 2u) to Rational(1327, 63), - mapOf(y to 3u) to Rational(240, 7), - mapOf(x to 1u, y to 3u) to Rational(-868, 9), - mapOf(x to 2u, y to 3u) to Rational(-8936, 315), - mapOf(x to 3u, y to 3u) to Rational(-77146, 315), - mapOf(x to 4u, y to 3u) to Rational(-4072, 315), - mapOf(x to 5u, y to 3u) to Rational(-2218, 15), - mapOf(x to 6u, y to 3u) to Rational(-104, 3), - mapOf(y to 4u) to Rational(100, 3), - mapOf(x to 1u, y to 4u) to Rational(-725, 3), - mapOf(x to 2u, y to 4u) to Rational(459, 1), - mapOf(x to 3u, y to 4u) to Rational(-2071, 15), - mapOf(x to 4u, y to 4u) to Rational(2831, 15), - mapOf(x to 5u, y to 4u) to Rational(632, 5), - mapOf(x to 6u, y to 4u) to Rational(16, 1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1255, 9), - mapOf(x to 1u) to Rational(-24781, 126), - mapOf(x to 2u) to Rational(1195, 14), - mapOf(x to 3u) to Rational(-1931, 147), - mapOf(x to 4u) to Rational(439, 147), - mapOf(x to 5u) to Rational(-172, 343), - mapOf(x to 6u) to Rational(4, 147), - mapOf(y to 1u) to Rational(-183, 1), - mapOf(x to 1u, y to 1u) to Rational(-30988, 441), - mapOf(x to 2u, y to 1u) to Rational(-56137, 294), - mapOf(x to 3u, y to 1u) to Rational(204308, 1029), - mapOf(x to 4u, y to 1u) to Rational(-3263, 441), - mapOf(x to 5u, y to 1u) to Rational(2662, 441), - mapOf(x to 6u, y to 1u) to Rational(-52, 63), - mapOf(y to 2u) to Rational(-87119, 294), - mapOf(x to 1u, y to 2u) to Rational(1077919, 686), - mapOf(x to 2u, y to 2u) to Rational(-35209, 147), - mapOf(x to 3u, y to 2u) to Rational(15041, 147), - mapOf(x to 4u, y to 2u) to Rational(240889, 1323), - mapOf(x to 5u, y to 2u) to Rational(27778, 1323), - mapOf(x to 6u, y to 2u) to Rational(1327, 189), - mapOf(y to 3u) to Rational(1620, 7), - mapOf(x to 1u, y to 3u) to Rational(-25716, 49), - mapOf(x to 2u, y to 3u) to Rational(-32078, 49), - mapOf(x to 3u, y to 3u) to Rational(-704038, 441), - mapOf(x to 4u, y to 3u) to Rational(-30190, 63), - mapOf(x to 5u, y to 3u) to Rational(-5414, 63), - mapOf(x to 6u, y to 3u) to Rational(-104, 9), - mapOf(y to 4u) to Rational(225, 1), - mapOf(x to 1u, y to 4u) to Rational(-10560, 7), - mapOf(x to 2u, y to 4u) to Rational(44176, 21), - mapOf(x to 3u, y to 4u) to Rational(28996, 21), - mapOf(x to 4u, y to 4u) to Rational(2405, 7), - mapOf(x to 5u, y to 4u) to Rational(1240, 21), - mapOf(x to 6u, y to 4u) to Rational(16, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - y to LabeledPolynomialAsIs( - mapOf() to Rational(8, 2), - mapOf(x to 1u) to Rational(-15, 5), - mapOf(x to 2u) to Rational(2, 7), - mapOf(y to 1u) to Rational(-18, 7), - mapOf(x to 1u, y to 1u) to Rational(-16, 6), - mapOf(x to 2u, y to 1u) to Rational(-13, 3), - mapOf(y to 2u) to Rational(-5, 1), - mapOf(x to 1u, y to 2u) to Rational(17, 1), - mapOf(x to 2u, y to 2u) to Rational(8, 2), - ), - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-6, 1), - mapOf(x to 1u) to Rational(-9, 8), - mapOf(x to 2u) to Rational(17, 5), - mapOf(y to 1u) to Rational(-2, 3), - mapOf(x to 1u, y to 1u) to Rational(1, 5), - mapOf(x to 2u, y to 1u) to Rational(-11, 7), - mapOf(y to 2u) to Rational(13, 6), - mapOf(x to 1u, y to 2u) to Rational(-15, 2), - mapOf(x to 2u, y to 2u) to Rational(-14, 4), - ) - )), - "test 4'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-409, 6), - mapOf(x to 1u) to Rational(-376, 9), - mapOf(x to 2u) to Rational(-1781, 81), - mapOf(x to 3u) to Rational(-128, 27), - mapOf(x to 4u) to Rational(-8, 9), - mapOf(y to 1u) to Rational(18701, 210), - mapOf(x to 1u, y to 1u) to Rational(614183, 7560), - mapOf(x to 2u, y to 1u) to Rational(90941, 1890), - mapOf(x to 3u, y to 1u) to Rational(1802, 135), - mapOf(x to 4u, y to 1u) to Rational(112, 45), - mapOf(y to 2u) to Rational(181421, 315), - mapOf(x to 1u, y to 2u) to Rational(77813, 378), - mapOf(x to 2u, y to 2u) to Rational(598583, 7560), - mapOf(x to 3u, y to 2u) to Rational(85, 27), - mapOf(x to 4u, y to 2u) to Rational(2, 5), - mapOf(y to 3u) to Rational(130997, 315), - mapOf(x to 1u, y to 3u) to Rational(1093, 420), - mapOf(x to 2u, y to 3u) to Rational(9551, 2520), - mapOf(x to 3u, y to 3u) to Rational(-14, 45), - mapOf(x to 4u, y to 3u) to Rational(22, 45), - mapOf(y to 4u) to Rational(-2801, 9), - mapOf(x to 1u, y to 4u) to Rational(4033, 90), - mapOf(x to 2u, y to 4u) to Rational(6429, 80), - mapOf(x to 3u, y to 4u) to Rational(2851, 90), - mapOf(x to 4u, y to 4u) to Rational(293, 45), - mapOf(y to 5u) to Rational(-220, 1), - mapOf(x to 1u, y to 5u) to Rational(127, 1), - mapOf(x to 2u, y to 5u) to Rational(202, 5), - mapOf(x to 3u, y to 5u) to Rational(-63, 5), - mapOf(x to 4u, y to 5u) to Rational(-12, 5), - mapOf(y to 6u) to Rational(100, 1), - mapOf(x to 1u, y to 6u) to Rational(-80, 1), - mapOf(x to 2u, y to 6u) to Rational(-24, 1), - mapOf(x to 3u, y to 6u) to Rational(16, 1), - mapOf(x to 4u, y to 6u) to Rational(4, 1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(5407, 9), - mapOf(x to 1u) to Rational(9568, 27), - mapOf(x to 2u) to Rational(4996, 27), - mapOf(x to 3u) to Rational(352, 9), - mapOf(x to 4u) to Rational(22, 3), - mapOf(y to 1u) to Rational(104411, 126), - mapOf(x to 1u, y to 1u) to Rational(6001, 126), - mapOf(x to 2u, y to 1u) to Rational(-796, 21), - mapOf(x to 3u, y to 1u) to Rational(-5389, 126), - mapOf(x to 4u, y to 1u) to Rational(-166, 21), - mapOf(y to 2u) to Rational(-35327, 126), - mapOf(x to 1u, y to 2u) to Rational(53, 252), - mapOf(x to 2u, y to 2u) to Rational(849197, 6048), - mapOf(x to 3u, y to 2u) to Rational(22361, 252), - mapOf(x to 4u, y to 2u) to Rational(773, 42), - mapOf(y to 3u) to Rational(-6067, 21), - mapOf(x to 1u, y to 3u) to Rational(39049, 126), - mapOf(x to 2u, y to 3u) to Rational(80303, 1008), - mapOf(x to 3u, y to 3u) to Rational(-3035, 63), - mapOf(x to 4u, y to 3u) to Rational(-209, 21), - mapOf(y to 4u) to Rational(3113, 21), - mapOf(x to 1u, y to 4u) to Rational(-22345, 126), - mapOf(x to 2u, y to 4u) to Rational(-30931, 1008), - mapOf(x to 3u, y to 4u) to Rational(5837, 126), - mapOf(x to 4u, y to 4u) to Rational(229, 21), - mapOf(y to 5u) to Rational(-2120, 21), - mapOf(x to 1u, y to 5u) to Rational(451, 7), - mapOf(x to 2u, y to 5u) to Rational(422, 21), - mapOf(x to 3u, y to 5u) to Rational(-181, 21), - mapOf(x to 4u, y to 5u) to Rational(-40, 21), - mapOf(y to 6u) to Rational(100, 3), - mapOf(x to 1u, y to 6u) to Rational(-80, 3), - mapOf(x to 2u, y to 6u) to Rational(-8, 1), - mapOf(x to 3u, y to 6u) to Rational(16, 3), - mapOf(x to 4u, y to 6u) to Rational(4, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(18, 1), - mapOf(x to 1u) to Rational(16, 3), - mapOf(x to 2u) to Rational(12, 6), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 4), - mapOf(x to 2u, y to 1u) to Rational(-1, 1), - mapOf(y to 2u) to Rational(-10, 1), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - )), - "test 5" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-409, 6), - mapOf(x to 1u) to Rational(-376, 9), - mapOf(x to 2u) to Rational(-1781, 81), - mapOf(x to 3u) to Rational(-128, 27), - mapOf(x to 4u) to Rational(-8, 9), - mapOf(y to 1u) to Rational(18701, 210), - mapOf(x to 1u, y to 1u) to Rational(614183, 7560), - mapOf(x to 2u, y to 1u) to Rational(90941, 1890), - mapOf(x to 3u, y to 1u) to Rational(1802, 135), - mapOf(x to 4u, y to 1u) to Rational(112, 45), - mapOf(y to 2u) to Rational(181421, 315), - mapOf(x to 1u, y to 2u) to Rational(77813, 378), - mapOf(x to 2u, y to 2u) to Rational(598583, 7560), - mapOf(x to 3u, y to 2u) to Rational(85, 27), - mapOf(x to 4u, y to 2u) to Rational(2, 5), - mapOf(y to 3u) to Rational(130997, 315), - mapOf(x to 1u, y to 3u) to Rational(1093, 420), - mapOf(x to 2u, y to 3u) to Rational(9551, 2520), - mapOf(x to 3u, y to 3u) to Rational(-14, 45), - mapOf(x to 4u, y to 3u) to Rational(22, 45), - mapOf(y to 4u) to Rational(-2801, 9), - mapOf(x to 1u, y to 4u) to Rational(4033, 90), - mapOf(x to 2u, y to 4u) to Rational(6429, 80), - mapOf(x to 3u, y to 4u) to Rational(2851, 90), - mapOf(x to 4u, y to 4u) to Rational(293, 45), - mapOf(y to 5u) to Rational(-220, 1), - mapOf(x to 1u, y to 5u) to Rational(127, 1), - mapOf(x to 2u, y to 5u) to Rational(202, 5), - mapOf(x to 3u, y to 5u) to Rational(-63, 5), - mapOf(x to 4u, y to 5u) to Rational(-12, 5), - mapOf(y to 6u) to Rational(100, 1), - mapOf(x to 1u, y to 6u) to Rational(-80, 1), - mapOf(x to 2u, y to 6u) to Rational(-24, 1), - mapOf(x to 3u, y to 6u) to Rational(16, 1), - mapOf(x to 4u, y to 6u) to Rational(4, 1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(5407, 9), - mapOf(x to 1u) to Rational(9568, 27), - mapOf(x to 2u) to Rational(4996, 27), - mapOf(x to 3u) to Rational(352, 9), - mapOf(x to 4u) to Rational(22, 3), - mapOf(y to 1u) to Rational(104411, 126), - mapOf(x to 1u, y to 1u) to Rational(6001, 126), - mapOf(x to 2u, y to 1u) to Rational(-796, 21), - mapOf(x to 3u, y to 1u) to Rational(-5389, 126), - mapOf(x to 4u, y to 1u) to Rational(-166, 21), - mapOf(y to 2u) to Rational(-35327, 126), - mapOf(x to 1u, y to 2u) to Rational(53, 252), - mapOf(x to 2u, y to 2u) to Rational(849197, 6048), - mapOf(x to 3u, y to 2u) to Rational(22361, 252), - mapOf(x to 4u, y to 2u) to Rational(773, 42), - mapOf(y to 3u) to Rational(-6067, 21), - mapOf(x to 1u, y to 3u) to Rational(39049, 126), - mapOf(x to 2u, y to 3u) to Rational(80303, 1008), - mapOf(x to 3u, y to 3u) to Rational(-3035, 63), - mapOf(x to 4u, y to 3u) to Rational(-209, 21), - mapOf(y to 4u) to Rational(3113, 21), - mapOf(x to 1u, y to 4u) to Rational(-22345, 126), - mapOf(x to 2u, y to 4u) to Rational(-30931, 1008), - mapOf(x to 3u, y to 4u) to Rational(5837, 126), - mapOf(x to 4u, y to 4u) to Rational(229, 21), - mapOf(y to 5u) to Rational(-2120, 21), - mapOf(x to 1u, y to 5u) to Rational(451, 7), - mapOf(x to 2u, y to 5u) to Rational(422, 21), - mapOf(x to 3u, y to 5u) to Rational(-181, 21), - mapOf(x to 4u, y to 5u) to Rational(-40, 21), - mapOf(y to 6u) to Rational(100, 3), - mapOf(x to 1u, y to 6u) to Rational(-80, 3), - mapOf(x to 2u, y to 6u) to Rational(-8, 1), - mapOf(x to 3u, y to 6u) to Rational(16, 3), - mapOf(x to 4u, y to 6u) to Rational(4, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - x to LabeledPolynomialAsIs( - mapOf() to Rational(18, 1), - mapOf(x to 1u) to Rational(16, 3), - mapOf(x to 2u) to Rational(12, 6), - mapOf(y to 1u) to Rational(13, 1), - mapOf(x to 1u, y to 1u) to Rational(-11, 4), - mapOf(x to 2u, y to 1u) to Rational(-1, 1), - mapOf(y to 2u) to Rational(-10, 1), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-6, 1), - mapOf(x to 1u) to Rational(-9, 8), - mapOf(x to 2u) to Rational(17, 5), - mapOf(y to 1u) to Rational(-2, 3), - mapOf(x to 1u, y to 1u) to Rational(1, 5), - mapOf(x to 2u, y to 1u) to Rational(-11, 7), - mapOf(y to 2u) to Rational(13, 6), - mapOf(x to 1u, y to 2u) to Rational(-15, 2), - mapOf(x to 2u, y to 2u) to Rational(-14, 4), - ) - )), - "test 5'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 6), - mapOf(x to 1u) to Rational(1, 6), - mapOf(x to 2u) to Rational(-2, 9), - mapOf(y to 1u) to Rational(15, 1), - mapOf(x to 1u, y to 1u) to Rational(18, 7), - mapOf(x to 2u, y to 1u) to Rational(2, 5), - mapOf(y to 2u) to Rational(12, 9), - mapOf(x to 1u, y to 2u) to Rational(-3, 5), - mapOf(x to 2u, y to 2u) to Rational(4, 4), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-11, 9), - mapOf(x to 1u) to Rational(4, 9), - mapOf(x to 2u) to Rational(11, 6), - mapOf(y to 1u) to Rational(-5, 6), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(-1, 7), - mapOf(y to 2u) to Rational(9, 1), - mapOf(x to 1u, y to 2u) to Rational(6, 7), - mapOf(x to 2u, y to 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - iota to LabeledPolynomialAsIs( - mapOf() to Rational(-6, 1), - mapOf(x to 1u) to Rational(-9, 8), - mapOf(x to 2u) to Rational(17, 5), - mapOf(y to 1u) to Rational(-2, 3), - mapOf(x to 1u, y to 1u) to Rational(1, 5), - mapOf(x to 2u, y to 1u) to Rational(-11, 7), - mapOf(y to 2u) to Rational(13, 6), - mapOf(x to 1u, y to 2u) to Rational(-15, 2), - mapOf(x to 2u, y to 2u) to Rational(-14, 4), - ) - )), - "test 6'" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_RationalFunction_substitute_RationalFunction_Map() { - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(0) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ), - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1) - ) - ) - )), - "test 1" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf(x to 4u) to Rational(-17166109, 793800), - mapOf(x to 3u, y to 1u) to Rational(-930960143, 5556600), - mapOf(x to 2u, y to 2u) to Rational(-144665109691, 350065800), - mapOf(x to 1u, y to 3u) to Rational(-17232577, 52920), - mapOf(y to 4u) to Rational(-68141, 1323), - ), - LabeledPolynomialAsIs( - mapOf(x to 4u) to Rational(-57522533, 14288400), - mapOf(x to 3u, y to 1u) to Rational(-13085162953, 300056400), - mapOf(x to 2u, y to 2u) to Rational(-92093367341, 525098700), - mapOf(x to 1u, y to 3u) to Rational(-1979342797, 6667920), - mapOf(y to 4u) to Rational(-3082727, 21168), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(11, 5), - mapOf(y to 1u) to Rational(8, 4), - ), - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1, 9), - mapOf(y to 1u) to Rational(11, 7), - ) - ), - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-2, 7), - mapOf(y to 1u) to Rational(-4, 3), - ), - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(3, 6), - mapOf(y to 1u) to Rational(12, 8), - ) - ), - )), - "test 2" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-130778291, 76800), - mapOf(x to 1u) to Rational(-445270919, 230400), - mapOf(x to 2u) to Rational(44578444937, 14515200), - mapOf(x to 3u) to Rational(17329402153, 1555200), - mapOf(x to 4u) to Rational(89239926809, 2332800), - mapOf(x to 5u) to Rational(2808812267, 145152), - mapOf(x to 6u) to Rational(-21362661007, 725760), - mapOf(x to 7u) to Rational(-258455443, 2016), - mapOf(x to 8u) to Rational(-21454693, 96), - mapOf(y to 1u) to Rational(-1002137, 15360), - mapOf(x to 1u, y to 1u) to Rational(-1704849697, 430080), - mapOf(x to 2u, y to 1u) to Rational(-57657676789, 4838400), - mapOf(x to 3u, y to 1u) to Rational(-101331731, 89600), - mapOf(x to 4u, y to 1u) to Rational(5362280079329, 130636800), - mapOf(x to 5u, y to 1u) to Rational(4069896167053, 130636800), - mapOf(x to 6u, y to 1u) to Rational(12011514569, 544320), - mapOf(x to 7u, y to 1u) to Rational(138293195623, 725760), - mapOf(x to 8u, y to 1u) to Rational(6228779419, 48384), - mapOf(y to 2u) to Rational(-32395872823, 8064000), - mapOf(x to 1u, y to 2u) to Rational(-7398505523, 2304000), - mapOf(x to 2u, y to 2u) to Rational(95217051699521, 3048192000), - mapOf(x to 3u, y to 2u) to Rational(198026968812079, 3657830400), - mapOf(x to 4u, y to 2u) to Rational(4291645618499, 228614400), - mapOf(x to 5u, y to 2u) to Rational(-33211690942439, 914457600), - mapOf(x to 6u, y to 2u) to Rational(-637385538163153, 1371686400), - mapOf(x to 7u, y to 2u) to Rational(-138671528276273, 182891520), - mapOf(x to 8u, y to 2u) to Rational(-14566368751, 217728), - mapOf(y to 3u) to Rational(-10538718719, 2016000), - mapOf(x to 1u, y to 3u) to Rational(-1844485375199, 84672000), - mapOf(x to 2u, y to 3u) to Rational(103968665891, 12096000), - mapOf(x to 3u, y to 3u) to Rational(175402107278351, 1828915200), - mapOf(x to 4u, y to 3u) to Rational(8020699588879, 114307200), - mapOf(x to 5u, y to 3u) to Rational(3414841894991, 38102400), - mapOf(x to 6u, y to 3u) to Rational(1848405591611, 4665600), - mapOf(x to 7u, y to 3u) to Rational(39486708738989, 137168640), - mapOf(x to 8u, y to 3u) to Rational(255926289517, 9144576), - mapOf(y to 4u) to Rational(-655379564629, 105840000), - mapOf(x to 1u, y to 4u) to Rational(-208336039441, 127008000), - mapOf(x to 2u, y to 4u) to Rational(40173146771411, 1143072000), - mapOf(x to 3u, y to 4u) to Rational(150473493581239, 2667168000), - mapOf(x to 4u, y to 4u) to Rational(38833783990483, 1143072000), - mapOf(x to 5u, y to 4u) to Rational(-1963676248203053, 4800902400), - mapOf(x to 6u, y to 4u) to Rational(-2598759412825747, 3200601600), - mapOf(x to 7u, y to 4u) to Rational(-192895352019667, 1280240640), - mapOf(x to 8u, y to 4u) to Rational(3737382679, 6858432), - mapOf(y to 5u) to Rational(-16959378721, 1890000), - mapOf(x to 1u, y to 5u) to Rational(-1864802244743, 79380000), - mapOf(x to 2u, y to 5u) to Rational(13449261536489, 666792000), - mapOf(x to 3u, y to 5u) to Rational(215272234137329, 2667168000), - mapOf(x to 4u, y to 5u) to Rational(6040691379277, 83349000), - mapOf(x to 5u, y to 5u) to Rational(153687143525887, 800150400), - mapOf(x to 6u, y to 5u) to Rational(475602854903563, 2400451200), - mapOf(x to 7u, y to 5u) to Rational(27315599358749, 640120320), - mapOf(x to 8u, y to 5u) to Rational(-2630413357, 10668672), - mapOf(y to 6u) to Rational(-6654999511, 2646000), - mapOf(x to 1u, y to 6u) to Rational(-67885252327, 15876000), - mapOf(x to 2u, y to 6u) to Rational(5786776220983, 2667168000), - mapOf(x to 3u, y to 6u) to Rational(60615922629083, 1143072000), - mapOf(x to 4u, y to 6u) to Rational(-34703539637627407, 672126336000), - mapOf(x to 5u, y to 6u) to Rational(-744694192134101, 2240421120), - mapOf(x to 6u, y to 6u) to Rational(-1782470617231, 14817600), - mapOf(x to 7u, y to 6u) to Rational(59123208433, 8890560), - mapOf(x to 8u, y to 6u) to Rational(-141653, 5292), - mapOf(y to 7u) to Rational(-338051969, 441000), - mapOf(x to 1u, y to 7u) to Rational(468850013, 1764000), - mapOf(x to 2u, y to 7u) to Rational(2102343426101, 222264000), - mapOf(x to 3u, y to 7u) to Rational(7836130602007, 1333584000), - mapOf(x to 4u, y to 7u) to Rational(16239111865997, 746807040), - mapOf(x to 5u, y to 7u) to Rational(3824649185383, 88905600), - mapOf(x to 6u, y to 7u) to Rational(56058614459, 3457440), - mapOf(x to 7u, y to 7u) to Rational(-396766339, 493920), - mapOf(x to 8u, y to 7u) to Rational(-165147, 2744), - mapOf(y to 8u) to Rational(-3088619, 58800), - mapOf(x to 1u, y to 8u) to Rational(155343347, 88200), - mapOf(x to 2u, y to 8u) to Rational(100098736469, 7408800), - mapOf(x to 3u, y to 8u) to Rational(109725511381, 7408800), - mapOf(x to 4u, y to 8u) to Rational(-2431199641013, 59270400), - mapOf(x to 5u, y to 8u) to Rational(-102872383249, 3457440), - mapOf(x to 6u, y to 8u) to Rational(1449461309, 576240), - mapOf(x to 7u, y to 8u) to Rational(812775, 1372), - mapOf(x to 8u, y to 8u) to Rational(-16461, 343) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(164202773, 230400), - mapOf(x to 1u) to Rational(-70345303, 518400), - mapOf(x to 2u) to Rational(-4229702731, 4665600), - mapOf(x to 3u) to Rational(3262171027, 6998400), - mapOf(x to 4u) to Rational(-25423104169, 13996800), - mapOf(x to 5u) to Rational(64061869, 349920), - mapOf(x to 6u) to Rational(-1655878091, 116640), - mapOf(x to 7u) to Rational(-7991441, 648), - mapOf(x to 8u) to Rational(-502591, 18), - mapOf(y to 1u) to Rational(-8780429, 3840), - mapOf(x to 1u, y to 1u) to Rational(434272361, 115200), - mapOf(x to 2u, y to 1u) to Rational(429825727, 41472), - mapOf(x to 3u, y to 1u) to Rational(-10066790339, 6998400), - mapOf(x to 4u, y to 1u) to Rational(70022035471, 20995200), - mapOf(x to 5u, y to 1u) to Rational(-32070283493, 1399680), - mapOf(x to 6u, y to 1u) to Rational(-22051101001, 1399680), - mapOf(x to 7u, y to 1u) to Rational(-126493427, 12960), - mapOf(x to 8u, y to 1u) to Rational(3050245, 864), - mapOf(y to 2u) to Rational(-1194654631, 345600), - mapOf(x to 1u, y to 2u) to Rational(-542961452671, 31104000), - mapOf(x to 2u, y to 2u) to Rational(-234000873607, 48988800), - mapOf(x to 3u, y to 2u) to Rational(140520538087, 3628800), - mapOf(x to 4u, y to 2u) to Rational(9215088876563, 130636800), - mapOf(x to 5u, y to 2u) to Rational(27590569647253, 293932800), - mapOf(x to 6u, y to 2u) to Rational(5129057792891, 97977600), - mapOf(x to 7u, y to 2u) to Rational(-106334191, 5103), - mapOf(x to 8u, y to 2u) to Rational(-1024113911, 435456), - mapOf(y to 3u) to Rational(76223843, 6000), - mapOf(x to 1u, y to 3u) to Rational(57425857357, 2592000), - mapOf(x to 2u, y to 3u) to Rational(-2044736497573, 46656000), - mapOf(x to 3u, y to 3u) to Rational(-26155810120031, 293932800), - mapOf(x to 4u, y to 3u) to Rational(-1064419459813, 6998400), - mapOf(x to 5u, y to 3u) to Rational(-753782018389, 4082400), - mapOf(x to 6u, y to 3u) to Rational(-291973360873, 2799360), - mapOf(x to 7u, y to 3u) to Rational(-46372122599, 816480), - mapOf(x to 8u, y to 3u) to Rational(3579859657, 653184), - mapOf(y to 4u) to Rational(-13374241901, 4320000), - mapOf(x to 1u, y to 4u) to Rational(306606499811, 54432000), - mapOf(x to 2u, y to 4u) to Rational(964267124745437, 13716864000), - mapOf(x to 3u, y to 4u) to Rational(21603809415373, 182891520), - mapOf(x to 4u, y to 4u) to Rational(1097860214654027, 6858432000), - mapOf(x to 5u, y to 4u) to Rational(161615254570669, 914457600), - mapOf(x to 6u, y to 4u) to Rational(758415239461, 22861440), - mapOf(x to 7u, y to 4u) to Rational(2585568355471, 274337280), - mapOf(x to 8u, y to 4u) to Rational(-70433747863, 9144576), - mapOf(y to 5u) to Rational(-9582586217, 2520000), - mapOf(x to 1u, y to 5u) to Rational(-19093471394171, 635040000), - mapOf(x to 2u, y to 5u) to Rational(-13010261944411, 381024000), - mapOf(x to 3u, y to 5u) to Rational(-259039825301861, 4572288000), - mapOf(x to 4u, y to 5u) to Rational(-305081119071079, 2286144000), - mapOf(x to 5u, y to 5u) to Rational(-1923114383311, 19595520), - mapOf(x to 6u, y to 5u) to Rational(-14181787253231, 228614400), - mapOf(x to 7u, y to 5u) to Rational(-3959584789, 4354560), - mapOf(x to 8u, y to 5u) to Rational(4691742523, 762048), - mapOf(y to 6u) to Rational(-588323437, 180000), - mapOf(x to 1u, y to 6u) to Rational(5952234691, 52920000), - mapOf(x to 2u, y to 6u) to Rational(21001851056959, 1088640000), - mapOf(x to 3u, y to 6u) to Rational(84668034357563, 2133734400), - mapOf(x to 4u, y to 6u) to Rational(2029754605811557, 25604812800), - mapOf(x to 5u, y to 6u) to Rational(11721216739823, 426746880), - mapOf(x to 6u, y to 6u) to Rational(-8275903187003, 2133734400), - mapOf(x to 7u, y to 6u) to Rational(-4730447299, 2540160), - mapOf(x to 8u, y to 6u) to Rational(-46069985, 21168), - mapOf(y to 7u) to Rational(-75711301, 117600), - mapOf(x to 1u, y to 7u) to Rational(32430417413, 7056000), - mapOf(x to 2u, y to 7u) to Rational(677988533153, 98784000), - mapOf(x to 3u, y to 7u) to Rational(-948417645827, 71124480), - mapOf(x to 4u, y to 7u) to Rational(-11320265215207, 711244800), - mapOf(x to 5u, y to 7u) to Rational(-676438627783, 50803200), - mapOf(x to 6u, y to 7u) to Rational(-7382274253, 1975680), - mapOf(x to 7u, y to 7u) to Rational(6505733, 2205), - mapOf(x to 8u, y to 7u) to Rational(450137, 882), - mapOf(y to 8u) to Rational(-8368253, 78400), - mapOf(x to 1u, y to 8u) to Rational(6833783, 117600), - mapOf(x to 2u, y to 8u) to Rational(4528971133, 5927040), - mapOf(x to 3u, y to 8u) to Rational(146252636617, 29635200), - mapOf(x to 4u, y to 8u) to Rational(8321882556889, 1659571200), - mapOf(x to 5u, y to 8u) to Rational(-4686033011, 1975680), - mapOf(x to 6u, y to 8u) to Rational(-1074445963, 987840), - mapOf(x to 7u, y to 8u) to Rational(-142313, 588), - mapOf(x to 8u, y to 8u) to Rational(-4281, 49) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-17, 5), - mapOf(x to 1u) to Rational(2, 6), - mapOf(x to 2u) to Rational(14, 1), - mapOf(y to 1u) to Rational(-6, 6), - mapOf(x to 1u, y to 1u) to Rational(-7, 3), - mapOf(x to 2u, y to 1u) to Rational(-2, 9), - mapOf(y to 2u) to Rational(-9, 6), - mapOf(x to 1u, y to 2u) to Rational(17, 4), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(5, 4), - mapOf(x to 1u) to Rational(-5, 9), - mapOf(x to 2u) to Rational(-3, 6), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(14, 5), - mapOf(x to 2u, y to 1u) to Rational(5, 2), - mapOf(y to 2u) to Rational(-18, 7), - mapOf(x to 1u, y to 2u) to Rational(-8, 2), - mapOf(x to 2u, y to 2u) to Rational(18, 9), - ) - ), - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(14, 4), - mapOf(x to 1u) to Rational(7, 6), - mapOf(x to 2u) to Rational(7, 2), - mapOf(y to 1u) to Rational(-15, 2), - mapOf(x to 1u, y to 1u) to Rational(-13, 8), - mapOf(x to 2u, y to 1u) to Rational(-14, 3), - mapOf(y to 2u) to Rational(-7, 6), - mapOf(x to 1u, y to 2u) to Rational(7, 4), - mapOf(x to 2u, y to 2u) to Rational(9, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-7, 4), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(-16, 2), - mapOf(y to 1u) to Rational(-15, 5), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(5, 4), - mapOf(y to 2u) to Rational(-12, 5), - mapOf(x to 1u, y to 2u) to Rational(-18, 2), - mapOf(x to 2u, y to 2u) to Rational(6, 7), - ) - ), - )), - "test 3" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-130778291, 76800), - mapOf(x to 1u) to Rational(-445270919, 230400), - mapOf(x to 2u) to Rational(44578444937, 14515200), - mapOf(x to 3u) to Rational(17329402153, 1555200), - mapOf(x to 4u) to Rational(89239926809, 2332800), - mapOf(x to 5u) to Rational(2808812267, 145152), - mapOf(x to 6u) to Rational(-21362661007, 725760), - mapOf(x to 7u) to Rational(-258455443, 2016), - mapOf(x to 8u) to Rational(-21454693, 96), - mapOf(y to 1u) to Rational(-1002137, 15360), - mapOf(x to 1u, y to 1u) to Rational(-1704849697, 430080), - mapOf(x to 2u, y to 1u) to Rational(-57657676789, 4838400), - mapOf(x to 3u, y to 1u) to Rational(-101331731, 89600), - mapOf(x to 4u, y to 1u) to Rational(5362280079329, 130636800), - mapOf(x to 5u, y to 1u) to Rational(4069896167053, 130636800), - mapOf(x to 6u, y to 1u) to Rational(12011514569, 544320), - mapOf(x to 7u, y to 1u) to Rational(138293195623, 725760), - mapOf(x to 8u, y to 1u) to Rational(6228779419, 48384), - mapOf(y to 2u) to Rational(-32395872823, 8064000), - mapOf(x to 1u, y to 2u) to Rational(-7398505523, 2304000), - mapOf(x to 2u, y to 2u) to Rational(95217051699521, 3048192000), - mapOf(x to 3u, y to 2u) to Rational(198026968812079, 3657830400), - mapOf(x to 4u, y to 2u) to Rational(4291645618499, 228614400), - mapOf(x to 5u, y to 2u) to Rational(-33211690942439, 914457600), - mapOf(x to 6u, y to 2u) to Rational(-637385538163153, 1371686400), - mapOf(x to 7u, y to 2u) to Rational(-138671528276273, 182891520), - mapOf(x to 8u, y to 2u) to Rational(-14566368751, 217728), - mapOf(y to 3u) to Rational(-10538718719, 2016000), - mapOf(x to 1u, y to 3u) to Rational(-1844485375199, 84672000), - mapOf(x to 2u, y to 3u) to Rational(103968665891, 12096000), - mapOf(x to 3u, y to 3u) to Rational(175402107278351, 1828915200), - mapOf(x to 4u, y to 3u) to Rational(8020699588879, 114307200), - mapOf(x to 5u, y to 3u) to Rational(3414841894991, 38102400), - mapOf(x to 6u, y to 3u) to Rational(1848405591611, 4665600), - mapOf(x to 7u, y to 3u) to Rational(39486708738989, 137168640), - mapOf(x to 8u, y to 3u) to Rational(255926289517, 9144576), - mapOf(y to 4u) to Rational(-655379564629, 105840000), - mapOf(x to 1u, y to 4u) to Rational(-208336039441, 127008000), - mapOf(x to 2u, y to 4u) to Rational(40173146771411, 1143072000), - mapOf(x to 3u, y to 4u) to Rational(150473493581239, 2667168000), - mapOf(x to 4u, y to 4u) to Rational(38833783990483, 1143072000), - mapOf(x to 5u, y to 4u) to Rational(-1963676248203053, 4800902400), - mapOf(x to 6u, y to 4u) to Rational(-2598759412825747, 3200601600), - mapOf(x to 7u, y to 4u) to Rational(-192895352019667, 1280240640), - mapOf(x to 8u, y to 4u) to Rational(3737382679, 6858432), - mapOf(y to 5u) to Rational(-16959378721, 1890000), - mapOf(x to 1u, y to 5u) to Rational(-1864802244743, 79380000), - mapOf(x to 2u, y to 5u) to Rational(13449261536489, 666792000), - mapOf(x to 3u, y to 5u) to Rational(215272234137329, 2667168000), - mapOf(x to 4u, y to 5u) to Rational(6040691379277, 83349000), - mapOf(x to 5u, y to 5u) to Rational(153687143525887, 800150400), - mapOf(x to 6u, y to 5u) to Rational(475602854903563, 2400451200), - mapOf(x to 7u, y to 5u) to Rational(27315599358749, 640120320), - mapOf(x to 8u, y to 5u) to Rational(-2630413357, 10668672), - mapOf(y to 6u) to Rational(-6654999511, 2646000), - mapOf(x to 1u, y to 6u) to Rational(-67885252327, 15876000), - mapOf(x to 2u, y to 6u) to Rational(5786776220983, 2667168000), - mapOf(x to 3u, y to 6u) to Rational(60615922629083, 1143072000), - mapOf(x to 4u, y to 6u) to Rational(-34703539637627407, 672126336000), - mapOf(x to 5u, y to 6u) to Rational(-744694192134101, 2240421120), - mapOf(x to 6u, y to 6u) to Rational(-1782470617231, 14817600), - mapOf(x to 7u, y to 6u) to Rational(59123208433, 8890560), - mapOf(x to 8u, y to 6u) to Rational(-141653, 5292), - mapOf(y to 7u) to Rational(-338051969, 441000), - mapOf(x to 1u, y to 7u) to Rational(468850013, 1764000), - mapOf(x to 2u, y to 7u) to Rational(2102343426101, 222264000), - mapOf(x to 3u, y to 7u) to Rational(7836130602007, 1333584000), - mapOf(x to 4u, y to 7u) to Rational(16239111865997, 746807040), - mapOf(x to 5u, y to 7u) to Rational(3824649185383, 88905600), - mapOf(x to 6u, y to 7u) to Rational(56058614459, 3457440), - mapOf(x to 7u, y to 7u) to Rational(-396766339, 493920), - mapOf(x to 8u, y to 7u) to Rational(-165147, 2744), - mapOf(y to 8u) to Rational(-3088619, 58800), - mapOf(x to 1u, y to 8u) to Rational(155343347, 88200), - mapOf(x to 2u, y to 8u) to Rational(100098736469, 7408800), - mapOf(x to 3u, y to 8u) to Rational(109725511381, 7408800), - mapOf(x to 4u, y to 8u) to Rational(-2431199641013, 59270400), - mapOf(x to 5u, y to 8u) to Rational(-102872383249, 3457440), - mapOf(x to 6u, y to 8u) to Rational(1449461309, 576240), - mapOf(x to 7u, y to 8u) to Rational(812775, 1372), - mapOf(x to 8u, y to 8u) to Rational(-16461, 343) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(164202773, 230400), - mapOf(x to 1u) to Rational(-70345303, 518400), - mapOf(x to 2u) to Rational(-4229702731, 4665600), - mapOf(x to 3u) to Rational(3262171027, 6998400), - mapOf(x to 4u) to Rational(-25423104169, 13996800), - mapOf(x to 5u) to Rational(64061869, 349920), - mapOf(x to 6u) to Rational(-1655878091, 116640), - mapOf(x to 7u) to Rational(-7991441, 648), - mapOf(x to 8u) to Rational(-502591, 18), - mapOf(y to 1u) to Rational(-8780429, 3840), - mapOf(x to 1u, y to 1u) to Rational(434272361, 115200), - mapOf(x to 2u, y to 1u) to Rational(429825727, 41472), - mapOf(x to 3u, y to 1u) to Rational(-10066790339, 6998400), - mapOf(x to 4u, y to 1u) to Rational(70022035471, 20995200), - mapOf(x to 5u, y to 1u) to Rational(-32070283493, 1399680), - mapOf(x to 6u, y to 1u) to Rational(-22051101001, 1399680), - mapOf(x to 7u, y to 1u) to Rational(-126493427, 12960), - mapOf(x to 8u, y to 1u) to Rational(3050245, 864), - mapOf(y to 2u) to Rational(-1194654631, 345600), - mapOf(x to 1u, y to 2u) to Rational(-542961452671, 31104000), - mapOf(x to 2u, y to 2u) to Rational(-234000873607, 48988800), - mapOf(x to 3u, y to 2u) to Rational(140520538087, 3628800), - mapOf(x to 4u, y to 2u) to Rational(9215088876563, 130636800), - mapOf(x to 5u, y to 2u) to Rational(27590569647253, 293932800), - mapOf(x to 6u, y to 2u) to Rational(5129057792891, 97977600), - mapOf(x to 7u, y to 2u) to Rational(-106334191, 5103), - mapOf(x to 8u, y to 2u) to Rational(-1024113911, 435456), - mapOf(y to 3u) to Rational(76223843, 6000), - mapOf(x to 1u, y to 3u) to Rational(57425857357, 2592000), - mapOf(x to 2u, y to 3u) to Rational(-2044736497573, 46656000), - mapOf(x to 3u, y to 3u) to Rational(-26155810120031, 293932800), - mapOf(x to 4u, y to 3u) to Rational(-1064419459813, 6998400), - mapOf(x to 5u, y to 3u) to Rational(-753782018389, 4082400), - mapOf(x to 6u, y to 3u) to Rational(-291973360873, 2799360), - mapOf(x to 7u, y to 3u) to Rational(-46372122599, 816480), - mapOf(x to 8u, y to 3u) to Rational(3579859657, 653184), - mapOf(y to 4u) to Rational(-13374241901, 4320000), - mapOf(x to 1u, y to 4u) to Rational(306606499811, 54432000), - mapOf(x to 2u, y to 4u) to Rational(964267124745437, 13716864000), - mapOf(x to 3u, y to 4u) to Rational(21603809415373, 182891520), - mapOf(x to 4u, y to 4u) to Rational(1097860214654027, 6858432000), - mapOf(x to 5u, y to 4u) to Rational(161615254570669, 914457600), - mapOf(x to 6u, y to 4u) to Rational(758415239461, 22861440), - mapOf(x to 7u, y to 4u) to Rational(2585568355471, 274337280), - mapOf(x to 8u, y to 4u) to Rational(-70433747863, 9144576), - mapOf(y to 5u) to Rational(-9582586217, 2520000), - mapOf(x to 1u, y to 5u) to Rational(-19093471394171, 635040000), - mapOf(x to 2u, y to 5u) to Rational(-13010261944411, 381024000), - mapOf(x to 3u, y to 5u) to Rational(-259039825301861, 4572288000), - mapOf(x to 4u, y to 5u) to Rational(-305081119071079, 2286144000), - mapOf(x to 5u, y to 5u) to Rational(-1923114383311, 19595520), - mapOf(x to 6u, y to 5u) to Rational(-14181787253231, 228614400), - mapOf(x to 7u, y to 5u) to Rational(-3959584789, 4354560), - mapOf(x to 8u, y to 5u) to Rational(4691742523, 762048), - mapOf(y to 6u) to Rational(-588323437, 180000), - mapOf(x to 1u, y to 6u) to Rational(5952234691, 52920000), - mapOf(x to 2u, y to 6u) to Rational(21001851056959, 1088640000), - mapOf(x to 3u, y to 6u) to Rational(84668034357563, 2133734400), - mapOf(x to 4u, y to 6u) to Rational(2029754605811557, 25604812800), - mapOf(x to 5u, y to 6u) to Rational(11721216739823, 426746880), - mapOf(x to 6u, y to 6u) to Rational(-8275903187003, 2133734400), - mapOf(x to 7u, y to 6u) to Rational(-4730447299, 2540160), - mapOf(x to 8u, y to 6u) to Rational(-46069985, 21168), - mapOf(y to 7u) to Rational(-75711301, 117600), - mapOf(x to 1u, y to 7u) to Rational(32430417413, 7056000), - mapOf(x to 2u, y to 7u) to Rational(677988533153, 98784000), - mapOf(x to 3u, y to 7u) to Rational(-948417645827, 71124480), - mapOf(x to 4u, y to 7u) to Rational(-11320265215207, 711244800), - mapOf(x to 5u, y to 7u) to Rational(-676438627783, 50803200), - mapOf(x to 6u, y to 7u) to Rational(-7382274253, 1975680), - mapOf(x to 7u, y to 7u) to Rational(6505733, 2205), - mapOf(x to 8u, y to 7u) to Rational(450137, 882), - mapOf(y to 8u) to Rational(-8368253, 78400), - mapOf(x to 1u, y to 8u) to Rational(6833783, 117600), - mapOf(x to 2u, y to 8u) to Rational(4528971133, 5927040), - mapOf(x to 3u, y to 8u) to Rational(146252636617, 29635200), - mapOf(x to 4u, y to 8u) to Rational(8321882556889, 1659571200), - mapOf(x to 5u, y to 8u) to Rational(-4686033011, 1975680), - mapOf(x to 6u, y to 8u) to Rational(-1074445963, 987840), - mapOf(x to 7u, y to 8u) to Rational(-142313, 588), - mapOf(x to 8u, y to 8u) to Rational(-4281, 49) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-17, 5), - mapOf(x to 1u) to Rational(2, 6), - mapOf(x to 2u) to Rational(14, 1), - mapOf(y to 1u) to Rational(-6, 6), - mapOf(x to 1u, y to 1u) to Rational(-7, 3), - mapOf(x to 2u, y to 1u) to Rational(-2, 9), - mapOf(y to 2u) to Rational(-9, 6), - mapOf(x to 1u, y to 2u) to Rational(17, 4), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(5, 4), - mapOf(x to 1u) to Rational(-5, 9), - mapOf(x to 2u) to Rational(-3, 6), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(14, 5), - mapOf(x to 2u, y to 1u) to Rational(5, 2), - mapOf(y to 2u) to Rational(-18, 7), - mapOf(x to 1u, y to 2u) to Rational(-8, 2), - mapOf(x to 2u, y to 2u) to Rational(18, 9), - ) - ), - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(14, 4), - mapOf(x to 1u) to Rational(7, 6), - mapOf(x to 2u) to Rational(7, 2), - mapOf(y to 1u) to Rational(-15, 2), - mapOf(x to 1u, y to 1u) to Rational(-13, 8), - mapOf(x to 2u, y to 1u) to Rational(-14, 3), - mapOf(y to 2u) to Rational(-7, 6), - mapOf(x to 1u, y to 2u) to Rational(7, 4), - mapOf(x to 2u, y to 2u) to Rational(9, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-7, 4), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(-16, 2), - mapOf(y to 1u) to Rational(-15, 5), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(5, 4), - mapOf(y to 2u) to Rational(-12, 5), - mapOf(x to 1u, y to 2u) to Rational(-18, 2), - mapOf(x to 2u, y to 2u) to Rational(6, 7), - ) - ), - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 8), - mapOf(x to 1u) to Rational(-12, 6), - mapOf(x to 2u) to Rational(7, 6), - mapOf(y to 1u) to Rational(-10, 4), - mapOf(x to 1u, y to 1u) to Rational(-7, 6), - mapOf(x to 2u, y to 1u) to Rational(8, 9), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(5, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(10, 6), - mapOf(x to 1u) to Rational(-18, 6), - mapOf(x to 2u) to Rational(5, 1), - mapOf(y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(8, 4), - mapOf(x to 2u, y to 1u) to Rational(-4, 9), - mapOf(y to 2u) to Rational(-6, 5), - mapOf(x to 1u, y to 2u) to Rational(-15, 8), - mapOf(x to 2u, y to 2u) to Rational(-18, 5), - ) - ), - )), - "test 3'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(2303, 64), - mapOf(x to 1u) to Rational(31843, 192), - mapOf(x to 2u) to Rational(118891, 576), - mapOf(x to 3u) to Rational(94453, 168), - mapOf(x to 4u) to Rational(-179203, 1512), - mapOf(x to 5u) to Rational(-16979, 126), - mapOf(x to 6u) to Rational(-13499, 12), - mapOf(y to 1u) to Rational(-4767, 64), - mapOf(x to 1u, y to 1u) to Rational(-58689, 256), - mapOf(x to 2u, y to 1u) to Rational(-757333, 4032), - mapOf(x to 3u, y to 1u) to Rational(-4921205, 4032), - mapOf(x to 4u, y to 1u) to Rational(-2930815, 4032), - mapOf(x to 5u, y to 1u) to Rational(-398803, 1512), - mapOf(x to 6u, y to 1u) to Rational(18835, 36), - mapOf(y to 2u) to Rational(224101, 960), - mapOf(x to 1u, y to 2u) to Rational(9139699, 40320), - mapOf(x to 2u, y to 2u) to Rational(3848803, 5760), - mapOf(x to 3u, y to 2u) to Rational(93102371, 241920), - mapOf(x to 4u, y to 2u) to Rational(-65821229, 141120), - mapOf(x to 5u, y to 2u) to Rational(-15675899, 7056), - mapOf(x to 6u, y to 2u) to Rational(10459, 189), - mapOf(y to 3u) to Rational(2411, 16), - mapOf(x to 1u, y to 3u) to Rational(1294543, 10080), - mapOf(x to 2u, y to 3u) to Rational(-1740199, 1440), - mapOf(x to 3u, y to 3u) to Rational(-266994841, 282240), - mapOf(x to 4u, y to 3u) to Rational(-41261893, 211680), - mapOf(x to 5u, y to 3u) to Rational(1717357, 3528), - mapOf(x to 6u, y to 3u) to Rational(69, 14), - mapOf(y to 4u) to Rational(13231, 360), - mapOf(x to 1u, y to 4u) to Rational(4858831, 25200), - mapOf(x to 2u, y to 4u) to Rational(15565759, 75600), - mapOf(x to 3u, y to 4u) to Rational(-15583391, 35280), - mapOf(x to 4u, y to 4u) to Rational(-13345747, 11760), - mapOf(x to 5u, y to 4u) to Rational(140103, 686), - mapOf(x to 6u, y to 4u) to Rational(-765, 49) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(31409, 576), - mapOf(x to 1u) to Rational(-337099, 1728), - mapOf(x to 2u) to Rational(-211429, 1728), - mapOf(x to 3u) to Rational(-259241, 432), - mapOf(x to 4u) to Rational(-13777, 36), - mapOf(x to 5u) to Rational(-41389, 72), - mapOf(x to 6u) to Rational(-7679, 48), - mapOf(y to 1u) to Rational(-3269, 12), - mapOf(x to 1u, y to 1u) to Rational(629569, 864), - mapOf(x to 2u, y to 1u) to Rational(53867, 324), - mapOf(x to 3u, y to 1u) to Rational(2290577, 1728), - mapOf(x to 4u, y to 1u) to Rational(101507, 216), - mapOf(x to 5u, y to 1u) to Rational(213109, 288), - mapOf(x to 6u, y to 1u) to Rational(17927, 144), - mapOf(y to 2u) to Rational(314587, 1080), - mapOf(x to 1u, y to 2u) to Rational(-109771, 144), - mapOf(x to 2u, y to 2u) to Rational(-6469, 16), - mapOf(x to 3u, y to 2u) to Rational(-298291681, 181440), - mapOf(x to 4u, y to 2u) to Rational(-59147357, 48384), - mapOf(x to 5u, y to 2u) to Rational(-4982365, 6048), - mapOf(x to 6u, y to 2u) to Rational(-18727, 576), - mapOf(y to 3u) to Rational(12379, 90), - mapOf(x to 1u, y to 3u) to Rational(-542911, 1620), - mapOf(x to 2u, y to 3u) to Rational(143123, 1260), - mapOf(x to 3u, y to 3u) to Rational(9859177, 30240), - mapOf(x to 4u, y to 3u) to Rational(9312529, 20160), - mapOf(x to 5u, y to 3u) to Rational(207001, 672), - mapOf(x to 6u, y to 3u) to Rational(203, 24), - mapOf(y to 4u) to Rational(9442, 675), - mapOf(x to 1u, y to 4u) to Rational(-13729, 300), - mapOf(x to 2u, y to 4u) to Rational(-3490471, 25200), - mapOf(x to 3u, y to 4u) to Rational(-333031, 840), - mapOf(x to 4u, y to 4u) to Rational(-7572211, 47040), - mapOf(x to 5u, y to 4u) to Rational(-1189, 56), - mapOf(x to 6u, y to 4u) to Rational(-405, 196) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(14, 4), - mapOf(x to 1u) to Rational(7, 6), - mapOf(x to 2u) to Rational(7, 2), - mapOf(y to 1u) to Rational(-15, 2), - mapOf(x to 1u, y to 1u) to Rational(-13, 8), - mapOf(x to 2u, y to 1u) to Rational(-14, 3), - mapOf(y to 2u) to Rational(-7, 6), - mapOf(x to 1u, y to 2u) to Rational(7, 4), - mapOf(x to 2u, y to 2u) to Rational(9, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-7, 4), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(-16, 2), - mapOf(y to 1u) to Rational(-15, 5), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(5, 4), - mapOf(y to 2u) to Rational(-12, 5), - mapOf(x to 1u, y to 2u) to Rational(-18, 2), - mapOf(x to 2u, y to 2u) to Rational(6, 7), - ) - ), - )), - "test 4" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(2303, 64), - mapOf(x to 1u) to Rational(31843, 192), - mapOf(x to 2u) to Rational(118891, 576), - mapOf(x to 3u) to Rational(94453, 168), - mapOf(x to 4u) to Rational(-179203, 1512), - mapOf(x to 5u) to Rational(-16979, 126), - mapOf(x to 6u) to Rational(-13499, 12), - mapOf(y to 1u) to Rational(-4767, 64), - mapOf(x to 1u, y to 1u) to Rational(-58689, 256), - mapOf(x to 2u, y to 1u) to Rational(-757333, 4032), - mapOf(x to 3u, y to 1u) to Rational(-4921205, 4032), - mapOf(x to 4u, y to 1u) to Rational(-2930815, 4032), - mapOf(x to 5u, y to 1u) to Rational(-398803, 1512), - mapOf(x to 6u, y to 1u) to Rational(18835, 36), - mapOf(y to 2u) to Rational(224101, 960), - mapOf(x to 1u, y to 2u) to Rational(9139699, 40320), - mapOf(x to 2u, y to 2u) to Rational(3848803, 5760), - mapOf(x to 3u, y to 2u) to Rational(93102371, 241920), - mapOf(x to 4u, y to 2u) to Rational(-65821229, 141120), - mapOf(x to 5u, y to 2u) to Rational(-15675899, 7056), - mapOf(x to 6u, y to 2u) to Rational(10459, 189), - mapOf(y to 3u) to Rational(2411, 16), - mapOf(x to 1u, y to 3u) to Rational(1294543, 10080), - mapOf(x to 2u, y to 3u) to Rational(-1740199, 1440), - mapOf(x to 3u, y to 3u) to Rational(-266994841, 282240), - mapOf(x to 4u, y to 3u) to Rational(-41261893, 211680), - mapOf(x to 5u, y to 3u) to Rational(1717357, 3528), - mapOf(x to 6u, y to 3u) to Rational(69, 14), - mapOf(y to 4u) to Rational(13231, 360), - mapOf(x to 1u, y to 4u) to Rational(4858831, 25200), - mapOf(x to 2u, y to 4u) to Rational(15565759, 75600), - mapOf(x to 3u, y to 4u) to Rational(-15583391, 35280), - mapOf(x to 4u, y to 4u) to Rational(-13345747, 11760), - mapOf(x to 5u, y to 4u) to Rational(140103, 686), - mapOf(x to 6u, y to 4u) to Rational(-765, 49) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(31409, 576), - mapOf(x to 1u) to Rational(-337099, 1728), - mapOf(x to 2u) to Rational(-211429, 1728), - mapOf(x to 3u) to Rational(-259241, 432), - mapOf(x to 4u) to Rational(-13777, 36), - mapOf(x to 5u) to Rational(-41389, 72), - mapOf(x to 6u) to Rational(-7679, 48), - mapOf(y to 1u) to Rational(-3269, 12), - mapOf(x to 1u, y to 1u) to Rational(629569, 864), - mapOf(x to 2u, y to 1u) to Rational(53867, 324), - mapOf(x to 3u, y to 1u) to Rational(2290577, 1728), - mapOf(x to 4u, y to 1u) to Rational(101507, 216), - mapOf(x to 5u, y to 1u) to Rational(213109, 288), - mapOf(x to 6u, y to 1u) to Rational(17927, 144), - mapOf(y to 2u) to Rational(314587, 1080), - mapOf(x to 1u, y to 2u) to Rational(-109771, 144), - mapOf(x to 2u, y to 2u) to Rational(-6469, 16), - mapOf(x to 3u, y to 2u) to Rational(-298291681, 181440), - mapOf(x to 4u, y to 2u) to Rational(-59147357, 48384), - mapOf(x to 5u, y to 2u) to Rational(-4982365, 6048), - mapOf(x to 6u, y to 2u) to Rational(-18727, 576), - mapOf(y to 3u) to Rational(12379, 90), - mapOf(x to 1u, y to 3u) to Rational(-542911, 1620), - mapOf(x to 2u, y to 3u) to Rational(143123, 1260), - mapOf(x to 3u, y to 3u) to Rational(9859177, 30240), - mapOf(x to 4u, y to 3u) to Rational(9312529, 20160), - mapOf(x to 5u, y to 3u) to Rational(207001, 672), - mapOf(x to 6u, y to 3u) to Rational(203, 24), - mapOf(y to 4u) to Rational(9442, 675), - mapOf(x to 1u, y to 4u) to Rational(-13729, 300), - mapOf(x to 2u, y to 4u) to Rational(-3490471, 25200), - mapOf(x to 3u, y to 4u) to Rational(-333031, 840), - mapOf(x to 4u, y to 4u) to Rational(-7572211, 47040), - mapOf(x to 5u, y to 4u) to Rational(-1189, 56), - mapOf(x to 6u, y to 4u) to Rational(-405, 196) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - y to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(14, 4), - mapOf(x to 1u) to Rational(7, 6), - mapOf(x to 2u) to Rational(7, 2), - mapOf(y to 1u) to Rational(-15, 2), - mapOf(x to 1u, y to 1u) to Rational(-13, 8), - mapOf(x to 2u, y to 1u) to Rational(-14, 3), - mapOf(y to 2u) to Rational(-7, 6), - mapOf(x to 1u, y to 2u) to Rational(7, 4), - mapOf(x to 2u, y to 2u) to Rational(9, 7), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-7, 4), - mapOf(x to 1u) to Rational(-6, 3), - mapOf(x to 2u) to Rational(-16, 2), - mapOf(y to 1u) to Rational(-15, 5), - mapOf(x to 1u, y to 1u) to Rational(4, 6), - mapOf(x to 2u, y to 1u) to Rational(5, 4), - mapOf(y to 2u) to Rational(-12, 5), - mapOf(x to 1u, y to 2u) to Rational(-18, 2), - mapOf(x to 2u, y to 2u) to Rational(6, 7), - ) - ), - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 8), - mapOf(x to 1u) to Rational(-12, 6), - mapOf(x to 2u) to Rational(7, 6), - mapOf(y to 1u) to Rational(-10, 4), - mapOf(x to 1u, y to 1u) to Rational(-7, 6), - mapOf(x to 2u, y to 1u) to Rational(8, 9), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(5, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(10, 6), - mapOf(x to 1u) to Rational(-18, 6), - mapOf(x to 2u) to Rational(5, 1), - mapOf(y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(8, 4), - mapOf(x to 2u, y to 1u) to Rational(-4, 9), - mapOf(y to 2u) to Rational(-6, 5), - mapOf(x to 1u, y to 2u) to Rational(-15, 8), - mapOf(x to 2u, y to 2u) to Rational(-18, 5), - ) - ), - )), - "test 4'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-506213, 2800), - mapOf(x to 1u) to Rational(9859, 315), - mapOf(x to 2u) to Rational(17384377, 11340), - mapOf(x to 3u) to Rational(-9662, 63), - mapOf(x to 4u) to Rational(-12563, 4), - mapOf(y to 1u) to Rational(-486293, 22400), - mapOf(x to 1u, y to 1u) to Rational(-6530947, 25200), - mapOf(x to 2u, y to 1u) to Rational(866125, 18144), - mapOf(x to 3u, y to 1u) to Rational(2948747, 2520), - mapOf(x to 4u, y to 1u) to Rational(1196611, 2016), - mapOf(y to 2u) to Rational(-20266021, 117600), - mapOf(x to 1u, y to 2u) to Rational(26656339, 44100), - mapOf(x to 2u, y to 2u) to Rational(19499183, 18144), - mapOf(x to 3u, y to 2u) to Rational(-19801849, 7560), - mapOf(x to 4u, y to 2u) to Rational(-2639635, 1296), - mapOf(y to 3u) to Rational(-5017697, 29400), - mapOf(x to 1u, y to 3u) to Rational(-606007, 1575), - mapOf(x to 2u, y to 3u) to Rational(127494487, 132300), - mapOf(x to 3u, y to 3u) to Rational(166567, 105), - mapOf(x to 4u, y to 3u) to Rational(486403, 18144), - mapOf(y to 4u) to Rational(-32182, 735), - mapOf(x to 1u, y to 4u) to Rational(2420671, 8820), - mapOf(x to 2u, y to 4u) to Rational(-12619193, 26460), - mapOf(x to 3u, y to 4u) to Rational(-6823067, 5670), - mapOf(x to 4u, y to 4u) to Rational(-2311693, 13608), - mapOf(y to 5u) to Rational(-13324, 245), - mapOf(x to 1u, y to 5u) to Rational(1966, 35), - mapOf(x to 2u, y to 5u) to Rational(1052719, 2520), - mapOf(x to 3u, y to 5u) to Rational(19153, 270), - mapOf(x to 4u, y to 5u) to Rational(701, 54), - mapOf(y to 6u) to Rational(4647, 196), - mapOf(x to 1u, y to 6u) to Rational(2197, 28), - mapOf(x to 2u, y to 6u) to Rational(-43853, 336), - mapOf(x to 3u, y to 6u) to Rational(-301, 3), - mapOf(x to 4u, y to 6u) to Rational(34, 3) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-2843, 1600), - mapOf(x to 1u) to Rational(-1483, 240), - mapOf(x to 2u) to Rational(110623, 1296), - mapOf(x to 3u) to Rational(1265, 72), - mapOf(x to 4u) to Rational(-5011, 16), - mapOf(y to 1u) to Rational(47743, 1800), - mapOf(x to 1u, y to 1u) to Rational(619229, 32400), - mapOf(x to 2u, y to 1u) to Rational(-5978369, 58320), - mapOf(x to 3u, y to 1u) to Rational(-86081, 1620), - mapOf(x to 4u, y to 1u) to Rational(6325, 72), - mapOf(y to 2u) to Rational(110951, 3360), - mapOf(x to 1u, y to 2u) to Rational(-9550649, 302400), - mapOf(x to 2u, y to 2u) to Rational(6542933, 85050), - mapOf(x to 3u, y to 2u) to Rational(4708291, 38880), - mapOf(x to 4u, y to 2u) to Rational(-433327, 1296), - mapOf(y to 3u) to Rational(56143, 600), - mapOf(x to 1u, y to 3u) to Rational(94243, 720), - mapOf(x to 2u, y to 3u) to Rational(-46779139, 226800), - mapOf(x to 3u, y to 3u) to Rational(-6948253, 12960), - mapOf(x to 4u, y to 3u) to Rational(-260261, 486), - mapOf(y to 4u) to Rational(-3205317, 19600), - mapOf(x to 1u, y to 4u) to Rational(-201253, 1050), - mapOf(x to 2u, y to 4u) to Rational(332192677, 302400), - mapOf(x to 3u, y to 4u) to Rational(351511, 360), - mapOf(x to 4u, y to 4u) to Rational(-40547, 81), - mapOf(y to 5u) to Rational(-65421, 1960), - mapOf(x to 1u, y to 5u) to Rational(-10118, 35), - mapOf(x to 2u, y to 5u) to Rational(-4341709, 10080), - mapOf(x to 3u, y to 5u) to Rational(-91703, 360), - mapOf(x to 4u, y to 5u) to Rational(-85, 9), - mapOf(y to 6u) to Rational(-25965, 784), - mapOf(x to 1u, y to 6u) to Rational(3351, 16), - mapOf(x to 2u, y to 6u) to Rational(595159, 1344), - mapOf(x to 3u, y to 6u) to Rational(-1381, 12), - mapOf(x to 4u, y to 6u) to Rational(-155, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-17, 5), - mapOf(x to 1u) to Rational(2, 6), - mapOf(x to 2u) to Rational(14, 1), - mapOf(y to 1u) to Rational(-6, 6), - mapOf(x to 1u, y to 1u) to Rational(-7, 3), - mapOf(x to 2u, y to 1u) to Rational(-2, 9), - mapOf(y to 2u) to Rational(-9, 6), - mapOf(x to 1u, y to 2u) to Rational(17, 4), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(5, 4), - mapOf(x to 1u) to Rational(-5, 9), - mapOf(x to 2u) to Rational(-3, 6), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(14, 5), - mapOf(x to 2u, y to 1u) to Rational(5, 2), - mapOf(y to 2u) to Rational(-18, 7), - mapOf(x to 1u, y to 2u) to Rational(-8, 2), - mapOf(x to 2u, y to 2u) to Rational(18, 9), - ) - ), - )), - "test 5" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-506213, 2800), - mapOf(x to 1u) to Rational(9859, 315), - mapOf(x to 2u) to Rational(17384377, 11340), - mapOf(x to 3u) to Rational(-9662, 63), - mapOf(x to 4u) to Rational(-12563, 4), - mapOf(y to 1u) to Rational(-486293, 22400), - mapOf(x to 1u, y to 1u) to Rational(-6530947, 25200), - mapOf(x to 2u, y to 1u) to Rational(866125, 18144), - mapOf(x to 3u, y to 1u) to Rational(2948747, 2520), - mapOf(x to 4u, y to 1u) to Rational(1196611, 2016), - mapOf(y to 2u) to Rational(-20266021, 117600), - mapOf(x to 1u, y to 2u) to Rational(26656339, 44100), - mapOf(x to 2u, y to 2u) to Rational(19499183, 18144), - mapOf(x to 3u, y to 2u) to Rational(-19801849, 7560), - mapOf(x to 4u, y to 2u) to Rational(-2639635, 1296), - mapOf(y to 3u) to Rational(-5017697, 29400), - mapOf(x to 1u, y to 3u) to Rational(-606007, 1575), - mapOf(x to 2u, y to 3u) to Rational(127494487, 132300), - mapOf(x to 3u, y to 3u) to Rational(166567, 105), - mapOf(x to 4u, y to 3u) to Rational(486403, 18144), - mapOf(y to 4u) to Rational(-32182, 735), - mapOf(x to 1u, y to 4u) to Rational(2420671, 8820), - mapOf(x to 2u, y to 4u) to Rational(-12619193, 26460), - mapOf(x to 3u, y to 4u) to Rational(-6823067, 5670), - mapOf(x to 4u, y to 4u) to Rational(-2311693, 13608), - mapOf(y to 5u) to Rational(-13324, 245), - mapOf(x to 1u, y to 5u) to Rational(1966, 35), - mapOf(x to 2u, y to 5u) to Rational(1052719, 2520), - mapOf(x to 3u, y to 5u) to Rational(19153, 270), - mapOf(x to 4u, y to 5u) to Rational(701, 54), - mapOf(y to 6u) to Rational(4647, 196), - mapOf(x to 1u, y to 6u) to Rational(2197, 28), - mapOf(x to 2u, y to 6u) to Rational(-43853, 336), - mapOf(x to 3u, y to 6u) to Rational(-301, 3), - mapOf(x to 4u, y to 6u) to Rational(34, 3) - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-2843, 1600), - mapOf(x to 1u) to Rational(-1483, 240), - mapOf(x to 2u) to Rational(110623, 1296), - mapOf(x to 3u) to Rational(1265, 72), - mapOf(x to 4u) to Rational(-5011, 16), - mapOf(y to 1u) to Rational(47743, 1800), - mapOf(x to 1u, y to 1u) to Rational(619229, 32400), - mapOf(x to 2u, y to 1u) to Rational(-5978369, 58320), - mapOf(x to 3u, y to 1u) to Rational(-86081, 1620), - mapOf(x to 4u, y to 1u) to Rational(6325, 72), - mapOf(y to 2u) to Rational(110951, 3360), - mapOf(x to 1u, y to 2u) to Rational(-9550649, 302400), - mapOf(x to 2u, y to 2u) to Rational(6542933, 85050), - mapOf(x to 3u, y to 2u) to Rational(4708291, 38880), - mapOf(x to 4u, y to 2u) to Rational(-433327, 1296), - mapOf(y to 3u) to Rational(56143, 600), - mapOf(x to 1u, y to 3u) to Rational(94243, 720), - mapOf(x to 2u, y to 3u) to Rational(-46779139, 226800), - mapOf(x to 3u, y to 3u) to Rational(-6948253, 12960), - mapOf(x to 4u, y to 3u) to Rational(-260261, 486), - mapOf(y to 4u) to Rational(-3205317, 19600), - mapOf(x to 1u, y to 4u) to Rational(-201253, 1050), - mapOf(x to 2u, y to 4u) to Rational(332192677, 302400), - mapOf(x to 3u, y to 4u) to Rational(351511, 360), - mapOf(x to 4u, y to 4u) to Rational(-40547, 81), - mapOf(y to 5u) to Rational(-65421, 1960), - mapOf(x to 1u, y to 5u) to Rational(-10118, 35), - mapOf(x to 2u, y to 5u) to Rational(-4341709, 10080), - mapOf(x to 3u, y to 5u) to Rational(-91703, 360), - mapOf(x to 4u, y to 5u) to Rational(-85, 9), - mapOf(y to 6u) to Rational(-25965, 784), - mapOf(x to 1u, y to 6u) to Rational(3351, 16), - mapOf(x to 2u, y to 6u) to Rational(595159, 1344), - mapOf(x to 3u, y to 6u) to Rational(-1381, 12), - mapOf(x to 4u, y to 6u) to Rational(-155, 3) - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - x to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(-17, 5), - mapOf(x to 1u) to Rational(2, 6), - mapOf(x to 2u) to Rational(14, 1), - mapOf(y to 1u) to Rational(-6, 6), - mapOf(x to 1u, y to 1u) to Rational(-7, 3), - mapOf(x to 2u, y to 1u) to Rational(-2, 9), - mapOf(y to 2u) to Rational(-9, 6), - mapOf(x to 1u, y to 2u) to Rational(17, 4), - mapOf(x to 2u, y to 2u) to Rational(2, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(5, 4), - mapOf(x to 1u) to Rational(-5, 9), - mapOf(x to 2u) to Rational(-3, 6), - mapOf(y to 1u) to Rational(6, 5), - mapOf(x to 1u, y to 1u) to Rational(14, 5), - mapOf(x to 2u, y to 1u) to Rational(5, 2), - mapOf(y to 2u) to Rational(-18, 7), - mapOf(x to 1u, y to 2u) to Rational(-8, 2), - mapOf(x to 2u, y to 2u) to Rational(18, 9), - ) - ), - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 8), - mapOf(x to 1u) to Rational(-12, 6), - mapOf(x to 2u) to Rational(7, 6), - mapOf(y to 1u) to Rational(-10, 4), - mapOf(x to 1u, y to 1u) to Rational(-7, 6), - mapOf(x to 2u, y to 1u) to Rational(8, 9), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(5, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(10, 6), - mapOf(x to 1u) to Rational(-18, 6), - mapOf(x to 2u) to Rational(5, 1), - mapOf(y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(8, 4), - mapOf(x to 2u, y to 1u) to Rational(-4, 9), - mapOf(y to 2u) to Rational(-6, 5), - mapOf(x to 1u, y to 2u) to Rational(-15, 8), - mapOf(x to 2u, y to 2u) to Rational(-18, 5), - ) - ), - )), - "test 5'" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ), - LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(10, 2), - mapOf(x to 1u) to Rational(6, 7), - mapOf(x to 2u) to Rational(-16, 1), - mapOf(y to 1u) to Rational(13, 8), - mapOf(x to 1u, y to 1u) to Rational(-12, 1), - mapOf(x to 2u, y to 1u) to Rational(16, 8), - mapOf(y to 2u) to Rational(10, 4), - mapOf(x to 1u, y to 2u) to Rational(4, 1), - mapOf(x to 2u, y to 2u) to Rational(-11, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1, 4), - mapOf(x to 1u) to Rational(-17, 4), - mapOf(x to 2u) to Rational(-14, 8), - mapOf(y to 1u) to Rational(17, 9), - mapOf(x to 1u, y to 1u) to Rational(1, 3), - mapOf(x to 2u, y to 1u) to Rational(7, 6), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-17, 1), - mapOf(x to 2u, y to 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - iota to LabeledRationalFunction( - LabeledPolynomialAsIs( - mapOf() to Rational(5, 8), - mapOf(x to 1u) to Rational(-12, 6), - mapOf(x to 2u) to Rational(7, 6), - mapOf(y to 1u) to Rational(-10, 4), - mapOf(x to 1u, y to 1u) to Rational(-7, 6), - mapOf(x to 2u, y to 1u) to Rational(8, 9), - mapOf(y to 2u) to Rational(16, 3), - mapOf(x to 1u, y to 2u) to Rational(-13, 4), - mapOf(x to 2u, y to 2u) to Rational(5, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(10, 6), - mapOf(x to 1u) to Rational(-18, 6), - mapOf(x to 2u) to Rational(5, 1), - mapOf(y to 1u) to Rational(17, 7), - mapOf(x to 1u, y to 1u) to Rational(8, 4), - mapOf(x to 2u, y to 1u) to Rational(-4, 9), - mapOf(y to 2u) to Rational(-6, 5), - mapOf(x to 1u, y to 2u) to Rational(-15, 8), - mapOf(x to 2u, y to 2u) to Rational(-18, 5), - ) - ), - )), - "test 6'" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_derivativeWithRespectTo_variable() { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-2), - mapOf(x to 1u) to Rational(2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).derivativeWithRespectTo(RationalField, x), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-2, 3), - mapOf(x to 1u) to Rational(1, 1), - mapOf(x to 2u) to Rational(-33, 8), - mapOf(x to 3u) to Rational(72, 1), - mapOf(y to 1u) to Rational(2, 3), - mapOf(x to 1u, y to 1u) to Rational(-22, 1), - mapOf(x to 2u, y to 1u) to Rational(-1, 1), - mapOf(x to 3u, y to 1u) to Rational(-36, 1), - mapOf(y to 2u) to Rational(-8, 5), - mapOf(x to 1u, y to 2u) to Rational(-1, 4), - mapOf(x to 2u, y to 2u) to Rational(12, 7), - mapOf(x to 3u, y to 2u) to Rational(-2, 1), - mapOf(y to 3u) to Rational(16, 8), - mapOf(x to 1u, y to 3u) to Rational(-4, 1), - mapOf(x to 2u, y to 3u) to Rational(9, 2), - mapOf(x to 3u, y to 3u) to Rational(20, 9), - mapOf(y to 4u) to Rational(-10, 1), - mapOf(x to 1u, y to 4u) to Rational(-14, 1), - mapOf(x to 2u, y to 4u) to Rational(3, 7), - mapOf(x to 3u, y to 4u) to Rational(20, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, x), - "test 2a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-18, 3), - mapOf(x to 1u) to Rational(2, 3), - mapOf(x to 2u) to Rational(-11, 1), - mapOf(x to 3u) to Rational(-1, 3), - mapOf(x to 4u) to Rational(-18, 2), - mapOf(y to 1u) to Rational(-20, 3), - mapOf(x to 1u, y to 1u) to Rational(-16, 5), - mapOf(x to 2u, y to 1u) to Rational(-1, 4), - mapOf(x to 3u, y to 1u) to Rational(8, 7), - mapOf(x to 4u, y to 1u) to Rational(-1, 1), - mapOf(y to 2u) to Rational(9, 7), - mapOf(x to 1u, y to 2u) to Rational(6, 1), - mapOf(x to 2u, y to 2u) to Rational(-6, 1), - mapOf(x to 3u, y to 2u) to Rational(9, 2), - mapOf(x to 4u, y to 2u) to Rational(5, 3), - mapOf(y to 3u) to Rational(-9, 1), - mapOf(x to 1u, y to 3u) to Rational(-40, 1), - mapOf(x to 2u, y to 3u) to Rational(-28, 1), - mapOf(x to 3u, y to 3u) to Rational(4, 7), - mapOf(x to 4u, y to 3u) to Rational(20, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, y), - "test 2b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(-1, 4), - mapOf(x to 2u, y to 2u) to Rational(12, 7), - mapOf(x to 3u, y to 2u) to Rational(-2, 1), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(-4, 1), - mapOf(x to 2u, y to 3u) to Rational(9, 2), - mapOf(x to 3u, y to 3u) to Rational(20, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(-14, 1), - mapOf(x to 2u, y to 4u) to Rational(3, 7), - mapOf(x to 3u, y to 4u) to Rational(20, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, x), - "test 3a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(-1, 4), - mapOf(x to 3u, y to 1u) to Rational(8, 7), - mapOf(x to 4u, y to 1u) to Rational(-1, 1), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-6, 1), - mapOf(x to 3u, y to 2u) to Rational(9, 2), - mapOf(x to 4u, y to 2u) to Rational(5, 3), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-28, 1), - mapOf(x to 3u, y to 3u) to Rational(4, 7), - mapOf(x to 4u, y to 3u) to Rational(20, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, y), - "test 3b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-2, 3), - mapOf(x to 1u) to Rational(1, 1), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(y to 1u) to Rational(2, 3), - mapOf(x to 1u, y to 1u) to Rational(-22, 1), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-8, 5), - mapOf(x to 1u, y to 2u) to Rational(-1, 4), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).derivativeWithRespectTo(RationalField, x), - "test 4a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-18, 3), - mapOf(x to 1u) to Rational(2, 3), - mapOf(x to 2u) to Rational(-11, 1), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-20, 3), - mapOf(x to 1u, y to 1u) to Rational(-16, 5), - mapOf(x to 2u, y to 1u) to Rational(-1, 4), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).derivativeWithRespectTo(RationalField, y), - "test 4b" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, iota), - "test 5" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthDerivativeWithRespectTo_variable_order() { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-2), - mapOf(x to 1u) to Rational(2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, x, 1u), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, x, 0u), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, x, 2u), - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, x, 3u), - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, x, 4u), - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, y, 0u), - "test 6" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, y, 1u), - "test 7" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, y, 2u), - "test 8" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1, 1), - mapOf(x to 1u) to Rational(-33, 4), - mapOf(x to 2u) to Rational(216, 1), - mapOf(y to 1u) to Rational(-22, 1), - mapOf(x to 1u, y to 1u) to Rational(-2, 1), - mapOf(x to 2u, y to 1u) to Rational(-108, 1), - mapOf(y to 2u) to Rational(-1, 4), - mapOf(x to 1u, y to 2u) to Rational(24, 7), - mapOf(x to 2u, y to 2u) to Rational(-6, 1), - mapOf(y to 3u) to Rational(-4, 1), - mapOf(x to 1u, y to 3u) to Rational(9, 1), - mapOf(x to 2u, y to 3u) to Rational(20, 3), - mapOf(y to 4u) to Rational(-14, 1), - mapOf(x to 1u, y to 4u) to Rational(6, 7), - mapOf(x to 2u, y to 4u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, x, 2u), - "test 9a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-20, 3), - mapOf(x to 1u) to Rational(-16, 5), - mapOf(x to 2u) to Rational(-1, 4), - mapOf(x to 3u) to Rational(8, 7), - mapOf(x to 4u) to Rational(-1, 1), - mapOf(y to 1u) to Rational(18, 7), - mapOf(x to 1u, y to 1u) to Rational(12, 1), - mapOf(x to 2u, y to 1u) to Rational(-12, 1), - mapOf(x to 3u, y to 1u) to Rational(9, 1), - mapOf(x to 4u, y to 1u) to Rational(10, 3), - mapOf(y to 2u) to Rational(-27, 1), - mapOf(x to 1u, y to 2u) to Rational(-120, 1), - mapOf(x to 2u, y to 2u) to Rational(-84, 1), - mapOf(x to 3u, y to 2u) to Rational(12, 7), - mapOf(x to 4u, y to 2u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, y, 2u), - "test 9b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-1, 4), - mapOf(x to 1u, y to 2u) to Rational(24, 7), - mapOf(x to 2u, y to 2u) to Rational(-6, 1), - mapOf(y to 3u) to Rational(-4, 1), - mapOf(x to 1u, y to 3u) to Rational(9, 1), - mapOf(x to 2u, y to 3u) to Rational(20, 3), - mapOf(y to 4u) to Rational(-14, 1), - mapOf(x to 1u, y to 4u) to Rational(6, 7), - mapOf(x to 2u, y to 4u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, x, 2u), - "test 10a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(-1, 4), - mapOf(x to 3u) to Rational(8, 7), - mapOf(x to 4u) to Rational(-1, 1), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(-12, 1), - mapOf(x to 3u, y to 1u) to Rational(9, 1), - mapOf(x to 4u, y to 1u) to Rational(10, 3), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-84, 1), - mapOf(x to 3u, y to 2u) to Rational(12, 7), - mapOf(x to 4u, y to 2u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, y, 2u), - "test 10b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1, 1), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(y to 1u) to Rational(-22, 1), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-1, 4), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, x, 2u), - "test 11a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-20, 3), - mapOf(x to 1u) to Rational(-16, 5), - mapOf(x to 2u) to Rational(-1, 4), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, y, 2u), - "test 11b" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthDerivativeWithRespectTo_variablesAndOrders() { - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-2), - mapOf(x to 1u) to Rational(2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 1u)), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 0u)), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 3u)), - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 4u)), - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(y to 0u)), - "test 6" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(y to 1u)), - "test 7" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 8" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf()), - "test 9" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-2), - mapOf(x to 1u) to Rational(2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf( - x to 1u, - y to 0u - )), - "test 10" - ) - assertEquals( - LabeledPolynomialAsIs(), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf( - x to 0u, - y to 1u - )), - "test 11" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1, 1), - mapOf(x to 1u) to Rational(-33, 4), - mapOf(x to 2u) to Rational(216, 1), - mapOf(y to 1u) to Rational(-22, 1), - mapOf(x to 1u, y to 1u) to Rational(-2, 1), - mapOf(x to 2u, y to 1u) to Rational(-108, 1), - mapOf(y to 2u) to Rational(-1, 4), - mapOf(x to 1u, y to 2u) to Rational(24, 7), - mapOf(x to 2u, y to 2u) to Rational(-6, 1), - mapOf(y to 3u) to Rational(-4, 1), - mapOf(x to 1u, y to 3u) to Rational(9, 1), - mapOf(x to 2u, y to 3u) to Rational(20, 3), - mapOf(y to 4u) to Rational(-14, 1), - mapOf(x to 1u, y to 4u) to Rational(6, 7), - mapOf(x to 2u, y to 4u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 12a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(2, 3), - mapOf(x to 1u) to Rational(-22, 1), - mapOf(x to 2u) to Rational(-1, 1), - mapOf(x to 3u) to Rational(-36, 1), - mapOf(y to 1u) to Rational(-16, 5), - mapOf(x to 1u, y to 1u) to Rational(-1, 2), - mapOf(x to 2u, y to 1u) to Rational(24, 7), - mapOf(x to 3u, y to 1u) to Rational(-4, 1), - mapOf(y to 2u) to Rational(6, 1), - mapOf(x to 1u, y to 2u) to Rational(-12, 1), - mapOf(x to 2u, y to 2u) to Rational(27, 2), - mapOf(x to 3u, y to 2u) to Rational(20, 3), - mapOf(y to 3u) to Rational(-40, 1), - mapOf(x to 1u, y to 3u) to Rational(-56, 1), - mapOf(x to 2u, y to 3u) to Rational(12, 7), - mapOf(x to 3u, y to 3u) to Rational(80, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 1u, y to 1u)), - "test 12b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-20, 3), - mapOf(x to 1u) to Rational(-16, 5), - mapOf(x to 2u) to Rational(-1, 4), - mapOf(x to 3u) to Rational(8, 7), - mapOf(x to 4u) to Rational(-1, 1), - mapOf(y to 1u) to Rational(18, 7), - mapOf(x to 1u, y to 1u) to Rational(12, 1), - mapOf(x to 2u, y to 1u) to Rational(-12, 1), - mapOf(x to 3u, y to 1u) to Rational(9, 1), - mapOf(x to 4u, y to 1u) to Rational(10, 3), - mapOf(y to 2u) to Rational(-27, 1), - mapOf(x to 1u, y to 2u) to Rational(-120, 1), - mapOf(x to 2u, y to 2u) to Rational(-84, 1), - mapOf(x to 3u, y to 2u) to Rational(12, 7), - mapOf(x to 4u, y to 2u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 12c" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-1, 4), - mapOf(x to 1u, y to 2u) to Rational(24, 7), - mapOf(x to 2u, y to 2u) to Rational(-6, 1), - mapOf(y to 3u) to Rational(-4, 1), - mapOf(x to 1u, y to 3u) to Rational(9, 1), - mapOf(x to 2u, y to 3u) to Rational(20, 3), - mapOf(y to 4u) to Rational(-14, 1), - mapOf(x to 1u, y to 4u) to Rational(6, 7), - mapOf(x to 2u, y to 4u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 13a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(-1, 2), - mapOf(x to 2u, y to 1u) to Rational(24, 7), - mapOf(x to 3u, y to 1u) to Rational(-4, 1), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(-12, 1), - mapOf(x to 2u, y to 2u) to Rational(27, 2), - mapOf(x to 3u, y to 2u) to Rational(20, 3), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(-56, 1), - mapOf(x to 2u, y to 3u) to Rational(12, 7), - mapOf(x to 3u, y to 3u) to Rational(80, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 1u, y to 1u)), - "test 13b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(-1, 4), - mapOf(x to 3u) to Rational(8, 7), - mapOf(x to 4u) to Rational(-1, 1), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(-12, 1), - mapOf(x to 3u, y to 1u) to Rational(9, 1), - mapOf(x to 4u, y to 1u) to Rational(10, 3), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-84, 1), - mapOf(x to 3u, y to 2u) to Rational(12, 7), - mapOf(x to 4u, y to 2u) to Rational(60, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 13c" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1, 1), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(y to 1u) to Rational(-22, 1), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-1, 4), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 14a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(2, 3), - mapOf(x to 1u) to Rational(-22, 1), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(y to 1u) to Rational(-16, 5), - mapOf(x to 1u, y to 1u) to Rational(-1, 2), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, mapOf(x to 1u, y to 1u)), - "test 14b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(-20, 3), - mapOf(x to 1u) to Rational(-16, 5), - mapOf(x to 2u) to Rational(-1, 4), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 14c" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_antiderivativeWithRespectTo_variable() { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - mapOf(x to 2u) to Rational(-1), - mapOf(x to 3u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).antiderivativeWithRespectTo(RationalField, x), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-6, 8), - mapOf(x to 2u) to Rational(-1, 3), - mapOf(x to 3u) to Rational(1, 6), - mapOf(x to 4u) to Rational(-11, 32), - mapOf(x to 5u) to Rational(18, 5), - mapOf(x to 1u, y to 1u) to Rational(-18, 3), - mapOf(x to 2u, y to 1u) to Rational(1, 3), - mapOf(x to 3u, y to 1u) to Rational(-11, 3), - mapOf(x to 4u, y to 1u) to Rational(-1, 12), - mapOf(x to 5u, y to 1u) to Rational(-18, 10), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(-4, 5), - mapOf(x to 3u, y to 2u) to Rational(-1, 24), - mapOf(x to 4u, y to 2u) to Rational(1, 7), - mapOf(x to 5u, y to 2u) to Rational(-1, 10), - mapOf(x to 1u, y to 3u) to Rational(3, 7), - mapOf(x to 2u, y to 3u) to Rational(1, 1), - mapOf(x to 3u, y to 3u) to Rational(-2, 3), - mapOf(x to 4u, y to 3u) to Rational(3, 8), - mapOf(x to 5u, y to 3u) to Rational(1, 9), - mapOf(x to 1u, y to 4u) to Rational(-18, 8), - mapOf(x to 2u, y to 4u) to Rational(-5, 1), - mapOf(x to 3u, y to 4u) to Rational(-7, 3), - mapOf(x to 4u, y to 4u) to Rational(1, 28), - mapOf(x to 5u, y to 4u) to Rational(1, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, x), - "test 2a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(-6, 8), - mapOf(x to 1u, y to 1u) to Rational(-2, 3), - mapOf(x to 2u, y to 1u) to Rational(1, 2), - mapOf(x to 3u, y to 1u) to Rational(-11, 8), - mapOf(x to 4u, y to 1u) to Rational(18, 1), - mapOf(y to 2u) to Rational(-9, 3), - mapOf(x to 1u, y to 2u) to Rational(1, 3), - mapOf(x to 2u, y to 2u) to Rational(-11, 2), - mapOf(x to 3u, y to 2u) to Rational(-1, 6), - mapOf(x to 4u, y to 2u) to Rational(-9, 2), - mapOf(y to 3u) to Rational(-10, 9), - mapOf(x to 1u, y to 3u) to Rational(-8, 15), - mapOf(x to 2u, y to 3u) to Rational(-1, 24), - mapOf(x to 3u, y to 3u) to Rational(4, 21), - mapOf(x to 4u, y to 3u) to Rational(-1, 6), - mapOf(y to 4u) to Rational(3, 28), - mapOf(x to 1u, y to 4u) to Rational(1, 2), - mapOf(x to 2u, y to 4u) to Rational(-1, 2), - mapOf(x to 3u, y to 4u) to Rational(3, 8), - mapOf(x to 4u, y to 4u) to Rational(5, 36), - mapOf(y to 5u) to Rational(-9, 20), - mapOf(x to 1u, y to 5u) to Rational(-2, 1), - mapOf(x to 2u, y to 5u) to Rational(-7, 5), - mapOf(x to 3u, y to 5u) to Rational(1, 35), - mapOf(x to 4u, y to 5u) to Rational(1, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, y), - "test 2b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(x to 5u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(-1, 24), - mapOf(x to 4u, y to 2u) to Rational(1, 7), - mapOf(x to 5u, y to 2u) to Rational(-1, 10), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(-2, 3), - mapOf(x to 4u, y to 3u) to Rational(3, 8), - mapOf(x to 5u, y to 3u) to Rational(1, 9), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(-7, 3), - mapOf(x to 4u, y to 4u) to Rational(1, 28), - mapOf(x to 5u, y to 4u) to Rational(1, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, x), - "test 3a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-1, 24), - mapOf(x to 3u, y to 3u) to Rational(4, 21), - mapOf(x to 4u, y to 3u) to Rational(-1, 6), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-1, 2), - mapOf(x to 3u, y to 4u) to Rational(3, 8), - mapOf(x to 4u, y to 4u) to Rational(5, 36), - mapOf(y to 5u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(-7, 5), - mapOf(x to 3u, y to 5u) to Rational(1, 35), - mapOf(x to 4u, y to 5u) to Rational(1, 1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, y), - "test 3b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(-6, 8), - mapOf(x to 2u) to Rational(-1, 3), - mapOf(x to 3u) to Rational(1, 6), - mapOf(x to 4u) to Rational(0), - mapOf(x to 5u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(-18, 3), - mapOf(x to 2u, y to 1u) to Rational(1, 3), - mapOf(x to 3u, y to 1u) to Rational(-11, 3), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(-10, 3), - mapOf(x to 2u, y to 2u) to Rational(-4, 5), - mapOf(x to 3u, y to 2u) to Rational(-1, 24), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(x to 5u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(x to 5u, y to 3u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(x to 5u, y to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).antiderivativeWithRespectTo(RationalField, x), - "test 4a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(-6, 8), - mapOf(x to 1u, y to 1u) to Rational(-2, 3), - mapOf(x to 2u, y to 1u) to Rational(1, 2), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-9, 3), - mapOf(x to 1u, y to 2u) to Rational(1, 3), - mapOf(x to 2u, y to 2u) to Rational(-11, 2), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(-10, 9), - mapOf(x to 1u, y to 3u) to Rational(-8, 15), - mapOf(x to 2u, y to 3u) to Rational(-1, 24), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(y to 5u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(0), - mapOf(x to 3u, y to 5u) to Rational(0), - mapOf(x to 4u, y to 5u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).antiderivativeWithRespectTo(RationalField, y), - "test 4b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(iota to 1u) to Rational(-6, 8), - mapOf(x to 1u, iota to 1u) to Rational(-2, 3), - mapOf(x to 2u, iota to 1u) to Rational(1, 2), - mapOf(x to 3u, iota to 1u) to Rational(-11, 8), - mapOf(x to 4u, iota to 1u) to Rational(18, 1), - mapOf(y to 1u, iota to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u, iota to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u, iota to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u, iota to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u, iota to 1u) to Rational(-18, 2), - mapOf(y to 2u, iota to 1u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u, iota to 1u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u, iota to 1u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u, iota to 1u) to Rational(4, 7), - mapOf(x to 4u, y to 2u, iota to 1u) to Rational(-4, 8), - mapOf(y to 3u, iota to 1u) to Rational(3, 7), - mapOf(x to 1u, y to 3u, iota to 1u) to Rational(16, 8), - mapOf(x to 2u, y to 3u, iota to 1u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u, iota to 1u) to Rational(12, 8), - mapOf(x to 4u, y to 3u, iota to 1u) to Rational(5, 9), - mapOf(y to 4u, iota to 1u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u, iota to 1u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u, iota to 1u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u, iota to 1u) to Rational(1, 7), - mapOf(x to 4u, y to 4u, iota to 1u) to Rational(15, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, iota), - "test 5" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthAntiderivativeWithRespectTo_variable_order() { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - mapOf(x to 2u) to Rational(-1), - mapOf(x to 3u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 1u), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 0u), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-1, 3), - mapOf(x to 4u) to Rational(1, 12), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 2u), - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 3u) to Rational(1, 6), - mapOf(x to 4u) to Rational(-1, 12), - mapOf(x to 5u) to Rational(1, 60), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 3u), - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 4u) to Rational(1, 24), - mapOf(x to 5u) to Rational(-1, 60), - mapOf(x to 6u) to Rational(1, 360), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 4u), - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, y, 0u), - "test 6" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(1), - mapOf(x to 1u, y to 1u) to Rational(-2), - mapOf(x to 2u, y to 1u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, y, 1u), - "test 7" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(1, 2), - mapOf(x to 1u, y to 2u) to Rational(-1), - mapOf(x to 2u, y to 2u) to Rational(1, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, y, 2u), - "test 8" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(-3, 8), - mapOf(x to 3u) to Rational(-1, 9), - mapOf(x to 4u) to Rational(1, 24), - mapOf(x to 5u) to Rational(-11, 160), - mapOf(x to 6u) to Rational(3, 5), - mapOf(x to 2u, y to 1u) to Rational(-9, 3), - mapOf(x to 3u, y to 1u) to Rational(1, 9), - mapOf(x to 4u, y to 1u) to Rational(-11, 12), - mapOf(x to 5u, y to 1u) to Rational(-1, 60), - mapOf(x to 6u, y to 1u) to Rational(-3, 10), - mapOf(x to 2u, y to 2u) to Rational(-5, 3), - mapOf(x to 3u, y to 2u) to Rational(-4, 15), - mapOf(x to 4u, y to 2u) to Rational(-1, 96), - mapOf(x to 5u, y to 2u) to Rational(1, 35), - mapOf(x to 6u, y to 2u) to Rational(-1, 60), - mapOf(x to 2u, y to 3u) to Rational(3, 14), - mapOf(x to 3u, y to 3u) to Rational(1, 3), - mapOf(x to 4u, y to 3u) to Rational(-1, 6), - mapOf(x to 5u, y to 3u) to Rational(3, 40), - mapOf(x to 6u, y to 3u) to Rational(1, 54), - mapOf(x to 2u, y to 4u) to Rational(-9, 8), - mapOf(x to 3u, y to 4u) to Rational(-5, 3), - mapOf(x to 4u, y to 4u) to Rational(-7, 12), - mapOf(x to 5u, y to 4u) to Rational(1, 140), - mapOf(x to 6u, y to 4u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, x, 2u), - "test 9a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(-3, 8), - mapOf(x to 1u, y to 2u) to Rational(-1, 3), - mapOf(x to 2u, y to 2u) to Rational(1, 4), - mapOf(x to 3u, y to 2u) to Rational(-11, 16), - mapOf(x to 4u, y to 2u) to Rational(9, 1), - mapOf(y to 3u) to Rational(-1, 1), - mapOf(x to 1u, y to 3u) to Rational(1, 9), - mapOf(x to 2u, y to 3u) to Rational(-11, 6), - mapOf(x to 3u, y to 3u) to Rational(-1, 18), - mapOf(x to 4u, y to 3u) to Rational(-9, 6), - mapOf(y to 4u) to Rational(-5, 18), - mapOf(x to 1u, y to 4u) to Rational(-2, 15), - mapOf(x to 2u, y to 4u) to Rational(-1, 96), - mapOf(x to 3u, y to 4u) to Rational(1, 21), - mapOf(x to 4u, y to 4u) to Rational(-1, 24), - mapOf(y to 5u) to Rational(3, 140), - mapOf(x to 1u, y to 5u) to Rational(1, 10), - mapOf(x to 2u, y to 5u) to Rational(-1, 10), - mapOf(x to 3u, y to 5u) to Rational(3, 40), - mapOf(x to 4u, y to 5u) to Rational(1, 36), - mapOf(y to 6u) to Rational(-3, 40), - mapOf(x to 1u, y to 6u) to Rational(-1, 3), - mapOf(x to 2u, y to 6u) to Rational(-7, 30), - mapOf(x to 3u, y to 6u) to Rational(1, 210), - mapOf(x to 4u, y to 6u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, y, 2u), - "test 9b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(x to 5u) to Rational(0), - mapOf(x to 6u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 6u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(-1, 96), - mapOf(x to 5u, y to 2u) to Rational(1, 35), - mapOf(x to 6u, y to 2u) to Rational(-1, 60), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(-1, 6), - mapOf(x to 5u, y to 3u) to Rational(3, 40), - mapOf(x to 6u, y to 3u) to Rational(1, 54), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(-7, 12), - mapOf(x to 5u, y to 4u) to Rational(1, 140), - mapOf(x to 6u, y to 4u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, x, 2u), - "test 10a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-1, 96), - mapOf(x to 3u, y to 4u) to Rational(1, 21), - mapOf(x to 4u, y to 4u) to Rational(-1, 24), - mapOf(y to 5u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(-1, 10), - mapOf(x to 3u, y to 5u) to Rational(3, 40), - mapOf(x to 4u, y to 5u) to Rational(1, 36), - mapOf(y to 6u) to Rational(0), - mapOf(x to 1u, y to 6u) to Rational(0), - mapOf(x to 2u, y to 6u) to Rational(-7, 30), - mapOf(x to 3u, y to 6u) to Rational(1, 210), - mapOf(x to 4u, y to 6u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, y, 2u), - "test 10b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(-3, 8), - mapOf(x to 3u) to Rational(-1, 9), - mapOf(x to 4u) to Rational(1, 24), - mapOf(x to 5u) to Rational(0), - mapOf(x to 6u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(-9, 3), - mapOf(x to 3u, y to 1u) to Rational(1, 9), - mapOf(x to 4u, y to 1u) to Rational(-11, 12), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 6u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-5, 3), - mapOf(x to 3u, y to 2u) to Rational(-4, 15), - mapOf(x to 4u, y to 2u) to Rational(-1, 96), - mapOf(x to 5u, y to 2u) to Rational(0), - mapOf(x to 6u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(x to 5u, y to 3u) to Rational(0), - mapOf(x to 6u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(x to 5u, y to 4u) to Rational(0), - mapOf(x to 6u, y to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, x, 2u), - "test 11a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(-3, 8), - mapOf(x to 1u, y to 2u) to Rational(-1, 3), - mapOf(x to 2u, y to 2u) to Rational(1, 4), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(-1, 1), - mapOf(x to 1u, y to 3u) to Rational(1, 9), - mapOf(x to 2u, y to 3u) to Rational(-11, 6), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(-5, 18), - mapOf(x to 1u, y to 4u) to Rational(-2, 15), - mapOf(x to 2u, y to 4u) to Rational(-1, 96), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(y to 5u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(0), - mapOf(x to 3u, y to 5u) to Rational(0), - mapOf(x to 4u, y to 5u) to Rational(0), - mapOf(y to 6u) to Rational(0), - mapOf(x to 1u, y to 6u) to Rational(0), - mapOf(x to 2u, y to 6u) to Rational(0), - mapOf(x to 3u, y to 6u) to Rational(0), - mapOf(x to 4u, y to 6u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, y, 2u), - "test 11b" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthAntiderivativeWithRespectTo_variablesAndOrders() { - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - mapOf(x to 2u) to Rational(-1), - mapOf(x to 3u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 1u)), - "test 1" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 0u), - "test 2" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-1, 3), - mapOf(x to 4u) to Rational(1, 12), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 2u), - "test 3" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 3u) to Rational(1, 6), - mapOf(x to 4u) to Rational(-1, 12), - mapOf(x to 5u) to Rational(1, 60), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 3u), - "test 4" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 4u) to Rational(1, 24), - mapOf(x to 5u) to Rational(-1, 60), - mapOf(x to 6u) to Rational(1, 360), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, x, 4u), - "test 5" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, y, 0u), - "test 6" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(1), - mapOf(x to 1u, y to 1u) to Rational(-2), - mapOf(x to 2u, y to 1u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, y, 1u), - "test 7" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(1, 2), - mapOf(x to 1u, y to 2u) to Rational(-1), - mapOf(x to 2u, y to 2u) to Rational(1, 2), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, y, 2u), - "test 8" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf()), - "test 9" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u) to Rational(1), - mapOf(x to 2u) to Rational(-1), - mapOf(x to 3u) to Rational(1, 3), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf( - x to 1u, - y to 0u - )), - "test 10" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 1u) to Rational(1), - mapOf(x to 1u, y to 1u) to Rational(-2), - mapOf(x to 2u, y to 1u) to Rational(1), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(1), - mapOf(x to 1u) to Rational(-2), - mapOf(x to 2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf( - x to 0u, - y to 1u - )), - "test 11" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(-3, 8), - mapOf(x to 3u) to Rational(-1, 9), - mapOf(x to 4u) to Rational(1, 24), - mapOf(x to 5u) to Rational(-11, 160), - mapOf(x to 6u) to Rational(3, 5), - mapOf(x to 2u, y to 1u) to Rational(-9, 3), - mapOf(x to 3u, y to 1u) to Rational(1, 9), - mapOf(x to 4u, y to 1u) to Rational(-11, 12), - mapOf(x to 5u, y to 1u) to Rational(-1, 60), - mapOf(x to 6u, y to 1u) to Rational(-3, 10), - mapOf(x to 2u, y to 2u) to Rational(-5, 3), - mapOf(x to 3u, y to 2u) to Rational(-4, 15), - mapOf(x to 4u, y to 2u) to Rational(-1, 96), - mapOf(x to 5u, y to 2u) to Rational(1, 35), - mapOf(x to 6u, y to 2u) to Rational(-1, 60), - mapOf(x to 2u, y to 3u) to Rational(3, 14), - mapOf(x to 3u, y to 3u) to Rational(1, 3), - mapOf(x to 4u, y to 3u) to Rational(-1, 6), - mapOf(x to 5u, y to 3u) to Rational(3, 40), - mapOf(x to 6u, y to 3u) to Rational(1, 54), - mapOf(x to 2u, y to 4u) to Rational(-9, 8), - mapOf(x to 3u, y to 4u) to Rational(-5, 3), - mapOf(x to 4u, y to 4u) to Rational(-7, 12), - mapOf(x to 5u, y to 4u) to Rational(1, 140), - mapOf(x to 6u, y to 4u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 12a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u, y to 1u) to Rational(-6, 8), - mapOf(x to 2u, y to 1u) to Rational(-1, 3), - mapOf(x to 3u, y to 1u) to Rational(1, 6), - mapOf(x to 4u, y to 1u) to Rational(-11, 32), - mapOf(x to 5u, y to 1u) to Rational(18, 5), - mapOf(x to 1u, y to 2u) to Rational(-9, 3), - mapOf(x to 2u, y to 2u) to Rational(1, 6), - mapOf(x to 3u, y to 2u) to Rational(-11, 6), - mapOf(x to 4u, y to 2u) to Rational(-1, 24), - mapOf(x to 5u, y to 2u) to Rational(-9, 10), - mapOf(x to 1u, y to 3u) to Rational(-10, 9), - mapOf(x to 2u, y to 3u) to Rational(-4, 15), - mapOf(x to 3u, y to 3u) to Rational(-1, 72), - mapOf(x to 4u, y to 3u) to Rational(1, 21), - mapOf(x to 5u, y to 3u) to Rational(-1, 30), - mapOf(x to 1u, y to 4u) to Rational(3, 28), - mapOf(x to 2u, y to 4u) to Rational(1, 4), - mapOf(x to 3u, y to 4u) to Rational(-1, 6), - mapOf(x to 4u, y to 4u) to Rational(3, 32), - mapOf(x to 5u, y to 4u) to Rational(1, 36), - mapOf(x to 1u, y to 5u) to Rational(-9, 20), - mapOf(x to 2u, y to 5u) to Rational(-1, 1), - mapOf(x to 3u, y to 5u) to Rational(-7, 15), - mapOf(x to 4u, y to 5u) to Rational(1, 140), - mapOf(x to 5u, y to 5u) to Rational(1, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 1u, y to 1u)), - "test 12b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(-3, 8), - mapOf(x to 1u, y to 2u) to Rational(-1, 3), - mapOf(x to 2u, y to 2u) to Rational(1, 4), - mapOf(x to 3u, y to 2u) to Rational(-11, 16), - mapOf(x to 4u, y to 2u) to Rational(9, 1), - mapOf(y to 3u) to Rational(-1, 1), - mapOf(x to 1u, y to 3u) to Rational(1, 9), - mapOf(x to 2u, y to 3u) to Rational(-11, 6), - mapOf(x to 3u, y to 3u) to Rational(-1, 18), - mapOf(x to 4u, y to 3u) to Rational(-9, 6), - mapOf(y to 4u) to Rational(-5, 18), - mapOf(x to 1u, y to 4u) to Rational(-2, 15), - mapOf(x to 2u, y to 4u) to Rational(-1, 96), - mapOf(x to 3u, y to 4u) to Rational(1, 21), - mapOf(x to 4u, y to 4u) to Rational(-1, 24), - mapOf(y to 5u) to Rational(3, 140), - mapOf(x to 1u, y to 5u) to Rational(1, 10), - mapOf(x to 2u, y to 5u) to Rational(-1, 10), - mapOf(x to 3u, y to 5u) to Rational(3, 40), - mapOf(x to 4u, y to 5u) to Rational(1, 36), - mapOf(y to 6u) to Rational(-3, 40), - mapOf(x to 1u, y to 6u) to Rational(-1, 3), - mapOf(x to 2u, y to 6u) to Rational(-7, 30), - mapOf(x to 3u, y to 6u) to Rational(1, 210), - mapOf(x to 4u, y to 6u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(-11, 8), - mapOf(x to 4u) to Rational(18, 1), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(-1, 3), - mapOf(x to 4u, y to 1u) to Rational(-18, 2), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(3, 7), - mapOf(x to 1u, y to 3u) to Rational(16, 8), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(-18, 8), - mapOf(x to 1u, y to 4u) to Rational(-10, 1), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 12c" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(x to 5u) to Rational(0), - mapOf(x to 6u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 6u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(-1, 96), - mapOf(x to 5u, y to 2u) to Rational(1, 35), - mapOf(x to 6u, y to 2u) to Rational(-1, 60), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(-1, 6), - mapOf(x to 5u, y to 3u) to Rational(3, 40), - mapOf(x to 6u, y to 3u) to Rational(1, 54), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(-7, 12), - mapOf(x to 5u, y to 4u) to Rational(1, 140), - mapOf(x to 6u, y to 4u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 13a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(x to 5u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(-1, 72), - mapOf(x to 4u, y to 3u) to Rational(1, 21), - mapOf(x to 5u, y to 3u) to Rational(-1, 30), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(-1, 6), - mapOf(x to 4u, y to 4u) to Rational(3, 32), - mapOf(x to 5u, y to 4u) to Rational(1, 36), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(0), - mapOf(x to 3u, y to 5u) to Rational(-7, 15), - mapOf(x to 4u, y to 5u) to Rational(1, 140), - mapOf(x to 5u, y to 5u) to Rational(1, 5), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 1u, y to 1u)), - "test 13b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(0), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-1, 96), - mapOf(x to 3u, y to 4u) to Rational(1, 21), - mapOf(x to 4u, y to 4u) to Rational(-1, 24), - mapOf(y to 5u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(-1, 10), - mapOf(x to 3u, y to 5u) to Rational(3, 40), - mapOf(x to 4u, y to 5u) to Rational(1, 36), - mapOf(y to 6u) to Rational(0), - mapOf(x to 1u, y to 6u) to Rational(0), - mapOf(x to 2u, y to 6u) to Rational(-7, 30), - mapOf(x to 3u, y to 6u) to Rational(1, 210), - mapOf(x to 4u, y to 6u) to Rational(1, 6), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(0), - mapOf(x to 1u) to Rational(0), - mapOf(x to 2u) to Rational(0), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(0), - mapOf(x to 1u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(0), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(4, 7), - mapOf(x to 4u, y to 2u) to Rational(-4, 8), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(-16, 8), - mapOf(x to 3u, y to 3u) to Rational(12, 8), - mapOf(x to 4u, y to 3u) to Rational(5, 9), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(-14, 2), - mapOf(x to 3u, y to 4u) to Rational(1, 7), - mapOf(x to 4u, y to 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 13c" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 2u) to Rational(-3, 8), - mapOf(x to 3u) to Rational(-1, 9), - mapOf(x to 4u) to Rational(1, 24), - mapOf(x to 5u) to Rational(0), - mapOf(x to 6u) to Rational(0), - mapOf(x to 2u, y to 1u) to Rational(-9, 3), - mapOf(x to 3u, y to 1u) to Rational(1, 9), - mapOf(x to 4u, y to 1u) to Rational(-11, 12), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 6u, y to 1u) to Rational(0), - mapOf(x to 2u, y to 2u) to Rational(-5, 3), - mapOf(x to 3u, y to 2u) to Rational(-4, 15), - mapOf(x to 4u, y to 2u) to Rational(-1, 96), - mapOf(x to 5u, y to 2u) to Rational(0), - mapOf(x to 6u, y to 2u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(x to 5u, y to 3u) to Rational(0), - mapOf(x to 6u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(x to 5u, y to 4u) to Rational(0), - mapOf(x to 6u, y to 4u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 2u)), - "test 14a" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(x to 1u, y to 1u) to Rational(-6, 8), - mapOf(x to 2u, y to 1u) to Rational(-1, 3), - mapOf(x to 3u, y to 1u) to Rational(1, 6), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(x to 5u, y to 1u) to Rational(0), - mapOf(x to 1u, y to 2u) to Rational(-9, 3), - mapOf(x to 2u, y to 2u) to Rational(1, 6), - mapOf(x to 3u, y to 2u) to Rational(-11, 6), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(x to 5u, y to 2u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(-10, 9), - mapOf(x to 2u, y to 3u) to Rational(-4, 15), - mapOf(x to 3u, y to 3u) to Rational(-1, 72), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(x to 5u, y to 3u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(x to 5u, y to 4u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(0), - mapOf(x to 3u, y to 5u) to Rational(0), - mapOf(x to 4u, y to 5u) to Rational(0), - mapOf(x to 5u, y to 5u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(x to 1u, y to 1u)), - "test 14b" - ) - assertEquals( - LabeledPolynomialAsIs( - mapOf(y to 2u) to Rational(-3, 8), - mapOf(x to 1u, y to 2u) to Rational(-1, 3), - mapOf(x to 2u, y to 2u) to Rational(1, 4), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(-1, 1), - mapOf(x to 1u, y to 3u) to Rational(1, 9), - mapOf(x to 2u, y to 3u) to Rational(-11, 6), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(-5, 18), - mapOf(x to 1u, y to 4u) to Rational(-2, 15), - mapOf(x to 2u, y to 4u) to Rational(-1, 96), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - mapOf(y to 5u) to Rational(0), - mapOf(x to 1u, y to 5u) to Rational(0), - mapOf(x to 2u, y to 5u) to Rational(0), - mapOf(x to 3u, y to 5u) to Rational(0), - mapOf(x to 4u, y to 5u) to Rational(0), - mapOf(y to 6u) to Rational(0), - mapOf(x to 1u, y to 6u) to Rational(0), - mapOf(x to 2u, y to 6u) to Rational(0), - mapOf(x to 3u, y to 6u) to Rational(0), - mapOf(x to 4u, y to 6u) to Rational(0), - ), - LabeledPolynomialAsIs( - mapOf() to Rational(-6, 8), - mapOf(x to 1u) to Rational(-2, 3), - mapOf(x to 2u) to Rational(1, 2), - mapOf(x to 3u) to Rational(0), - mapOf(x to 4u) to Rational(0), - mapOf(y to 1u) to Rational(-18, 3), - mapOf(x to 1u, y to 1u) to Rational(2, 3), - mapOf(x to 2u, y to 1u) to Rational(-11, 1), - mapOf(x to 3u, y to 1u) to Rational(0), - mapOf(x to 4u, y to 1u) to Rational(0), - mapOf(y to 2u) to Rational(-10, 3), - mapOf(x to 1u, y to 2u) to Rational(-8, 5), - mapOf(x to 2u, y to 2u) to Rational(-1, 8), - mapOf(x to 3u, y to 2u) to Rational(0), - mapOf(x to 4u, y to 2u) to Rational(0), - mapOf(y to 3u) to Rational(0), - mapOf(x to 1u, y to 3u) to Rational(0), - mapOf(x to 2u, y to 3u) to Rational(0), - mapOf(x to 3u, y to 3u) to Rational(0), - mapOf(x to 4u, y to 3u) to Rational(0), - mapOf(y to 4u) to Rational(0), - mapOf(x to 1u, y to 4u) to Rational(0), - mapOf(x to 2u, y to 4u) to Rational(0), - mapOf(x to 3u, y to 4u) to Rational(0), - mapOf(x to 4u, y to 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(y to 2u)), - "test 14c" - ) - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialTest.kt deleted file mode 100644 index 5f7e1a95b..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialTest.kt +++ /dev/null @@ -1,544 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("LocalVariableName") - -package space.kscience.kmath.functions - -import space.kscience.kmath.functions.testUtils.IntModuloRing -import space.kscience.kmath.functions.testUtils.ListPolynomial -import space.kscience.kmath.functions.testUtils.Rational -import space.kscience.kmath.functions.testUtils.RationalField -import kotlin.test.* - - -class ListPolynomialTest { - @Test - fun test_Polynomial_Int_plus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)), - ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + -3, - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)) + 2, - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(-2)) + 2, - "test 3" - ) - val polynomial_4 = ListPolynomial() - assertSame( - polynomial_4, - polynomial_4 + 0, - "test 4" - ) - val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)) - assertSame( - polynomial_5, - polynomial_5 + 0, - "test 5" - ) - assertEquals( - ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)) + 1, - "test 6" - ) - assertEquals( - ListPolynomial(Rational(-1)), - ListPolynomial(Rational(-2)) + 1, - "test 7" - ) - assertEquals( - ListPolynomial(Rational(2)), - ListPolynomial() + 2, - "test 8" - ) - } - } - @Test - fun test_Polynomial_Int_minus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)), - ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - -3, - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(2), Rational(0), Rational(0), Rational(0)) - 2, - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(2)) - 2, - "test 3" - ) - val polynomial_4 = ListPolynomial() - assertSame( - polynomial_4, - polynomial_4 - 0, - "test 4" - ) - val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)) - assertEquals( - polynomial_5, - polynomial_5 - 0, - "test 5" - ) - assertEquals( - ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(2), Rational(0), Rational(0), Rational(0)) - 1, - "test 6" - ) - assertEquals( - ListPolynomial(Rational(1)), - ListPolynomial(Rational(2)) - 1, - "test 7" - ) - assertEquals( - ListPolynomial(Rational(-2)), - ListPolynomial() - 2, - "test 8" - ) - } - } - @Test - fun test_Polynomial_Int_times() { - IntModuloRing(35).listPolynomialSpace { - assertEquals( - ListPolynomial(34, 2, 1, 20, 2), - ListPolynomial(22, 26, 13, 15, 26) * 27, - "test 1" - ) - assertEquals( - ListPolynomial(0, 0, 0, 0, 0), - ListPolynomial(7, 0, 49, 21, 14) * 15, - "test 2" - ) - val polynomial = ListPolynomial(22, 26, 13, 15, 26) - assertSame( - zero, - polynomial * 0, - "test 3" - ) - assertSame( - polynomial, - polynomial * 1, - "test 4" - ) - } - } - @Test - fun test_Int_Polynomial_plus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)), - -3 + ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - 2 + ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - 2 + ListPolynomial(Rational(-2)), - "test 3" - ) - val polynomial_4 = ListPolynomial() - assertSame( - polynomial_4, - 0 + polynomial_4, - "test 4" - ) - val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)) - assertSame( - polynomial_5, - 0 + polynomial_5, - "test 5" - ) - assertEquals( - ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)), - 1 + ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(-1)), - 1 + ListPolynomial(Rational(-2)), - "test 7" - ) - assertEquals( - ListPolynomial(Rational(2)), - 2 + ListPolynomial(), - "test 8" - ) - } - } - @Test - fun test_Int_Polynomial_minus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)), - 3 - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - -2 - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - -2 - ListPolynomial(Rational(-2)), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(-32, 9), Rational(-8, -9), Rational(8, 7)), - 0 - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)), - "test 4" - ) - assertEquals( - ListPolynomial(), - 0 - ListPolynomial(), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)), - -1 - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(1)), - -1 - ListPolynomial(Rational(-2)), - "test 7" - ) - assertEquals( - ListPolynomial(Rational(-2)), - -2 - ListPolynomial(), - "test 8" - ) - } - } - @Test - fun test_Int_Polynomial_times() { - IntModuloRing(35).listPolynomialSpace { - assertEquals( - ListPolynomial(34, 2, 1, 20, 2), - 27 * ListPolynomial(22, 26, 13, 15, 26), - "test 1" - ) - assertEquals( - ListPolynomial(0, 0, 0, 0, 0), - 15 * ListPolynomial(7, 0, 49, 21, 14), - "test 2" - ) - val polynomial = ListPolynomial(22, 26, 13, 15, 26) - assertSame( - zero, - 0 * polynomial, - "test 3" - ) - assertSame( - polynomial, - 1 * polynomial, - "test 4" - ) - } - } - @Test - fun test_Polynomial_Constant_plus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)), - ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + Rational(-3), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)) + Rational(2), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(-2)) + Rational(2), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial() + Rational(0), - "test 4" - ) - assertEquals( - ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)) + Rational(1), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(-1)), - ListPolynomial(Rational(-2)) + Rational(1), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(2)), - ListPolynomial() + Rational(2), - "test 7" - ) - } - } - @Test - fun test_Polynomial_Constant_minus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)), - ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - Rational(-3), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(2), Rational(0), Rational(0), Rational(0)) - Rational(2), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(2)) - Rational(2), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial() - Rational(0), - "test 4" - ) - assertEquals( - ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(2), Rational(0), Rational(0), Rational(0)) - Rational(1), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(1)), - ListPolynomial(Rational(2)) - Rational(1), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(-2)), - ListPolynomial() - Rational(2), - "test 7" - ) - } - } - @Test - fun test_Polynomial_Constant_times() { - IntModuloRing(35).listPolynomialSpace { - assertEquals( - ListPolynomial(34, 2, 1, 20, 2), - ListPolynomial(22, 26, 13, 15, 26) * 27.asConstant(), - "test 1" - ) - assertEquals( - ListPolynomial(0, 0, 0, 0, 0), - ListPolynomial(7, 0, 49, 21, 14) * 15.asConstant(), - "test 2" - ) - } - } - @Test - fun test_Constant_Polynomial_plus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)), - Rational(-3) + ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - Rational(2) + ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - Rational(2) + ListPolynomial(Rational(-2)), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(0)), - Rational(0) + ListPolynomial(), - "test 4" - ) - assertEquals( - ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)), - Rational(1) + ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(-1)), - Rational(1) + ListPolynomial(Rational(-2)), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(2)), - Rational(2) + ListPolynomial(), - "test 7" - ) - } - } - @Test - fun test_Constant_Polynomial_minus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)), - Rational(3) - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0)), - Rational(-2) - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0)), - Rational(-2) - ListPolynomial(Rational(-2)), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(0)), - Rational(0) - ListPolynomial(), - "test 4" - ) - assertEquals( - ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)), - Rational(-1) - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(1)), - Rational(-1) - ListPolynomial(Rational(-2)), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(-2)), - Rational(-2) - ListPolynomial(), - "test 7" - ) - } - } - @Test - fun test_Constant_Polynomial_times() { - IntModuloRing(35).listPolynomialSpace { - assertEquals( - ListPolynomial(34, 2, 1, 20, 2), - 27 * ListPolynomial(22, 26, 13, 15, 26), - "test 1" - ) - assertEquals( - ListPolynomial(0, 0, 0, 0, 0), - 15 * ListPolynomial(7, 0, 49, 21, 14), - "test 2" - ) - } - } - @Test - fun test_Polynomial_unaryMinus() { - RationalField.listPolynomialSpace { - assertEquals( - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)), - -ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7), Rational(0), Rational(0)), - -ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7), Rational(0), Rational(0)), - "test 2" - ) - } - } - @Test - fun test_Polynomial_Polynomial_plus() { - RationalField.listPolynomialSpace { - // (5/9 - 8/9 x - 8/7 x^2) + (-5/7 + 5/1 x + 5/8 x^2) ?= -10/63 + 37/9 x - 29/56 x^2 - assertEquals( - ListPolynomial(Rational(-10, 63), Rational(37, 9), Rational(-29, 56)), - ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + - ListPolynomial(Rational(-5, 7), Rational(5, 1), Rational(5, 8)), - "test 1" - ) - // (-2/9 - 8/3 x) + (0 + 9/4 x + 2/4 x^2) ?= -2/9 - 5/12 x + 2/4 x^2 - assertEquals( - ListPolynomial(Rational(-2, 9), Rational(-5, 12), Rational(2, 4)), - ListPolynomial(Rational(-2, 9), Rational(-8, 3)) + - ListPolynomial(Rational(0), Rational(9, 4), Rational(2, 4)), - "test 2" - ) - // (-4/7 - 2/6 x + 0 x^2 + 0 x^3) + (-6/3 - 7/2 x + 2/3 x^2) ?= -18/7 - 23/6 x + 2/3 x^2 - assertEquals( - ListPolynomial(Rational(-18, 7), Rational(-23, 6), Rational(2, 3), Rational(0)), - ListPolynomial(Rational(-4, 7), Rational(-2, 6), Rational(0), Rational(0)) + - ListPolynomial(Rational(-6, 3), Rational(-7, 2), Rational(2, 3)), - "test 3" - ) - // (-2/4 - 6/9 x - 4/9 x^2) + (2/4 + 6/9 x + 4/9 x^2) ?= 0 - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(-2, 4), Rational(-6, 9), Rational(-4, 9)) + - ListPolynomial(Rational(2, 4), Rational(6, 9), Rational(4, 9)), - "test 4" - ) - } - } - @Test - fun test_Polynomial_Polynomial_minus() { - RationalField.listPolynomialSpace { - // (5/9 - 8/9 x - 8/7 x^2) - (-5/7 + 5/1 x + 5/8 x^2) ?= 80/63 - 53/9 x - 99/56 x^2 - assertEquals( - ListPolynomial(Rational(80, 63), Rational(-53, 9), Rational(-99, 56)), - ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - - ListPolynomial(Rational(-5, 7), Rational(5, 1), Rational(5, 8)), - "test 1" - ) - // (-2/9 - 8/3 x) - (0 + 9/4 x + 2/4 x^2) ?= -2/9 - 59/12 x - 2/4 x^2 - assertEquals( - ListPolynomial(Rational(-2, 9), Rational(-59, 12), Rational(-2, 4)), - ListPolynomial(Rational(-2, 9), Rational(-8, 3)) - - ListPolynomial(Rational(0), Rational(9, 4), Rational(2, 4)), - "test 2" - ) - // (-4/7 - 2/6 x + 0 x^2 + 0 x^3) - (-6/3 - 7/2 x + 2/3 x^2) ?= 10/7 + 19/6 x - 2/3 x^2 - assertEquals( - ListPolynomial(Rational(10, 7), Rational(19, 6), Rational(-2, 3), Rational(0)), - ListPolynomial(Rational(-4, 7), Rational(-2, 6), Rational(0), Rational(0)) - - ListPolynomial(Rational(-6, 3), Rational(-7, 2), Rational(2, 3)), - "test 3" - ) - // (-2/4 - 6/9 x - 4/9 x^2) - (-2/4 - 6/9 x - 4/9 x^2) ?= 0 - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(-2, 4), Rational(-6, 9), Rational(-4, 9)) - - ListPolynomial(Rational(-2, 4), Rational(-6, 9), Rational(-4, 9)), - "test 4" - ) - } - } - @Test - fun test_Polynomial_Polynomial_times() { - IntModuloRing(35).listPolynomialSpace { - // (1 + x + x^2) * (1 - x + x^2) ?= 1 + x^2 + x^4 - assertEquals( - ListPolynomial(1, 0, 1, 0, 1), - ListPolynomial(1, -1, 1) * ListPolynomial(1, 1, 1), - "test 1" - ) - // Spoiler: 5 * 7 = 0 - assertEquals( - ListPolynomial(0, 0, 0, 0, 0), - ListPolynomial(5, -25, 10) * ListPolynomial(21, 14, -7), - "test 2" - ) - } - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialUtilTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialUtilTest.kt deleted file mode 100644 index 48ea89a46..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialUtilTest.kt +++ /dev/null @@ -1,982 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.functions.testUtils.Rational -import space.kscience.kmath.functions.testUtils.RationalField -import space.kscience.kmath.functions.testUtils.assertFailsWithTypeAndMessage -import kotlin.test.Ignore -import kotlin.test.Test -import kotlin.test.assertEquals - - -@OptIn(UnstableKMathAPI::class) -class ListPolynomialUtilTest { - @Test - fun test_Polynomial_substitute_Double() { - assertEquals( - 0.0, - ListPolynomial(1.0, -2.0, 1.0).substitute(1.0), - 0.001, - "test 1" - ) - assertEquals( - 0.0, - ListPolynomial(1.0, -2.0, 1.0).substitute(1.0), - 0.001, - "test 1" - ) - assertEquals( - 1.1931904761904761, - ListPolynomial(0.625, 2.6666666666666665, 0.5714285714285714, 1.5).substitute(0.2), - 0.001, - "test 2" - ) - assertEquals( - 0.5681904761904762, - ListPolynomial(0.0, 2.6666666666666665, 0.5714285714285714, 1.5).substitute(0.2), - 0.001, - "test 3" - ) - assertEquals( - 1.1811904761904761, - ListPolynomial(0.625, 2.6666666666666665, 0.5714285714285714, 0.0).substitute(0.2), - 0.001, - "test 4" - ) - assertEquals( - 1.1703333333333332, - ListPolynomial(0.625, 2.6666666666666665, 0.0, 1.5).substitute(0.2), - 0.001, - "test 5" - ) - } - @Test - fun test_Polynomial_substitute_Constant() { - assertEquals( - Rational(0), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).substitute(RationalField, Rational(1)), - "test 1" - ) - assertEquals( - Rational(25057, 21000), - ListPolynomial(Rational(5, 8), Rational(8, 3), Rational(4, 7), Rational(3, 2)) - .substitute(RationalField, Rational(1, 5)), - "test 2" - ) - assertEquals( - Rational(2983, 5250), - ListPolynomial(Rational(0), Rational(8, 3), Rational(4, 7), Rational(3, 2)) - .substitute(RationalField, Rational(1, 5)), - "test 3" - ) - assertEquals( - Rational(4961, 4200), - ListPolynomial(Rational(5, 8), Rational(8, 3), Rational(4, 7), Rational(0)) - .substitute(RationalField, Rational(1, 5)), - "test 4" - ) - assertEquals( - Rational(3511, 3000), - ListPolynomial(Rational(5, 8), Rational(8, 3), Rational(0), Rational(3, 2)) - .substitute(RationalField, Rational(1, 5)), - "test 5" - ) - } - @Test - fun test_Polynomial_substitute_Polynomial() { - assertEquals( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).substitute(RationalField, ListPolynomial(Rational(1))), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(709, 378), Rational(155, 252), Rational(19, 525), Rational(2, 875)), - ListPolynomial(Rational(1, 7), Rational(9, 4), Rational(1, 3), Rational(2, 7)) - .substitute(RationalField, ListPolynomial(Rational(6, 9), Rational(1, 5))), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(655, 378), Rational(155, 252), Rational(19, 525), Rational(2, 875)), - ListPolynomial(Rational(0), Rational(9, 4), Rational(1, 3), Rational(2, 7)) - .substitute(RationalField, ListPolynomial(Rational(6, 9), Rational(1, 5))), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(677, 378), Rational(97, 180), Rational(1, 75), Rational(0)), - ListPolynomial(Rational(1, 7), Rational(9, 4), Rational(1, 3), Rational(0)) - .substitute(RationalField, ListPolynomial(Rational(6, 9), Rational(1, 5))), - "test 4" - ) - assertEquals( - ListPolynomial(Rational(653, 378), Rational(221, 420), Rational(4, 175), Rational(2, 875)), - ListPolynomial(Rational(1, 7), Rational(9, 4), Rational(0), Rational(2, 7)) - .substitute(RationalField, ListPolynomial(Rational(6, 9), Rational(1, 5))), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(89, 54), Rational(0), Rational(0), Rational(0)), - ListPolynomial(Rational(0), Rational(9, 4), Rational(1, 3), Rational(0)) - .substitute(RationalField, ListPolynomial(Rational(6, 9), Rational(0))), - "test 6" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_Polynomial_substitute_RationalFunction() { - assertEquals( - ListRationalFunction(ListPolynomial(Rational(0)), ListPolynomial(Rational(1))), - ListPolynomial(Rational(1), Rational(-2), Rational(1)) - .substitute(RationalField, ListRationalFunction(ListPolynomial(Rational(1)), ListPolynomial(Rational(1)))), - "test 1" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(66349, 243), - Rational(-17873, 405), - Rational(173533, 3780), - Rational(-91141, 567), - Rational(5773909, 105840), - Rational(-23243, 630), - Rational(1573, 27) - ), - ListPolynomial( - Rational(169, 81), - Rational(-130, 27), - Rational(115, 18), - Rational(-797, 54), - Rational(1985, 144), - Rational(-55, 6), - Rational(121, 9) - ) - ), - ListPolynomial( - Rational(13, 3), - Rational(-9, 5), - Rational(5, 5) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(15, 1), - Rational(6, 9), - Rational(-3, 7) - ), - ListPolynomial( - Rational(-13, 9), - Rational(10, 6), - Rational(-10, 8), - Rational(11, 3) - ) - ) - ), - "test 2" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(0, 1), - Rational(0, 1), - Rational(-14, 9), - Rational(31, 14), - Rational(-5077, 980), - Rational(99, 35) - ), - ListPolynomial( - Rational(0, 1), - Rational(0, 1), - Rational(25, 9), - Rational(-25, 6), - Rational(1985, 144), - Rational(-55, 6), - Rational(121, 9) - ) - ), - ListPolynomial( - Rational(0), - Rational(-9, 5), - Rational(5, 5) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(0), - Rational(6, 9), - Rational(-3, 7) - ), - ListPolynomial( - Rational(0), - Rational(10, 6), - Rational(-10, 8), - Rational(11, 3) - ) - ) - ), - "test 3" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(-898, 27), - Rational(271, 45), - Rational(-65, 12) , - Rational(0), - Rational(0), - Rational(0), - Rational(0) - ), - ListPolynomial( - Rational(-13, 9), - Rational(5, 3), - Rational(-5, 4), - Rational(0), - Rational(0), - Rational(0), - Rational(0) - ) - ), - ListPolynomial( - Rational(13, 3), - Rational(-9, 5), - Rational(0) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(15, 1), - Rational(6, 9), - Rational(0) - ), - ListPolynomial( - Rational(-13, 9), - Rational(10, 6), - Rational(-10, 8), - Rational(0) - ) - ) - ), - "test 4" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(56872, 243), - Rational(0, 1), - Rational(-90, 7), - Rational(-3718, 81), - Rational(9, 49), - Rational(0, 1), - Rational(1573, 27) - ), - ListPolynomial( - Rational(169, 81), - Rational(0, 1), - Rational(0, 1), - Rational(-286, 27), - Rational(0, 1), - Rational(0, 1), - Rational(121, 9) - ) - ), - ListPolynomial( - Rational(13, 3), - Rational(0), - Rational(5, 5) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(15, 1), - Rational(0), - Rational(-3, 7) - ), - ListPolynomial( - Rational(-13, 9), - Rational(0), - Rational(0), - Rational(11, 3) - ) - ) - ), - "test 5" - ) - } - @Test - fun test_RationalFunction_substitute_Double() { - assertEquals( - 0.0, - ListRationalFunction( - ListPolynomial(1.0, -2.0, 1.0), - ListPolynomial(-6.302012278484357, 5.831971885376948, -9.271604788393432, 5.494387848015814, -3.7187384450880785) - ).substitute(1.0), - 0.001, - "test 1" - ) - assertEquals( - 2.693702616649797, - ListRationalFunction( - ListPolynomial(-5.848840571263625, -1.660411278951134, -3.793740946372443, -9.624569269490076), - ListPolynomial(-2.9680680215311073, -1.862973627119981, 4.776550592888336, -2.7320154512368466) - ).substitute(-7.53452770353279), - 0.001, - "test 2" - ) - assertEquals( - 2.692226268901378, - ListRationalFunction( - ListPolynomial(0.0, -1.660411278951134, -3.793740946372443, -9.624569269490076), - ListPolynomial(0.0, -1.862973627119981, 4.776550592888336, -2.7320154512368466) - ).substitute(-7.53452770353279), - 0.001, - "test 3" - ) - assertEquals( - -0.7394904842099175, - ListRationalFunction( - ListPolynomial(-5.848840571263625, -1.660411278951134, -3.793740946372443, 0.0), - ListPolynomial(-2.9680680215311073, -1.862973627119981, 4.776550592888336, 0.0) - ).substitute(-7.53452770353279), - 0.001, - "test 4" - ) - assertEquals( - 3.526835209398159, - ListRationalFunction( - ListPolynomial(-5.848840571263625, 0.0, 0.0, -9.624569269490076), - ListPolynomial(-2.9680680215311073, 0.0, 0.0, -2.7320154512368466) - ).substitute(-7.53452770353279), - 0.001, - "test 5" - ) - } - @Test - fun test_RationalFunction_substitute_Constant() { - assertEquals( - Rational(0), - ListRationalFunction( - ListPolynomial(Rational(1), Rational(-2), Rational(1)), - ListPolynomial(Rational(1)), - ).substitute(RationalField, Rational(1)), - "test 1" - ) - assertEquals( - Rational(1149615, 61306), - ListRationalFunction( - ListPolynomial(Rational(17, 7), Rational(18, 3), Rational(18, 8), Rational(9, 1)), - ListPolynomial(Rational(11, 9), Rational(-6, 5), Rational(-12, 7), Rational(2, 1)), - ).substitute(RationalField, Rational(-7, 8)), - "test 2" - ) - assertEquals( - Rational(3495, 586), - ListRationalFunction( - ListPolynomial(Rational(0), Rational(18, 3), Rational(18, 8), Rational(9, 1)), - ListPolynomial(Rational(0), Rational(-6, 5), Rational(-12, 7), Rational(2, 1)), - ).substitute(RationalField, Rational(-7, 8)), - "test 3" - ) - assertEquals( - Rational(-88605, 77392), - ListRationalFunction( - ListPolynomial(Rational(17, 7), Rational(18, 3), Rational(18, 8), Rational(0)), - ListPolynomial(Rational(11, 9), Rational(-6, 5), Rational(-12, 7), Rational(0)), - ).substitute(RationalField, Rational(-7, 8)), - "test 4" - ) - assertEquals( - Rational(116145, 3794), - ListRationalFunction( - ListPolynomial(Rational(17, 7), Rational(0), Rational(0), Rational(9, 1)), - ListPolynomial(Rational(11, 9), Rational(0), Rational(0), Rational(2, 1)), - ).substitute(RationalField, Rational(-7, 8)), - "test 5" - ) - } - @Test - fun test_RationalFunction_substitute_Polynomial() { - assertEquals( - ListRationalFunction( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(1)) - ), - ListRationalFunction( - ListPolynomial(Rational(1), Rational(-2), Rational(1)), - ListPolynomial(Rational(1)), - ).substitute(RationalField, ListPolynomial(Rational(1))), - "test 1" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(-283303, 36), - Rational(-23593, 24), - Rational(368713, 192), - Rational(1455, 8), - Rational(-272171, 1536), - Rational(-2149, 192), - Rational(469, 64), - Rational(11, 48), - Rational(-11, 96) - ), - ListPolynomial( - Rational(5797, 12), - Rational(595, 16), - Rational(-5285, 72), - Rational(-745, 192), - Rational(1105, 288), - Rational(5, 48), - Rational(-5, 72) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(2, 9), - Rational(11, 3), - Rational(-9, 4), - Rational(-6, 1), - Rational(-11, 6) - ), - ListPolynomial( - Rational(-2, 3), - Rational(-15, 4), - Rational(5, 9), - Rational(-5, 9) - ) - ).substitute(RationalField, - ListPolynomial( - Rational(-9, 1), - Rational(-1, 4), - Rational(2, 4) - ) - ), - "test 2" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(0, 1), - Rational(-11, 12), - Rational(325, 192), - Rational(21, 32), - Rational(-1739, 1536), - Rational(227, 192), - Rational(-59, 64), - Rational(11, 48), - Rational(-11, 96) - ), - ListPolynomial( - Rational(0, 1), - Rational(15, 16), - Rational(-265, 144), - Rational(-25, 192), - Rational(25, 288), - Rational(5, 48), - Rational(-5, 72) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(0, 9), - Rational(11, 3), - Rational(-9, 4), - Rational(-6, 1), - Rational(-11, 6) - ), - ListPolynomial( - Rational(0, 3), - Rational(-15, 4), - Rational(5, 9), - Rational(-5, 9) - ) - ).substitute(RationalField, - ListPolynomial( - Rational(0, 1), - Rational(-1, 4), - Rational(2, 4) - ) - ), - "test 3" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(149723, 36), - Rational(8483, 24), - Rational(639, 64), - Rational(3, 32), - Rational(0), - Rational(0), - Rational(0), - Rational(0), - Rational(0) - ), - ListPolynomial( - Rational(937, 12), - Rational(55, 16), - Rational(5, 144), - Rational(0), - Rational(0), - Rational(0), - Rational(0) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(2, 9), - Rational(11, 3), - Rational(-9, 4), - Rational(-6, 1), - Rational(0) - ), - ListPolynomial( - Rational(-2, 3), - Rational(-15, 4), - Rational(5, 9), - Rational(0) - ) - ).substitute(RationalField, - ListPolynomial( - Rational(-9, 1), - Rational(-1, 4), - Rational(0) - ) - ), - "test 4" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(-216509, 18), - Rational(0, 1), - Rational(2673, 1), - Rational(0, 1), - Rational(-891, 4), - Rational(0, 1), - Rational(33, 4), - Rational(0, 1), - Rational(-11, 96) - ), - ListPolynomial( - Rational(1213, 3), - Rational(0, 1), - Rational(-135, 2), - Rational(0, 1), - Rational(15, 4), - Rational(0, 1), - Rational(-5, 72) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(2, 9), - Rational(0), - Rational(0), - Rational(0), - Rational(-11, 6) - ), - ListPolynomial( - Rational(-2, 3), - Rational(0), - Rational(0), - Rational(-5, 9) - ) - ).substitute(RationalField, - ListPolynomial( - Rational(-9, 1), - Rational(0), - Rational(2, 4) - ) - ), - "test 5" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_RationalFunction_substitute_RationalFunction() { - assertEquals( - ListRationalFunction( - ListPolynomial(Rational(0)), - ListPolynomial(Rational(1)) - ), - ListRationalFunction( - ListPolynomial(Rational(1), Rational(-2), Rational(1)), - ListPolynomial(Rational(1)) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial(Rational(1)), - ListPolynomial(Rational(1)) - ) - ), - "test 1" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(130087, 3888), - Rational(-2866333, 65610), - Rational(-5076229, 97200), - Rational(222136997, 3280500), - Rational(754719329, 20995200), - Rational(-12010283, 324000), - Rational(-2011967, 172800), - Rational(18607, 2880), - Rational(4705, 4096) - ), - ListPolynomial( - Rational(-143820355, 3779136), - Rational(73886869, 1574640), - Rational(1440175193, 15746400), - Rational(-5308968857, 52488000), - Rational(-186910083731, 2099520000), - Rational(125043463, 1555200), - Rational(5299123, 388800), - Rational(-213757, 15360), - Rational(1380785, 147456) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(1, 1), - Rational(-10, 5), - Rational(18, 8), - Rational(-8, 8) - ), - ListPolynomial( - Rational(-14, 8), - Rational(-14, 8), - Rational(-19, 6), - Rational(14, 3), - Rational(8, 9) - ) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(14, 9), - Rational(-2, 5), - Rational(-14, 7) - ), - ListPolynomial( - Rational(-6, 4), - Rational(5, 9), - Rational(1, 8) - ) - ) - ), - "test 2" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(0, 1), - Rational(0, 1), - Rational(0, 1), - Rational(0, 1), - Rational(5173, 18225), - Rational(904291, 364500), - Rational(283127, 43200), - Rational(37189, 5760), - Rational(147, 128) - ), - ListPolynomial( - Rational(0, 1), - Rational(0, 1), - Rational(0, 1), - Rational(0, 1), - Rational(-163589, 911250), - Rational(-881831, 291600), - Rational(-10722229, 777600), - Rational(-640921, 46080), - Rational(86303, 9216) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(0), - Rational(-10, 5), - Rational(18, 8), - Rational(-8, 8) - ), - ListPolynomial( - Rational(0), - Rational(-14, 8), - Rational(-19, 6), - Rational(14, 3), - Rational(8, 9) - ) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(0), - Rational(-2, 5), - Rational(-14, 7) - ), - ListPolynomial( - Rational(0), - Rational(5, 9), - Rational(1, 8) - ) - ) - ), - "test 3" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(445, 16), - Rational(-2011, 54), - Rational(1359199, 72900), - Rational(-135733, 32805), - Rational(2254, 6561), - Rational(0, 1), - Rational(0, 1), - Rational(0, 1), - Rational(0, 1) - ), - ListPolynomial( - Rational(-2018387, 46656), - Rational(82316437, 1574640), - Rational(-9335047, 393660), - Rational(15765889, 3280500), - Rational(-242089, 656100), - Rational(0, 1), - Rational(0, 1), - Rational(0, 1), - Rational(0, 1) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(1, 1), - Rational(-10, 5), - Rational(18, 8), - Rational(0) - ), - ListPolynomial( - Rational(-14, 8), - Rational(-14, 8), - Rational(-19, 6), - Rational(14, 3), - Rational(0) - ) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(14, 9), - Rational(-2, 5), - Rational(0) - ), - ListPolynomial( - Rational(-6, 4), - Rational(5, 9), - Rational(0) - ) - ) - ), - "test 4" - ) - assertEquals( - ListRationalFunction( - ListPolynomial( - Rational(41635, 3888), - Rational(0, 1), - Rational(-279187, 11664), - Rational(0, 1), - Rational(103769, 3456), - Rational(0, 1), - Rational(-11017, 768), - Rational(0, 1), - Rational(4097, 4096) - ), - ListPolynomial( - Rational(-13811791, 3779136), - Rational(0, 1), - Rational(-9999395, 419904), - Rational(0, 1), - Rational(6376601, 124416), - Rational(0, 1), - Rational(-3668315, 82944), - Rational(0, 1), - Rational(2097089, 147456) - ) - ), - ListRationalFunction( - ListPolynomial( - Rational(1, 1), - Rational(0), - Rational(0), - Rational(-8, 8) - ), - ListPolynomial( - Rational(-14, 8), - Rational(0), - Rational(0), - Rational(0), - Rational(8, 9) - ) - ).substitute(RationalField, - ListRationalFunction( - ListPolynomial( - Rational(14, 9), - Rational(0), - Rational(-14, 7) - ), - ListPolynomial( - Rational(-6, 4), - Rational(0), - Rational(1, 8) - ) - ) - ), - "test 5" - ) - } - @Test - fun test_Polynomial_derivative() { - assertEquals( - ListPolynomial(Rational(-2), Rational(2)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).derivative(RationalField), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(-8, 3), Rational(8, 9), Rational(15, 7), Rational(-20, 9)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).derivative(RationalField), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(8, 9), Rational(15, 7), Rational(-20, 9)), - ListPolynomial(Rational(0), Rational(0), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).derivative(RationalField), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(-8, 3), Rational(8, 9), Rational(15, 7), Rational(0)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(0)).derivative(RationalField), - "test 4" - ) - } - @Test - fun test_Polynomial_nthDerivative() { - assertEquals( - ListPolynomial(Rational(-2), Rational(2)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthDerivative(RationalField, 1), - "test 1" - ) - assertFailsWithTypeAndMessage( - "Order of derivative must be non-negative", - "test2" - ) { - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthDerivative(RationalField, -1) - } - assertEquals( - ListPolynomial(Rational(1), Rational(-2), Rational(1)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthDerivative(RationalField, 0), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(2)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthDerivative(RationalField, 2), - "test 4" - ) - assertEquals( - ListPolynomial(), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthDerivative(RationalField, 3), - "test 5" - ) - assertEquals( - ListPolynomial(), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthDerivative(RationalField, 4), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(8, 9), Rational(30, 7), Rational(-20, 3)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).nthDerivative(RationalField, 2), - "test 7" - ) - assertEquals( - ListPolynomial(Rational(8, 9), Rational(30, 7), Rational(-20, 3)), - ListPolynomial(Rational(0), Rational(0), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).nthDerivative(RationalField, 2), - "test 8" - ) - assertEquals( - ListPolynomial(Rational(8, 9), Rational(30, 7), Rational(0)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(0)).nthDerivative(RationalField, 2), - "test 9" - ) - } - @Test - fun test_Polynomial_antiderivative() { - assertEquals( - ListPolynomial(Rational(0), Rational(1), Rational(-1), Rational(1, 3)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).antiderivative(RationalField), - "test 1" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(1, 5), Rational(-4, 3), Rational(4, 27), Rational(5, 28), Rational(-1, 9)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).antiderivative(RationalField), - "test 2" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(4, 27), Rational(5, 28), Rational(-1, 9)), - ListPolynomial(Rational(0), Rational(0), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).antiderivative(RationalField), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(1, 5), Rational(-4, 3), Rational(4, 27), Rational(5, 28), Rational(0)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(0)).antiderivative(RationalField), - "test 4" - ) - } - @Test - fun test_Polynomial_nthAntiderivative() { - assertEquals( - ListPolynomial(Rational(0), Rational(1), Rational(-1), Rational(1, 3)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthAntiderivative(RationalField, 1), - "test 1" - ) - assertFailsWithTypeAndMessage( - "Order of antiderivative must be non-negative", - "test2" - ) { - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthAntiderivative(RationalField, -1) - } - assertEquals( - ListPolynomial(Rational(1), Rational(-2), Rational(1)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthAntiderivative(RationalField, 0), - "test 3" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(1, 2), Rational(-1, 3), Rational(1, 12)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthAntiderivative(RationalField, 2), - "test 4" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(1, 6), Rational(-1, 12), Rational(1, 60)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthAntiderivative(RationalField, 3), - "test 5" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0), Rational(1, 24), Rational(-1, 60), Rational(1, 360)), - ListPolynomial(Rational(1), Rational(-2), Rational(1)).nthAntiderivative(RationalField, 4), - "test 6" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(1, 10), Rational(-4, 9), Rational(1, 27), Rational(1, 28), Rational(-1, 54)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).nthAntiderivative(RationalField, 2), - "test 7" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(0), Rational(0), Rational(1, 27), Rational(1, 28), Rational(-1, 54)), - ListPolynomial(Rational(0), Rational(0), Rational(4, 9), Rational(5, 7), Rational(-5, 9)).nthAntiderivative(RationalField, 2), - "test 8" - ) - assertEquals( - ListPolynomial(Rational(0), Rational(0), Rational(1, 10), Rational(-4, 9), Rational(1, 27), Rational(1, 28), Rational(0)), - ListPolynomial(Rational(1, 5), Rational(-8, 3), Rational(4, 9), Rational(5, 7), Rational(0)).nthAntiderivative(RationalField, 2), - "test 9" - ) - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt deleted file mode 100644 index ad6240fb9..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt +++ /dev/null @@ -1,123 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.algebra -import space.kscience.kmath.operations.invoke -import kotlin.test.Test -import kotlin.test.assertEquals - - -class NumberedConstructorsTest { - @Test - @UnstableKMathAPI - fun testDSL1() { - assertEquals( - NumberedPolynomialAsIs( - listOf(2u, 0u, 3u) to 5, - listOf(0u, 1u) to -6, - ), - Int.algebra.numberedPolynomialSpace { - NumberedPolynomialDSL1 { - 5 { 0 pow 2u; 2 pow 3u } - (-6) { 1 pow 1u } - } - }, - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to -1, - ), - Int.algebra.numberedPolynomialSpace { - NumberedPolynomialDSL1 { - 5 { } - (-6) { } - } - }, - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to -1, - ), - Int.algebra.numberedPolynomialSpace { - NumberedPolynomialDSL1 { - 5 { 0 pow 1u; 0 pow 1u } - (-6) { 0 pow 2u } - } - }, - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to -1, - ), - Int.algebra.numberedPolynomialSpace { - NumberedPolynomialDSL1 { - 5 { 0 pow 1u; 0 pow 1u } - (-6) { 0 pow 2u; 2 pow 0u } - } - }, - "test 3" - ) - } - @Test - @UnstableKMathAPI - fun testFabric() { - assertEquals( - NumberedPolynomialAsIs( - listOf(2u, 0u, 3u) to 5, - listOf(0u, 1u) to -6, - ), - Int.algebra { - NumberedPolynomial( - listOf(2u, 0u, 3u) to 5, - listOf(0u, 1u) to -6, - ) - }, - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u, 0u, 3u) to 5, - listOf(0u, 1u) to -6, - ), - Int.algebra { - NumberedPolynomial( - listOf(2u, 0u, 3u, 0u) to 5, - listOf(0u, 1u, 0u, 0u) to -6, - ) - }, - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to -1, - ), - Int.algebra { - NumberedPolynomial( - listOf(0u) to 5, - listOf(0u, 0u) to -6, - ) - }, - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0, - ), - Int.algebra { - NumberedPolynomial( - listOf(0u) to 5, - listOf(0u, 0u) to -5, - ) - }, - "test 4" - ) - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt deleted file mode 100644 index c2f86198c..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt +++ /dev/null @@ -1,1740 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("LocalVariableName") - -package space.kscience.kmath.functions - -import space.kscience.kmath.functions.testUtils.IntModuloRing -import space.kscience.kmath.functions.testUtils.Rational -import space.kscience.kmath.functions.testUtils.RationalField -import space.kscience.kmath.functions.testUtils.m -import space.kscience.kmath.functions.testUtils.o -import kotlin.test.Test -import kotlin.test.assertEquals -import kotlin.test.assertSame -import kotlin.test.fail - - -class NumberedPolynomialTest { - @Test - fun test_Polynomial_Int_plus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + -3, - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-3, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + -3, - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + -3, - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ) + -3, - "test 4" - ) - val polynomial_5 = NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_5, - polynomial_5 + 0, - "test 5" - ) - val polynomial_6 = NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_6, - polynomial_6 + 0, - "test 6" - ) - val polynomial_7 = NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_7, - polynomial_7 + 0, - "test 7" - ) - } - } - @Test - fun test_Polynomial_Int_minus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - 3, - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-3, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - 3, - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - 3, - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ) - 3, - "test 4" - ) - val polynomial_5 = NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_5, - polynomial_5 - 0, - "test 5" - ) - val polynomial_6 = NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_6, - polynomial_6 - 0, - "test 6" - ) - val polynomial_7 = NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_7, - polynomial_7 - 0, - "test 7" - ) - } - } - @Test - fun test_Polynomial_Int_times() { - IntModuloRing(35).numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to m(34), - listOf(3u) to m(2), - listOf(0u, 1u) to m(1), - listOf(1u) to m(20), - listOf(0u, 0u, 2u) to m(2), - ), - NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ) * 27, - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(0), - listOf(3u) to m(0), - listOf(0u, 1u) to m(0), - listOf(1u) to m(0), - listOf(0u, 0u, 2u) to m(0), - ), - NumberedPolynomial( - listOf() to m(7), - listOf(3u) to m(0), - listOf(0u, 1u) to m(49), - listOf(1u) to m(21), - listOf(0u, 0u, 2u) to m(14), - ) * 15, - "test 2" - ) - val polynomial = NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ) - assertSame( - zero, - polynomial * 0, - "test 3" - ) - assertSame( - polynomial, - polynomial * 1, - "test 4" - ) - } - } - @Test - fun test_Int_Polynomial_plus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - -3 + NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-3, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - -3 + NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - -3 + NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - -3 + NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - "test 4" - ) - val polynomial_5 = NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_5, - 0 + polynomial_5, - "test 5" - ) - val polynomial_6 = NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_6, - 0 + polynomial_6, - "test 6" - ) - val polynomial_7 = NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - assertSame( - polynomial_7, - 0 + polynomial_7, - "test 7" - ) - } - } - @Test - fun test_Int_Polynomial_minus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(22, 9), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - 3 - NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(3, 1), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - 3 - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - 3 - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - 3 - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - "test 4" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(22, 9), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - 0 - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 5" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - 0 - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 6" - ) - assertEquals( - NumberedPolynomial( - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - 0 - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 7" - ) - } - } - @Test - fun test_Int_Polynomial_times() { - IntModuloRing(35).numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to m(34), - listOf(3u) to m(2), - listOf(0u, 1u) to m(1), - listOf(1u) to m(20), - listOf(0u, 0u, 2u) to m(2), - ), - 27 * NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(0), - listOf(3u) to m(0), - listOf(0u, 1u) to m(0), - listOf(1u) to m(0), - listOf(0u, 0u, 2u) to m(0), - ), - 15 * NumberedPolynomial( - listOf() to m(7), - listOf(3u) to m(0), - listOf(0u, 1u) to m(49), - listOf(1u) to m(21), - listOf(0u, 0u, 2u) to m(14), - ), - "test 2" - ) - val polynomial = NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ) - assertSame( - zero, - 0 * polynomial, - "test 3" - ) - assertSame( - polynomial, - 1 * polynomial, - "test 4" - ) - } - } - @Test - fun test_Polynomial_Constant_plus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + Rational(-3), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-3, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + Rational(-3), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + Rational(-3), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ) + Rational(-3), - "test 4" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + Rational(0), - "test 5" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + Rational(0), - "test 6" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) + Rational(0), - "test 7" - ) - } - } - @Test - fun test_Polynomial_Constant_minus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - Rational(3), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-3, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - Rational(3), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - Rational(3), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ) - Rational(3), - "test 4" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - Rational(0), - "test 5" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - Rational(0), - "test 6" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ) - Rational(0), - "test 7" - ) - } - } - @Test - fun test_Polynomial_Constant_times() { - IntModuloRing(35).numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to m(34), - listOf(3u) to m(2), - listOf(0u, 1u) to m(1), - listOf(1u) to m(20), - listOf(0u, 0u, 2u) to m(2), - ), - NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ) * m(27), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(0), - listOf(3u) to m(0), - listOf(0u, 1u) to m(0), - listOf(1u) to m(0), - listOf(0u, 0u, 2u) to m(0), - ), - NumberedPolynomial( - listOf() to m(7), - listOf(3u) to m(0), - listOf(0u, 1u) to m(49), - listOf(1u) to m(21), - listOf(0u, 0u, 2u) to m(14), - ) * m(15), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(0), - listOf(3u) to m(0), - listOf(0u, 1u) to m(0), - listOf(1u) to m(0), - listOf(0u, 0u, 2u) to m(0), - ), - NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ) * m(0), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ), - NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ) * m(1), - "test 4" - ) - } - } - @Test - fun test_Constant_Polynomial_plus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - Rational(-3) + NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-3, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - Rational(-3) + NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - Rational(-3) + NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - Rational(-3) + NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - "test 4" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - Rational(0) + NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 5" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - Rational(0) + NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 6" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - Rational(0) + NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 7" - ) - } - } - @Test - fun test_Constant_Polynomial_minus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(22, 9), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - Rational(3) - NumberedPolynomial( - listOf() to Rational(5, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(3, 1), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - Rational(3) - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 1), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - Rational(3) - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - Rational(3) - NumberedPolynomial( - listOf() to Rational(27, 9), - listOf(3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - ), - "test 4" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(22, 9), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - Rational(0) - NumberedPolynomial( - listOf() to Rational(-22, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 5" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - Rational(0) - NumberedPolynomial( - listOf() to Rational(0, 9), - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 6" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(3u) to Rational(8, 9), - listOf(0u, 4u) to Rational(8, 7), - ), - Rational(0) - NumberedPolynomial( - listOf(3u) to Rational(-8, 9), - listOf(0u, 4u) to Rational(-8, 7), - ), - "test 7" - ) - } - } - @Test - fun test_Constant_Polynomial_times() { - IntModuloRing(35).numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to m(34), - listOf(3u) to m(2), - listOf(0u, 1u) to m(1), - listOf(1u) to m(20), - listOf(0u, 0u, 2u) to m(2), - ), - m(27) * NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(0), - listOf(3u) to m(0), - listOf(0u, 1u) to m(0), - listOf(1u) to m(0), - listOf(0u, 0u, 2u) to m(0), - ), - m(15) * NumberedPolynomial( - listOf() to m(7), - listOf(3u) to m(0), - listOf(0u, 1u) to m(49), - listOf(1u) to m(21), - listOf(0u, 0u, 2u) to m(14), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(0), - listOf(3u) to m(0), - listOf(0u, 1u) to m(0), - listOf(1u) to m(0), - listOf(0u, 0u, 2u) to m(0), - ), - m(0) * NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ), - m(1) * NumberedPolynomial( - listOf() to m(22), - listOf(3u) to m(26), - listOf(0u, 1u) to m(13), - listOf(1u) to m(15), - listOf(0u, 0u, 2u) to m(26), - ), - "test 4" - ) - } - } - @Test - fun test_Polynomial_unaryMinus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf(5u) to Rational(-5, 9), - listOf() to Rational(8, 9), - listOf(0u, 0u, 0u, 0u, 0u, 0u, 13u) to Rational(8, 7), - ), - -NumberedPolynomial( - listOf(5u) to Rational(5, 9), - listOf() to Rational(-8, 9), - listOf(0u, 0u, 0u, 0u, 0u, 0u, 13u) to Rational(-8, 7), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf(5u) to Rational(-5, 9), - listOf() to Rational(8, 9), - listOf(0u, 0u, 0u, 0u, 0u, 0u, 13u) to Rational(8, 7), - listOf(0u, 4u) to Rational(0), - listOf(5u) to Rational(0), - ), - -NumberedPolynomial( - listOf(5u) to Rational(5, 9), - listOf() to Rational(-8, 9), - listOf(0u, 0u, 0u, 0u, 0u, 0u, 13u) to Rational(-8, 7), - listOf(0u, 4u) to Rational(0), - listOf(5u) to Rational(0), - ), - "test 2" - ) - } - } - @Test - fun test_Polynomial_Polynomial_plus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-17, 2), - listOf(1u) to Rational(-1, 3), - listOf(2u) to Rational(-25, 21), - listOf(0u, 1u) to Rational(146, 63), - listOf(1u, 1u) to Rational(-3, 5), - listOf(2u, 1u) to Rational(61, 15), - listOf(0u, 2u) to Rational(157, 63), - listOf(1u, 2u) to Rational(-55, 21), - listOf(2u, 2u) to Rational(11, 24), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(-7, 7), - listOf(2u, 1u) to Rational(12, 5), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) + NumberedPolynomial( - listOf() to Rational(-20, 2), - listOf(1u) to Rational(0, 9), - listOf(2u) to Rational(-20, 7), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(7, 9), - listOf(1u, 2u) to Rational(5, 7), - listOf(2u, 2u) to Rational(-2, 3), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-17, 2), - listOf(1u) to Rational(-1, 3), - listOf(2u) to Rational(-25, 21), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(157, 63), - listOf(1u, 2u) to Rational(-55, 21), - listOf(2u, 2u) to Rational(11, 24), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) + NumberedPolynomial( - listOf() to Rational(-20, 2), - listOf(1u) to Rational(0, 9), - listOf(2u) to Rational(-20, 7), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(7, 9), - listOf(1u, 2u) to Rational(5, 7), - listOf(2u, 2u) to Rational(-2, 3), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-17, 2), - listOf(1u) to Rational(-1, 3), - listOf(2u) to Rational(-25, 21), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) + NumberedPolynomial( - listOf() to Rational(-20, 2), - listOf(1u) to Rational(0, 9), - listOf(2u) to Rational(-20, 7), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(-7, 7), - listOf(2u, 1u) to Rational(12, 5), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) + NumberedPolynomial( - listOf() to Rational(-6, 4), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(-10, 6), - listOf(0u, 1u) to Rational(-17, 7), - listOf(1u, 1u) to Rational(7, 7), - listOf(2u, 1u) to Rational(-12, 5), - listOf(0u, 2u) to Rational(-12, 7), - listOf(1u, 2u) to Rational(10, 3), - listOf(2u, 2u) to Rational(-9, 8), - ), - "test 4" - ) - } - } - @Test - fun test_Polynomial_Polynomial_minus() { - RationalField.numberedPolynomialSpace { - assertEquals( - NumberedPolynomial( - listOf() to Rational(-17, 2), - listOf(1u) to Rational(-1, 3), - listOf(2u) to Rational(-25, 21), - listOf(0u, 1u) to Rational(146, 63), - listOf(1u, 1u) to Rational(-3, 5), - listOf(2u, 1u) to Rational(61, 15), - listOf(0u, 2u) to Rational(157, 63), - listOf(1u, 2u) to Rational(-55, 21), - listOf(2u, 2u) to Rational(11, 24), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(-7, 7), - listOf(2u, 1u) to Rational(12, 5), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) - NumberedPolynomial( - listOf() to Rational(20, 2), - listOf(1u) to Rational(0, 9), - listOf(2u) to Rational(20, 7), - listOf(0u, 1u) to Rational(1, 9), - listOf(1u, 1u) to Rational(-2, 5), - listOf(2u, 1u) to Rational(-10, 6), - listOf(0u, 2u) to Rational(-7, 9), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(2, 3), - ), - "test 1" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-17, 2), - listOf(1u) to Rational(-1, 3), - listOf(2u) to Rational(-25, 21), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(157, 63), - listOf(1u, 2u) to Rational(-55, 21), - listOf(2u, 2u) to Rational(11, 24), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) - NumberedPolynomial( - listOf() to Rational(20, 2), - listOf(1u) to Rational(0, 9), - listOf(2u) to Rational(20, 7), - listOf(0u, 1u) to Rational(1, 9), - listOf(1u, 1u) to Rational(-2, 5), - listOf(2u, 1u) to Rational(-10, 6), - listOf(0u, 2u) to Rational(-7, 9), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(2, 3), - ), - "test 2" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(-17, 2), - listOf(1u) to Rational(-1, 3), - listOf(2u) to Rational(-25, 21), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(2, 5), - listOf(2u, 1u) to Rational(10, 6), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) - NumberedPolynomial( - listOf() to Rational(20, 2), - listOf(1u) to Rational(0, 9), - listOf(2u) to Rational(20, 7), - listOf(0u, 1u) to Rational(1, 9), - listOf(1u, 1u) to Rational(-2, 5), - listOf(2u, 1u) to Rational(-10, 6), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - ), - "test 3" - ) - assertEquals( - NumberedPolynomial( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - ), - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(-7, 7), - listOf(2u, 1u) to Rational(12, 5), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ) - NumberedPolynomial( - listOf() to Rational(6, 4), - listOf(1u) to Rational(-2, 6), - listOf(2u) to Rational(10, 6), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(-7, 7), - listOf(2u, 1u) to Rational(12, 5), - listOf(0u, 2u) to Rational(12, 7), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(9, 8), - ), - "test 4" - ) - } - } - @Test - fun test_Polynomial_Polynomial_times() { - IntModuloRing(35).numberedPolynomialSpace { - // (p + q + r) * (p^2 + q^2 + r^2 - pq - pr - qr) = p^3 + q^3 + r^3 - 3pqr - assertEquals( - NumberedPolynomial( - listOf(3u) to m(1), - listOf(0u, 3u) to m(1), - listOf(0u, 0u, 3u) to m(1), - listOf(1u, 2u) to m(0), - listOf(0u, 1u, 2u) to m(0), - listOf(2u, 0u, 1u) to m(0), - listOf(1u, 0u, 2u) to m(0), - listOf(2u, 1u) to m(0), - listOf(0u, 2u, 1u) to m(0), - listOf(1u, 1u, 1u) to m(-3), - ), - NumberedPolynomial( - listOf(1u) to m(1), - listOf(0u, 1u) to m(1), - listOf(0u, 0u, 1u) to m(1), - ) * NumberedPolynomial( - listOf(2u) to m(1), - listOf(0u, 2u) to m(1), - listOf(0u, 0u, 2u) to m(1), - listOf(1u, 1u) to m(-1), - listOf(0u, 1u, 1u) to m(-1), - listOf(1u, 0u, 1u) to m(-1), - ), - "test 1" - ) - // Spoiler: 5 * 7 = 0 - assertEquals( - NumberedPolynomial( - listOf(2u) to m(0), - listOf(0u, 2u) to m(0), - listOf(0u, 0u, 2u) to m(0), - listOf(1u, 1u) to m(0), - listOf(0u, 1u, 1u) to m(0), - listOf(1u, 0u, 1u) to m(0), - ), - NumberedPolynomial( - listOf(1u) to m(5), - listOf(0u, 1u) to m(-25), - listOf(0u, 0u, 1u) to m(10), - ) * NumberedPolynomial( - listOf(1u) to m(21), - listOf(0u, 1u) to m(14), - listOf(0u, 0u, 1u) to m(-7), - ), - "test 2" - ) - } - } - @Test - fun test_lastVariable() { - RationalField.numberedPolynomialSpace { - assertEquals( - -1, - NumberedPolynomial().lastVariable, - "test 1" - ) - assertEquals( - -1, - NumberedPolynomial( - listOf() to o - ).lastVariable, - "test 2" - ) - assertEquals( - 2, - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ).lastVariable, - "test 3" - ) - assertEquals( - 3, - NumberedPolynomial( - listOf(0u, 1u, 2u, 1u, 0u) to o - ).also { println(it) }.lastVariable, - "test 4" - ) - assertEquals( - 2, - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ).lastVariable, - "test 5" - ) - } - } - @Test - fun test_degree() { - RationalField.numberedPolynomialSpace { - assertEquals( - -1, - NumberedPolynomial().degree, - "test 1" - ) - assertEquals( - 0, - NumberedPolynomial( - listOf() to o - ).degree, - "test 2" - ) - assertEquals( - 6, - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ).degree, - "test 3" - ) - assertEquals( - 4, - NumberedPolynomial( - listOf(0u, 1u, 2u, 1u, 0u) to o - ).degree, - "test 4" - ) - assertEquals( - 3, - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ).degree, - "test 5" - ) - assertEquals( - 4, - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - listOf(0u, 0u, 0u, 4u) to o, - ).degree, - "test 6" - ) - } - } - @Test - fun test_degrees() { - RationalField.numberedPolynomialSpace { - assertEquals( - listOf(), - NumberedPolynomial().degrees, - "test 1" - ) - assertEquals( - listOf(), - NumberedPolynomial( - listOf() to o - ).degrees, - "test 2" - ) - assertEquals( - listOf(1u, 2u, 3u), - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ).degrees, - "test 3" - ) - assertEquals( - listOf(0u, 1u, 2u, 1u), - NumberedPolynomial( - listOf(0u, 1u, 2u, 1u, 0u) to o - ).degrees, - "test 4" - ) - assertEquals( - listOf(2u, 1u, 1u), - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ).degrees, - "test 5" - ) - assertEquals( - listOf(2u, 2u, 2u, 4u), - NumberedPolynomial( - listOf() to o, - listOf(1u, 2u) to o, - listOf(0u, 1u, 2u) to o, - listOf(2u, 0u, 1u) to o, - listOf(0u, 0u, 0u, 4u) to o, - ).degrees, - "test 6" - ) - } - } - @Test - fun test_degreeBy() { - RationalField.numberedPolynomialSpace { - fun NumberedPolynomial.collectDegrees(limit: Int = lastVariable + 2): List = List(limit) { degreeBy(it) } - assertEquals( - listOf(0u), - NumberedPolynomial().collectDegrees(), - "test 1" - ) - assertEquals( - listOf(0u), - NumberedPolynomial( - listOf() to o - ).collectDegrees(), - "test 2" - ) - assertEquals( - listOf(1u, 2u, 3u, 0u), - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ).collectDegrees(), - "test 3" - ) - assertEquals( - listOf(0u, 1u, 2u, 1u, 0u), - NumberedPolynomial( - listOf(0u, 1u, 2u, 1u, 0u) to o - ).collectDegrees(), - "test 4" - ) - assertEquals( - listOf(2u, 1u, 1u, 0u), - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ).collectDegrees(), - "test 5" - ) - assertEquals( - listOf(2u, 2u, 2u, 4u, 0u), - NumberedPolynomial( - listOf() to o, - listOf(1u, 2u) to o, - listOf(0u, 1u, 2u) to o, - listOf(2u, 0u, 1u) to o, - listOf(0u, 0u, 0u, 4u) to o, - ).collectDegrees(), - "test 6" - ) - } - } - @Test - fun test_degreeBy_Collection() { - RationalField.numberedPolynomialSpace { - fun NumberedPolynomial.checkDegreeBy(message: String? = null) { - val lastVariable = lastVariable - val indexCollectionSequence: Sequence> = sequence { - val appearances = MutableList(lastVariable + 2) { 0 } - while (true) { - yield( - buildList { - for ((variable, count) in appearances.withIndex()) repeat(count) { add(variable) } - } - ) - val indexChange = appearances.indexOfFirst { it < 4 } - if (indexChange == -1) break - appearances[indexChange] += 1 - for (index in 0 until indexChange) appearances[index] = 0 - } - } - for (indexCollection in indexCollectionSequence) { - val expected = coefficients.keys.maxOfOrNull { degs -> degs.slice(indexCollection.distinct().filter { it in degs.indices }).sum() } ?: 0u - val actual = degreeBy(indexCollection) - if (actual != expected) - fail("${message ?: ""} Incorrect answer for variable collection $indexCollection: expected $expected, actual $actual") - } - } - NumberedPolynomial().checkDegreeBy("test 1") - NumberedPolynomial( - listOf() to o - ).checkDegreeBy("test 2") - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ).checkDegreeBy("test 3") - NumberedPolynomial( - listOf(0u, 1u, 2u, 1u, 0u) to o - ).checkDegreeBy("test 4") - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ).checkDegreeBy("test 5") - NumberedPolynomial( - listOf() to o, - listOf(1u, 2u) to o, - listOf(0u, 1u, 2u) to o, - listOf(2u, 0u, 1u) to o, - listOf(0u, 0u, 0u, 4u) to o, - ).checkDegreeBy("test 6") - } - } - @Test - fun test_countOfVariables() { - RationalField.numberedPolynomialSpace { - assertEquals( - 0, - NumberedPolynomial().countOfVariables, - "test 1" - ) - assertEquals( - 0, - NumberedPolynomial( - listOf() to o - ).countOfVariables, - "test 2" - ) - assertEquals( - 3, - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ).countOfVariables, - "test 3" - ) - assertEquals( - 3, - NumberedPolynomial( - listOf(0u, 1u, 2u, 1u, 0u) to o - ).countOfVariables, - "test 4" - ) - assertEquals( - 3, - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ).countOfVariables, - "test 5" - ) - assertEquals( - 4, - NumberedPolynomial( - listOf() to o, - listOf(1u, 2u) to o, - listOf(0u, 1u, 2u) to o, - listOf(2u, 0u, 1u) to o, - listOf(0u, 0u, 0u, 4u) to o, - ).countOfVariables, - "test 6" - ) - } - } - @Test - fun test_RF_countOfVariables() { - RationalField.numberedRationalFunctionSpace { - assertEquals( - 0, - NumberedRationalFunction( - NumberedPolynomial() - ).countOfVariables, - "test 1" - ) - assertEquals( - 0, - NumberedRationalFunction( - NumberedPolynomial(), - NumberedPolynomial() - ).countOfVariables, - "test 2" - ) - assertEquals( - 0, - NumberedRationalFunction( - NumberedPolynomial( - listOf() to o - ) - ).countOfVariables, - "test 3" - ) - assertEquals( - 3, - NumberedRationalFunction( - NumberedPolynomial( - listOf(1u, 2u, 3u) to o - ) - ).countOfVariables, - "test 4" - ) - assertEquals( - 3, - NumberedRationalFunction( - NumberedPolynomial( - listOf(0u, 1u, 0u, 1u) to o - ), - NumberedPolynomial( - listOf(0u, 0u, 2u) to o - ) - ).countOfVariables, - "test 5" - ) - assertEquals( - 3, - NumberedRationalFunction( - NumberedPolynomial( - listOf() to o, - listOf(0u, 1u) to o, - listOf(2u, 0u, 1u) to o, - ) - ).countOfVariables, - "test 6" - ) - assertEquals( - 4, - NumberedRationalFunction( - NumberedPolynomial( - listOf() to o, - listOf(1u, 2u) to o, - listOf(2u, 0u, 1u) to o, - ), NumberedPolynomial( - listOf(0u, 1u, 2u) to o, - listOf(0u, 0u, 0u, 4u) to o, - ) - ).countOfVariables, - "test 7" - ) - } - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt deleted file mode 100644 index e5d1ddf48..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt +++ /dev/null @@ -1,12021 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.functions.testUtils.Rational -import space.kscience.kmath.functions.testUtils.RationalField -import space.kscience.kmath.functions.testUtils.assertFailsWithTypeAndMessage -import kotlin.test.Ignore -import kotlin.test.Test -import kotlin.test.assertEquals -import space.kscience.kmath.functions.testUtils.bufferOf -import space.kscience.kmath.functions.testUtils.assertEquals - - -class NumberedPolynomialUtilTest { - @Test - fun test_Polynomial_substitute_Double_Map() { - assertEquals( - NumberedPolynomialAsIs(emptyList() to 0.0), - NumberedPolynomialAsIs( - listOf() to 1.0, - listOf(1u) to -2.0, - listOf(2u) to 1.0, - ).substitute(mapOf( - 0 to 1.0 - )), - 0.001, - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf()), - 0.001, - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 5 to 0.9211194782050933 - )), - 0.001, - "test 2'" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(0u, 1u) to 0.4561746111587508, - listOf(0u, 2u) to 0.2700930201481795, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 0 to 0.0 - )), - 0.001, - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(0u, 1u) to 0.4561746111587508, - listOf(0u, 2u) to 0.2700930201481795, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 0 to 0.0, - 5 to 0.9211194782050933 - )), - 0.001, - "test 3'" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.433510890645169, - listOf(1u) to 0.6264844682514724, - listOf(2u) to 0.8405727903771333, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 1 to 0.8400458576651112 - )), - 0.001, - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.433510890645169, - listOf(1u) to 0.6264844682514724, - listOf(2u) to 0.8405727903771333, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 1 to 0.8400458576651112, - 5 to 0.9211194782050933 - )), - 0.001, - "test 4'" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.934530767358133, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 0 to 0.4846192734143442, - 1 to 0.8400458576651112, - )), - 0.001, - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.934530767358133, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(mapOf( - 0 to 0.4846192734143442, - 1 to 0.8400458576651112, - 5 to 0.9211194782050933 - )), - 0.001, - "test 5'" - ) - } - @Test - fun test_Polynomial_substitute_Constant_Map() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substitute(RationalField, mapOf( - 0 to Rational(1) - )), - "test 1" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(143, 150) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to Rational(-2, 5), - 1 to Rational(12, 9), - )), - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(143, 150) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to Rational(-2, 5), - 1 to Rational(12, 9), - 5 to Rational(57, 179), - )), - "test 2'" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+y+%3D+12%2F9 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-67, 18), - listOf(1u) to Rational(-70, 9), - listOf(2u) to Rational(88, 9), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 1 to Rational(12, 9), - )), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-67, 18), - listOf(1u) to Rational(-70, 9), - listOf(2u) to Rational(88, 9), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 1 to Rational(12, 9), - 5 to Rational(57, 179), - )), - "test 3'" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-83, 50), - listOf(0u, 1u) to Rational(29, 25), - listOf(0u, 2u) to Rational(3, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to Rational(-2, 5), - )), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-83, 50), - listOf(0u, 1u) to Rational(29, 25), - listOf(0u, 2u) to Rational(3, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to Rational(-2, 5), - 5 to Rational(57, 179), - )), - "test 4'" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf()), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 5 to Rational(57, 179), - )), - "test 5'" - ) - // https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(47639065216, 2562890625) - ), - NumberedPolynomialAsIs( - listOf(8u) to Rational(-3, 2), - listOf(7u, 1u) to Rational(8, 6), - listOf(6u, 2u) to Rational(14, 6), - listOf(5u, 3u) to Rational(-3, 1), - listOf(4u, 4u) to Rational(-19, 2), - listOf(3u, 5u) to Rational(9, 4), - listOf(2u, 6u) to Rational(5, 5), - listOf(1u, 7u) to Rational(18, 9), - listOf(0u, 8u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to Rational(-2, 5), - 1 to Rational(12, 9), - )), - "test 6" - ) - } - @Test - fun test_Polynomial_substitute_Polynomial_Map() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - )), - "test 1" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-5%2F1+s+%2B+2%2F8+t%2C+y+%3D+11%2F7+t - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(0u, 1u) to Rational(-92, 21), - listOf(0u, 2u) to Rational(-2627, 2352), - listOf(0u, 3u) to Rational(4565, 3136), - listOf(0u, 4u) to Rational(605, 1568), - listOf(1u) to Rational(-20, 3), - listOf(1u, 1u) to Rational(1445, 21), - listOf(1u, 2u) to Rational(-13145, 392), - listOf(1u, 3u) to Rational(-3025, 196), - listOf(2u) to Rational(175, 3), - listOf(2u, 1u) to Rational(2475, 28), - listOf(2u, 2u) to Rational(15125, 98), - listOf(3u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf(1u) to Rational(-5, 1), - listOf(0u, 1u) to Rational(2, 8), - ), - 1 to NumberedPolynomialAsIs( - listOf(1u) to Rational(0, 5), - listOf(0u, 1u) to Rational(11, 7), - ), - )), - "test 2" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = (0/6 + 14/8 s + -14/2 s^2) + (-3/5 + 11/1 s + 3/7 s^2) t + (-3/7 + -18/5 s + -9/1 s^2) t^2, y = (-9/2 + 2/7 s + 9/1 s^2) + (13/1 + -1/8 s + 2/8 s^2) t + (19/4 + 15/7 s + -19/4 s^2) t^2 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(129, 4), - listOf(1u) to Rational(48583, 336), - listOf(2u) to Rational(-913477, 1568), - listOf(3u) to Rational(-967567, 672), - listOf(4u) to Rational(4722043, 1344), - listOf(5u) to Rational(8855, 2), - listOf(6u) to Rational(-311971, 32), - listOf(7u) to Rational(-17325, 4), - listOf(8u) to Rational(19845, 2), - listOf(0u, 1u) to Rational(-827, 4), - listOf(1u, 1u) to Rational(191927, 840), - listOf(2u, 1u) to Rational(9592627, 2352), - listOf(3u, 1u) to Rational(-105400711, 53760), - listOf(4u, 1u) to Rational(-10054101459, 439040), - listOf(5u, 1u) to Rational(2127351, 128), - listOf(6u, 1u) to Rational(116680973, 3136), - listOf(7u, 1u) to Rational(-220445, 7), - listOf(8u, 1u) to Rational(-2655, 4), - listOf(0u, 2u) to Rational(30567, 100), - listOf(1u, 2u) to Rational(-156284953, 39200), - listOf(2u, 2u) to Rational(-57661541711, 6585600), - listOf(3u, 2u) to Rational(131931579, 3136), - listOf(4u, 2u) to Rational(98818124791, 3512320), - listOf(5u, 2u) to Rational(-94458855053, 878080), - listOf(6u, 2u) to Rational(13937705305, 1229312), - listOf(7u, 2u) to Rational(335706887, 21952), - listOf(8u, 2u) to Rational(23549165, 1568), - listOf(0u, 3u) to Rational(111367, 1400), - listOf(1u, 3u) to Rational(4937369, 700), - listOf(2u, 3u) to Rational(-4449423711, 274400), - listOf(3u, 3u) to Rational(-351873325703, 4390400), - listOf(4u, 3u) to Rational(23495875029, 307328), - listOf(5u, 3u) to Rational(17576300919, 878080), - listOf(6u, 3u) to Rational(230316993, 12544), - listOf(7u, 3u) to Rational(-191130515, 21952), - listOf(8u, 3u) to Rational(332435, 392), - listOf(0u, 4u) to Rational(-275084, 1225), - listOf(1u, 4u) to Rational(-266774603, 137200), - listOf(2u, 4u) to Rational(2176279167121, 30732800), - listOf(3u, 4u) to Rational(10904913303, 2195200), - listOf(4u, 4u) to Rational(-10769286147, 2195200), - listOf(5u, 4u) to Rational(-26277119793, 439040), - listOf(6u, 4u) to Rational(25859735869, 6146560), - listOf(7u, 4u) to Rational(38906289, 2744), - listOf(8u, 4u) to Rational(-3072025, 392), - listOf(0u, 5u) to Rational(9573, 98), - listOf(1u, 5u) to Rational(-4154651399, 548800), - listOf(2u, 5u) to Rational(3446069019, 548800), - listOf(3u, 5u) to Rational(-7851500623, 137200), - listOf(4u, 5u) to Rational(-53205142903, 1920800), - listOf(5u, 5u) to Rational(-31953611, 3430), - listOf(6u, 5u) to Rational(1447380313, 109760), - listOf(7u, 5u) to Rational(764158625, 21952), - listOf(8u, 5u) to Rational(1153515, 784), - listOf(0u, 6u) to Rational(1722351, 7840), - listOf(1u, 6u) to Rational(-164554821, 109760), - listOf(2u, 6u) to Rational(-79096147243, 7683200), - listOf(3u, 6u) to Rational(-624721089, 15680), - listOf(4u, 6u) to Rational(11147305567, 548800), - listOf(5u, 6u) to Rational(8318333679, 109760), - listOf(6u, 6u) to Rational(32981871553, 1536640), - listOf(7u, 6u) to Rational(-225359619, 21952), - listOf(8u, 6u) to Rational(-3973995, 392), - listOf(0u, 7u) to Rational(67203, 784), - listOf(1u, 7u) to Rational(39281469, 54880), - listOf(2u, 7u) to Rational(70162551, 27440), - listOf(3u, 7u) to Rational(413630709, 54880), - listOf(4u, 7u) to Rational(4640410269, 192080), - listOf(5u, 7u) to Rational(802712247, 54880), - listOf(6u, 7u) to Rational(-473517603, 27440), - listOf(7u, 7u) to Rational(-17055459, 1568), - listOf(8u, 7u) to Rational(-12825, 14), - listOf(0u, 8u) to Rational(16245, 1568), - listOf(1u, 8u) to Rational(503253, 2744), - listOf(2u, 8u) to Rational(125292591, 96040), - listOf(3u, 8u) to Rational(12033171, 2744), - listOf(4u, 8u) to Rational(154352673, 27440), - listOf(5u, 8u) to Rational(-1302291, 392), - listOf(6u, 8u) to Rational(-20265741, 1960), - listOf(7u, 8u) to Rational(-26163, 56), - listOf(8u, 8u) to Rational(146205, 32), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - 1 to NumberedPolynomialAsIs( - listOf() to Rational(-9, 2), - listOf(1u) to Rational(2, 7), - listOf(2u) to Rational(9, 1), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-1, 8), - listOf(2u, 1u) to Rational(2, 8), - listOf(0u, 2u) to Rational(19, 4), - listOf(1u, 2u) to Rational(15, 7), - listOf(2u, 2u) to Rational(-19, 4), - ), - )), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(129, 4), - listOf(1u) to Rational(48583, 336), - listOf(2u) to Rational(-913477, 1568), - listOf(3u) to Rational(-967567, 672), - listOf(4u) to Rational(4722043, 1344), - listOf(5u) to Rational(8855, 2), - listOf(6u) to Rational(-311971, 32), - listOf(7u) to Rational(-17325, 4), - listOf(8u) to Rational(19845, 2), - listOf(0u, 1u) to Rational(-827, 4), - listOf(1u, 1u) to Rational(191927, 840), - listOf(2u, 1u) to Rational(9592627, 2352), - listOf(3u, 1u) to Rational(-105400711, 53760), - listOf(4u, 1u) to Rational(-10054101459, 439040), - listOf(5u, 1u) to Rational(2127351, 128), - listOf(6u, 1u) to Rational(116680973, 3136), - listOf(7u, 1u) to Rational(-220445, 7), - listOf(8u, 1u) to Rational(-2655, 4), - listOf(0u, 2u) to Rational(30567, 100), - listOf(1u, 2u) to Rational(-156284953, 39200), - listOf(2u, 2u) to Rational(-57661541711, 6585600), - listOf(3u, 2u) to Rational(131931579, 3136), - listOf(4u, 2u) to Rational(98818124791, 3512320), - listOf(5u, 2u) to Rational(-94458855053, 878080), - listOf(6u, 2u) to Rational(13937705305, 1229312), - listOf(7u, 2u) to Rational(335706887, 21952), - listOf(8u, 2u) to Rational(23549165, 1568), - listOf(0u, 3u) to Rational(111367, 1400), - listOf(1u, 3u) to Rational(4937369, 700), - listOf(2u, 3u) to Rational(-4449423711, 274400), - listOf(3u, 3u) to Rational(-351873325703, 4390400), - listOf(4u, 3u) to Rational(23495875029, 307328), - listOf(5u, 3u) to Rational(17576300919, 878080), - listOf(6u, 3u) to Rational(230316993, 12544), - listOf(7u, 3u) to Rational(-191130515, 21952), - listOf(8u, 3u) to Rational(332435, 392), - listOf(0u, 4u) to Rational(-275084, 1225), - listOf(1u, 4u) to Rational(-266774603, 137200), - listOf(2u, 4u) to Rational(2176279167121, 30732800), - listOf(3u, 4u) to Rational(10904913303, 2195200), - listOf(4u, 4u) to Rational(-10769286147, 2195200), - listOf(5u, 4u) to Rational(-26277119793, 439040), - listOf(6u, 4u) to Rational(25859735869, 6146560), - listOf(7u, 4u) to Rational(38906289, 2744), - listOf(8u, 4u) to Rational(-3072025, 392), - listOf(0u, 5u) to Rational(9573, 98), - listOf(1u, 5u) to Rational(-4154651399, 548800), - listOf(2u, 5u) to Rational(3446069019, 548800), - listOf(3u, 5u) to Rational(-7851500623, 137200), - listOf(4u, 5u) to Rational(-53205142903, 1920800), - listOf(5u, 5u) to Rational(-31953611, 3430), - listOf(6u, 5u) to Rational(1447380313, 109760), - listOf(7u, 5u) to Rational(764158625, 21952), - listOf(8u, 5u) to Rational(1153515, 784), - listOf(0u, 6u) to Rational(1722351, 7840), - listOf(1u, 6u) to Rational(-164554821, 109760), - listOf(2u, 6u) to Rational(-79096147243, 7683200), - listOf(3u, 6u) to Rational(-624721089, 15680), - listOf(4u, 6u) to Rational(11147305567, 548800), - listOf(5u, 6u) to Rational(8318333679, 109760), - listOf(6u, 6u) to Rational(32981871553, 1536640), - listOf(7u, 6u) to Rational(-225359619, 21952), - listOf(8u, 6u) to Rational(-3973995, 392), - listOf(0u, 7u) to Rational(67203, 784), - listOf(1u, 7u) to Rational(39281469, 54880), - listOf(2u, 7u) to Rational(70162551, 27440), - listOf(3u, 7u) to Rational(413630709, 54880), - listOf(4u, 7u) to Rational(4640410269, 192080), - listOf(5u, 7u) to Rational(802712247, 54880), - listOf(6u, 7u) to Rational(-473517603, 27440), - listOf(7u, 7u) to Rational(-17055459, 1568), - listOf(8u, 7u) to Rational(-12825, 14), - listOf(0u, 8u) to Rational(16245, 1568), - listOf(1u, 8u) to Rational(503253, 2744), - listOf(2u, 8u) to Rational(125292591, 96040), - listOf(3u, 8u) to Rational(12033171, 2744), - listOf(4u, 8u) to Rational(154352673, 27440), - listOf(5u, 8u) to Rational(-1302291, 392), - listOf(6u, 8u) to Rational(-20265741, 1960), - listOf(7u, 8u) to Rational(-26163, 56), - listOf(8u, 8u) to Rational(146205, 32), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - 1 to NumberedPolynomialAsIs( - listOf() to Rational(-9, 2), - listOf(1u) to Rational(2, 7), - listOf(2u) to Rational(9, 1), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-1, 8), - listOf(2u, 1u) to Rational(2, 8), - listOf(0u, 2u) to Rational(19, 4), - listOf(1u, 2u) to Rational(15, 7), - listOf(2u, 2u) to Rational(-19, 4), - ), - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-11, 3), - listOf(1u) to Rational(5, 2), - listOf(2u) to Rational(13, 7), - listOf(0u, 1u) to Rational(16, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(6, 1), - listOf(0u, 2u) to Rational(-14, 3), - listOf(1u, 2u) to Rational(-2, 7), - listOf(2u, 2u) to Rational(-10, 8), - ) - )), - "test 3'" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = s, y = (-9/2 + 2/7 s + 9/1 s^2) + (13/1 + -1/8 s + 2/8 s^2) t + (19/4 + 15/7 s + -19/4 s^2) t^2 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(129, 4), - listOf(1u) to Rational(6817, 84), - listOf(2u) to Rational(-21445, 294), - listOf(3u) to Rational(-12151, 49), - listOf(4u) to Rational(-17789, 196), - listOf(5u) to Rational(1224, 7), - listOf(6u) to Rational(405, 2), - listOf(0u, 1u) to Rational(-156), - listOf(1u, 1u) to Rational(-2440, 7), - listOf(2u, 1u) to Rational(-1571, 112), - listOf(3u, 1u) to Rational(107515, 224), - listOf(4u, 1u) to Rational(64965, 112), - listOf(5u, 1u) to Rational(209, 56), - listOf(6u, 1u) to Rational(45, 4), - listOf(0u, 2u) to Rational(112), - listOf(1u, 2u) to Rational(1449, 8), - listOf(2u, 2u) to Rational(1306309, 3136), - listOf(3u, 2u) to Rational(483207, 1568), - listOf(4u, 2u) to Rational(1978437, 6272), - listOf(5u, 2u) to Rational(-18231, 224), - listOf(6u, 2u) to Rational(-6835, 32), - listOf(0u, 3u) to Rational(247, 2), - listOf(1u, 3u) to Rational(33771, 112), - listOf(2u, 3u) to Rational(2073, 7), - listOf(3u, 3u) to Rational(-23463, 224), - listOf(4u, 3u) to Rational(-33825, 112), - listOf(5u, 3u) to Rational(201, 224), - listOf(6u, 3u) to Rational(-95, 16), - listOf(0u, 4u) to Rational(361, 16), - listOf(1u, 4u) to Rational(3667, 56), - listOf(2u, 4u) to Rational(88729, 1568), - listOf(3u, 4u) to Rational(-2476, 49), - listOf(4u, 4u) to Rational(-23419, 196), - listOf(5u, 4u) to Rational(-323, 56), - listOf(6u, 4u) to Rational(1805, 32), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 1 to NumberedPolynomialAsIs( - listOf() to Rational(-9, 2), - listOf(1u) to Rational(2, 7), - listOf(2u) to Rational(9, 1), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-1, 8), - listOf(2u, 1u) to Rational(2, 8), - listOf(0u, 2u) to Rational(19, 4), - listOf(1u, 2u) to Rational(15, 7), - listOf(2u, 2u) to Rational(-19, 4), - ), - )), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(129, 4), - listOf(1u) to Rational(6817, 84), - listOf(2u) to Rational(-21445, 294), - listOf(3u) to Rational(-12151, 49), - listOf(4u) to Rational(-17789, 196), - listOf(5u) to Rational(1224, 7), - listOf(6u) to Rational(405, 2), - listOf(0u, 1u) to Rational(-156), - listOf(1u, 1u) to Rational(-2440, 7), - listOf(2u, 1u) to Rational(-1571, 112), - listOf(3u, 1u) to Rational(107515, 224), - listOf(4u, 1u) to Rational(64965, 112), - listOf(5u, 1u) to Rational(209, 56), - listOf(6u, 1u) to Rational(45, 4), - listOf(0u, 2u) to Rational(112), - listOf(1u, 2u) to Rational(1449, 8), - listOf(2u, 2u) to Rational(1306309, 3136), - listOf(3u, 2u) to Rational(483207, 1568), - listOf(4u, 2u) to Rational(1978437, 6272), - listOf(5u, 2u) to Rational(-18231, 224), - listOf(6u, 2u) to Rational(-6835, 32), - listOf(0u, 3u) to Rational(247, 2), - listOf(1u, 3u) to Rational(33771, 112), - listOf(2u, 3u) to Rational(2073, 7), - listOf(3u, 3u) to Rational(-23463, 224), - listOf(4u, 3u) to Rational(-33825, 112), - listOf(5u, 3u) to Rational(201, 224), - listOf(6u, 3u) to Rational(-95, 16), - listOf(0u, 4u) to Rational(361, 16), - listOf(1u, 4u) to Rational(3667, 56), - listOf(2u, 4u) to Rational(88729, 1568), - listOf(3u, 4u) to Rational(-2476, 49), - listOf(4u, 4u) to Rational(-23419, 196), - listOf(5u, 4u) to Rational(-323, 56), - listOf(6u, 4u) to Rational(1805, 32), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 1 to NumberedPolynomialAsIs( - listOf() to Rational(-9, 2), - listOf(1u) to Rational(2, 7), - listOf(2u) to Rational(9, 1), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-1, 8), - listOf(2u, 1u) to Rational(2, 8), - listOf(0u, 2u) to Rational(19, 4), - listOf(1u, 2u) to Rational(15, 7), - listOf(2u, 2u) to Rational(-19, 4), - ), - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-11, 3), - listOf(1u) to Rational(5, 2), - listOf(2u) to Rational(13, 7), - listOf(0u, 1u) to Rational(16, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(6, 1), - listOf(0u, 2u) to Rational(-14, 3), - listOf(1u, 2u) to Rational(-2, 7), - listOf(2u, 2u) to Rational(-10, 8), - ) - )), - "test 4'" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = (0/6 + 14/8 s + -14/2 s^2) + (-3/5 + 11/1 s + 3/7 s^2) t + (-3/7 + -18/5 s + -9/1 s^2) t^2, y = t - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(7, 3), - listOf(2u) to Rational(-35, 16), - listOf(3u) to Rational(-343, 6), - listOf(4u) to Rational(343, 3), - listOf(0u, 1u) to Rational(-19, 5), - listOf(1u, 1u) to Rational(-823, 120), - listOf(2u, 1u) to Rational(1232417, 6720), - listOf(3u, 1u) to Rational(-9863, 24), - listOf(4u, 1u) to Rational(385, 4), - listOf(0u, 2u) to Rational(2439, 350), - listOf(1u, 2u) to Rational(-5793, 40), - listOf(2u, 2u) to Rational(1172113, 3360), - listOf(3u, 2u) to Rational(-13531, 40), - listOf(4u, 2u) to Rational(2824, 7), - listOf(0u, 3u) to Rational(3417, 700), - listOf(1u, 3u) to Rational(1191, 200), - listOf(2u, 3u) to Rational(8383, 28), - listOf(3u, 3u) to Rational(-220279, 280), - listOf(4u, 3u) to Rational(49179, 196), - listOf(0u, 4u) to Rational(57, 35), - listOf(1u, 4u) to Rational(-33771, 700), - listOf(2u, 4u) to Rational(196279, 1225), - listOf(3u, 4u) to Rational(-32259, 140), - listOf(4u, 4u) to Rational(23868, 49), - listOf(0u, 5u) to Rational(333, 196), - listOf(1u, 5u) to Rational(-204, 35), - listOf(2u, 5u) to Rational(-307233, 2450), - listOf(3u, 5u) to Rational(-12492, 35), - listOf(4u, 5u) to Rational(4563, 28), - listOf(0u, 6u) to Rational(45, 98), - listOf(1u, 6u) to Rational(54, 7), - listOf(2u, 6u) to Rational(1809, 35), - listOf(3u, 6u) to Rational(162), - listOf(4u, 6u) to Rational(405, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - )), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(7, 3), - listOf(2u) to Rational(-35, 16), - listOf(3u) to Rational(-343, 6), - listOf(4u) to Rational(343, 3), - listOf(0u, 1u) to Rational(-19, 5), - listOf(1u, 1u) to Rational(-823, 120), - listOf(2u, 1u) to Rational(1232417, 6720), - listOf(3u, 1u) to Rational(-9863, 24), - listOf(4u, 1u) to Rational(385, 4), - listOf(0u, 2u) to Rational(2439, 350), - listOf(1u, 2u) to Rational(-5793, 40), - listOf(2u, 2u) to Rational(1172113, 3360), - listOf(3u, 2u) to Rational(-13531, 40), - listOf(4u, 2u) to Rational(2824, 7), - listOf(0u, 3u) to Rational(3417, 700), - listOf(1u, 3u) to Rational(1191, 200), - listOf(2u, 3u) to Rational(8383, 28), - listOf(3u, 3u) to Rational(-220279, 280), - listOf(4u, 3u) to Rational(49179, 196), - listOf(0u, 4u) to Rational(57, 35), - listOf(1u, 4u) to Rational(-33771, 700), - listOf(2u, 4u) to Rational(196279, 1225), - listOf(3u, 4u) to Rational(-32259, 140), - listOf(4u, 4u) to Rational(23868, 49), - listOf(0u, 5u) to Rational(333, 196), - listOf(1u, 5u) to Rational(-204, 35), - listOf(2u, 5u) to Rational(-307233, 2450), - listOf(3u, 5u) to Rational(-12492, 35), - listOf(4u, 5u) to Rational(4563, 28), - listOf(0u, 6u) to Rational(45, 98), - listOf(1u, 6u) to Rational(54, 7), - listOf(2u, 6u) to Rational(1809, 35), - listOf(3u, 6u) to Rational(162), - listOf(4u, 6u) to Rational(405, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-11, 3), - listOf(1u) to Rational(5, 2), - listOf(2u) to Rational(13, 7), - listOf(0u, 1u) to Rational(16, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(6, 1), - listOf(0u, 2u) to Rational(-14, 3), - listOf(1u, 2u) to Rational(-2, 7), - listOf(2u, 2u) to Rational(-10, 8), - ) - )), - "test 5'" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, mapOf( - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-11, 3), - listOf(1u) to Rational(5, 2), - listOf(2u) to Rational(13, 7), - listOf(0u, 1u) to Rational(16, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(6, 1), - listOf(0u, 2u) to Rational(-14, 3), - listOf(1u, 2u) to Rational(-2, 7), - listOf(2u, 2u) to Rational(-10, 8), - ) - )), - "test 6'" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_Polynomial_substitute_RationalFunction_Map() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(4u) to Rational(-194071, 4900), - listOf(3u, 1u) to Rational(394811, 225), - listOf(2u, 2u) to Rational(-444183161, 66150), - listOf(1u, 3u) to Rational(70537618, 59535), - listOf(0u, 4u) to Rational(9655504, 2835), - ), - NumberedPolynomialAsIs( - listOf(4u) to Rational(9, 1), - listOf(3u, 1u) to Rational(61, 1), - listOf(2u, 2u) to Rational(2137, 36), - listOf(1u, 3u) to Rational(-1342, 9), - listOf(0u, 4u) to Rational(484, 9), - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(17, 7), - listOf(0u, 1u) to Rational(-13, 1), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(-18, 6), - listOf(0u, 1u) to Rational(11, 6), - ) - ), - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(18, 5), - listOf(0u, 1u) to Rational(-16, 3), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(-1, 1), - listOf(0u, 1u) to Rational(-4, 1), - ) - ), - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-6443599, 10000), - listOf(1u) to Rational(166251223, 210000), - listOf(2u) to Rational(-4606805099, 3528000), - listOf(3u) to Rational(51204379, 19600), - listOf(4u) to Rational(-529045460659, 277830000), - listOf(5u) to Rational(2630836709, 1488375), - listOf(6u) to Rational(-42675691369, 25004700), - listOf(7u) to Rational(495825223, 1250235), - listOf(8u) to Rational(-22531756, 1750329), - listOf(0u, 1u) to Rational(-2526552797, 420000), - listOf(1u, 1u) to Rational(31108840471, 2520000), - listOf(2u, 1u) to Rational(-4789740847, 1102500), - listOf(3u, 1u) to Rational(186594307807, 11340000), - listOf(4u, 1u) to Rational(-11677815943, 1488375), - listOf(5u, 1u) to Rational(-181118486447, 27783000), - listOf(6u, 1u) to Rational(-16123292162, 14586075), - listOf(7u, 1u) to Rational(-140339343808, 26254935), - listOf(8u, 1u) to Rational(4570171616, 5250987), - listOf(0u, 2u) to Rational(-181436530573, 10080000), - listOf(1u, 2u) to Rational(6700437957491, 105840000), - listOf(2u, 2u) to Rational(-3527267461, 1417500), - listOf(3u, 2u) to Rational(-38084563451, 5556600), - listOf(4u, 2u) to Rational(-565662040631, 13891500), - listOf(5u, 2u) to Rational(-35479071126397, 583443000), - listOf(6u, 2u) to Rational(-11717559078469, 525098700), - listOf(7u, 2u) to Rational(-2043385293517, 225042300), - listOf(8u, 2u) to Rational(-3644439630451, 551353635), - listOf(0u, 3u) to Rational(-1760423269, 126000), - listOf(1u, 3u) to Rational(310176758299, 2352000), - listOf(2u, 3u) to Rational(-907229584837, 21168000), - listOf(3u, 3u) to Rational(-16717135885963, 95256000), - listOf(4u, 3u) to Rational(-43762928025353, 333396000), - listOf(5u, 3u) to Rational(-328427480571607, 3000564000), - listOf(6u, 3u) to Rational(-7722675917197, 210039480), - listOf(7u, 3u) to Rational(1713350137019, 1225230300), - listOf(8u, 3u) to Rational(156695935643, 31505922), - listOf(0u, 4u) to Rational(18362364269, 1008000), - listOf(1u, 4u) to Rational(955674858553, 10584000), - listOf(2u, 4u) to Rational(-71937470607371, 444528000), - listOf(3u, 4u) to Rational(-34097985615163, 95256000), - listOf(4u, 4u) to Rational(-340736178775883, 2000376000), - listOf(5u, 4u) to Rational(-511324523441897, 10501974000), - listOf(6u, 4u) to Rational(-125375649409151, 8821658160), - listOf(7u, 4u) to Rational(-2813518533421, 1575296100), - listOf(8u, 4u) to Rational(-17044089109, 5250987), - listOf(0u, 5u) to Rational(600086461, 20160), - listOf(1u, 5u) to Rational(-18959931367, 423360), - listOf(2u, 5u) to Rational(-9178804929607, 44452800), - listOf(3u, 5u) to Rational(-1460114275979, 5334336), - listOf(4u, 5u) to Rational(-342533479090169, 4200789600), - listOf(5u, 5u) to Rational(20335453022963, 4200789600), - listOf(6u, 5u) to Rational(-21649775090197, 6301184400), - listOf(7u, 5u) to Rational(-197301716069, 131274675), - listOf(8u, 5u) to Rational(18711357470, 15752961), - listOf(0u, 6u) to Rational(621417991, 100800), - listOf(1u, 6u) to Rational(-159236792977, 2116800), - listOf(2u, 6u) to Rational(-6602528890883, 66679200), - listOf(3u, 6u) to Rational(-1086091664047, 19051200), - listOf(4u, 6u) to Rational(3769375009003, 1680315840), - listOf(5u, 6u) to Rational(-12920385574769, 1050197400), - listOf(6u, 6u) to Rational(-90219591809287, 6301184400), - listOf(7u, 6u) to Rational(656361553391, 1575296100), - listOf(8u, 6u) to Rational(757900793, 2250423), - listOf(0u, 7u) to Rational(-100770017, 15120), - listOf(1u, 7u) to Rational(-316364851, 17640), - listOf(2u, 7u) to Rational(-85118560057, 6667920), - listOf(3u, 7u) to Rational(6286563719, 416745), - listOf(4u, 7u) to Rational(26803885301, 1714608), - listOf(5u, 7u) to Rational(-13767154393, 4286520), - listOf(6u, 7u) to Rational(-3875138933, 1224720), - listOf(7u, 7u) to Rational(65193755, 333396), - listOf(8u, 7u) to Rational(90974351, 2500470), - listOf(0u, 8u) to Rational(-3182197, 1260), - listOf(1u, 8u) to Rational(24899923, 8820), - listOf(2u, 8u) to Rational(-19999556, 19845), - listOf(3u, 8u) to Rational(3276587, 3969), - listOf(4u, 8u) to Rational(13719549239, 5000940), - listOf(5u, 8u) to Rational(-961839938, 1250235), - listOf(6u, 8u) to Rational(-198184871, 833490), - listOf(7u, 8u) to Rational(230659711, 5000940), - listOf(8u, 8u) to Rational(292447, 35721) - ), - NumberedPolynomialAsIs( - listOf() to Rational(9, 100), - listOf(1u) to Rational(-21, 50), - listOf(2u) to Rational(293, 700), - listOf(3u) to Rational(29, 210), - listOf(4u) to Rational(3233, 8820), - listOf(5u) to Rational(-289, 441), - listOf(6u) to Rational(-1, 9), - listOf(7u) to Rational(-20, 441), - listOf(8u) to Rational(100, 441), - listOf(0u, 1u) to Rational(-57, 80), - listOf(1u, 1u) to Rational(-121, 400), - listOf(2u, 1u) to Rational(37117, 8400), - listOf(3u, 1u) to Rational(-4853, 3150), - listOf(4u, 1u) to Rational(1166203, 132300), - listOf(5u, 1u) to Rational(-2708, 567), - listOf(6u, 1u) to Rational(-287159, 416745), - listOf(7u, 1u) to Rational(-478204, 83349), - listOf(8u, 1u) to Rational(176320, 83349), - listOf(0u, 2u) to Rational(-6239, 6400), - listOf(1u, 2u) to Rational(264211, 11200), - listOf(2u, 2u) to Rational(-1591999, 100800), - listOf(3u, 2u) to Rational(12450091, 529200), - listOf(4u, 2u) to Rational(9230759, 226800), - listOf(5u, 2u) to Rational(18995554, 2083725), - listOf(6u, 2u) to Rational(136706258, 6251175), - listOf(7u, 2u) to Rational(-120907496, 3750705), - listOf(8u, 2u) to Rational(117200176, 15752961), - listOf(0u, 3u) to Rational(5653, 320), - listOf(1u, 3u) to Rational(-130853, 8400), - listOf(2u, 3u) to Rational(-20939327, 151200), - listOf(3u, 3u) to Rational(2566691, 25200), - listOf(4u, 3u) to Rational(-68441519, 476280), - listOf(5u, 3u) to Rational(2462904247, 12502350), - listOf(6u, 3u) to Rational(353667161, 18753525), - listOf(7u, 3u) to Rational(-1689134372, 26254935), - listOf(8u, 3u) to Rational(35084104, 2250423), - listOf(0u, 4u) to Rational(-3587, 300), - listOf(1u, 4u) to Rational(-10513243, 33600), - listOf(2u, 4u) to Rational(30766733, 176400), - listOf(3u, 4u) to Rational(-65680021, 198450), - listOf(4u, 4u) to Rational(-8108910547, 20003760), - listOf(5u, 4u) to Rational(2922125159, 6251175), - listOf(6u, 4u) to Rational(-4245279943, 131274675), - listOf(7u, 4u) to Rational(-371946872, 3750705), - listOf(8u, 4u) to Rational(61286752, 2250423), - listOf(0u, 5u) to Rational(-20477, 160), - listOf(1u, 5u) to Rational(215741, 1120), - listOf(2u, 5u) to Rational(30785843, 31752), - listOf(3u, 5u) to Rational(-357495959, 317520), - listOf(4u, 5u) to Rational(-1611242993, 10001880), - listOf(5u, 5u) to Rational(345925495, 500094), - listOf(6u, 5u) to Rational(-755948411, 3750705), - listOf(7u, 5u) to Rational(-108643496, 1250235), - listOf(8u, 5u) to Rational(1122512, 35721), - listOf(0u, 6u) to Rational(358037, 2880), - listOf(1u, 6u) to Rational(3895837, 3360), - listOf(2u, 6u) to Rational(359419201, 1270080), - listOf(3u, 6u) to Rational(-158522587, 105840), - listOf(4u, 6u) to Rational(10909002599, 20003760), - listOf(5u, 6u) to Rational(76846972, 138915), - listOf(6u, 6u) to Rational(-327696553, 1250235), - listOf(7u, 6u) to Rational(-1687328, 35721), - listOf(8u, 6u) to Rational(1016836, 35721), - listOf(0u, 7u) to Rational(658, 3), - listOf(1u, 7u) to Rational(48035, 168), - listOf(2u, 7u) to Rational(-5777875, 5292), - listOf(3u, 7u) to Rational(-7893899, 10584), - listOf(4u, 7u) to Rational(10191652, 11907), - listOf(5u, 7u) to Rational(2920121, 23814), - listOf(6u, 7u) to Rational(-2699780, 11907), - listOf(7u, 7u) to Rational(4556, 441), - listOf(8u, 7u) to Rational(3440, 189), - listOf(0u, 8u) to Rational(64, 1), - listOf(1u, 8u) to Rational(-808, 7), - listOf(2u, 8u) to Rational(-360895, 1764), - listOf(3u, 8u) to Rational(257657, 882), - listOf(4u, 8u) to Rational(3779917, 15876), - listOf(5u, 8u) to Rational(-610279, 3969), - listOf(6u, 8u) to Rational(-25091, 441), - listOf(7u, 8u) to Rational(9560, 567), - listOf(8u, 8u) to Rational(400, 81) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(18, 5), - listOf(1u) to Rational(-17, 5), - listOf(2u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(-5, 1), - listOf(2u, 1u) to Rational(-9, 1), - listOf(0u, 2u) to Rational(-8, 8), - listOf(1u, 2u) to Rational(2, 7), - listOf(2u, 2u) to Rational(-13, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-4, 8), - listOf(1u) to Rational(15, 9), - listOf(2u) to Rational(-10, 9), - listOf(0u, 1u) to Rational(5, 3), - listOf(1u, 1u) to Rational(4, 1), - listOf(2u, 1u) to Rational(-2, 7), - listOf(0u, 2u) to Rational(2, 2), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(-18, 9), - ) - ), - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-6443599, 10000), - listOf(1u) to Rational(166251223, 210000), - listOf(2u) to Rational(-4606805099, 3528000), - listOf(3u) to Rational(51204379, 19600), - listOf(4u) to Rational(-529045460659, 277830000), - listOf(5u) to Rational(2630836709, 1488375), - listOf(6u) to Rational(-42675691369, 25004700), - listOf(7u) to Rational(495825223, 1250235), - listOf(8u) to Rational(-22531756, 1750329), - listOf(0u, 1u) to Rational(-2526552797, 420000), - listOf(1u, 1u) to Rational(31108840471, 2520000), - listOf(2u, 1u) to Rational(-4789740847, 1102500), - listOf(3u, 1u) to Rational(186594307807, 11340000), - listOf(4u, 1u) to Rational(-11677815943, 1488375), - listOf(5u, 1u) to Rational(-181118486447, 27783000), - listOf(6u, 1u) to Rational(-16123292162, 14586075), - listOf(7u, 1u) to Rational(-140339343808, 26254935), - listOf(8u, 1u) to Rational(4570171616, 5250987), - listOf(0u, 2u) to Rational(-181436530573, 10080000), - listOf(1u, 2u) to Rational(6700437957491, 105840000), - listOf(2u, 2u) to Rational(-3527267461, 1417500), - listOf(3u, 2u) to Rational(-38084563451, 5556600), - listOf(4u, 2u) to Rational(-565662040631, 13891500), - listOf(5u, 2u) to Rational(-35479071126397, 583443000), - listOf(6u, 2u) to Rational(-11717559078469, 525098700), - listOf(7u, 2u) to Rational(-2043385293517, 225042300), - listOf(8u, 2u) to Rational(-3644439630451, 551353635), - listOf(0u, 3u) to Rational(-1760423269, 126000), - listOf(1u, 3u) to Rational(310176758299, 2352000), - listOf(2u, 3u) to Rational(-907229584837, 21168000), - listOf(3u, 3u) to Rational(-16717135885963, 95256000), - listOf(4u, 3u) to Rational(-43762928025353, 333396000), - listOf(5u, 3u) to Rational(-328427480571607, 3000564000), - listOf(6u, 3u) to Rational(-7722675917197, 210039480), - listOf(7u, 3u) to Rational(1713350137019, 1225230300), - listOf(8u, 3u) to Rational(156695935643, 31505922), - listOf(0u, 4u) to Rational(18362364269, 1008000), - listOf(1u, 4u) to Rational(955674858553, 10584000), - listOf(2u, 4u) to Rational(-71937470607371, 444528000), - listOf(3u, 4u) to Rational(-34097985615163, 95256000), - listOf(4u, 4u) to Rational(-340736178775883, 2000376000), - listOf(5u, 4u) to Rational(-511324523441897, 10501974000), - listOf(6u, 4u) to Rational(-125375649409151, 8821658160), - listOf(7u, 4u) to Rational(-2813518533421, 1575296100), - listOf(8u, 4u) to Rational(-17044089109, 5250987), - listOf(0u, 5u) to Rational(600086461, 20160), - listOf(1u, 5u) to Rational(-18959931367, 423360), - listOf(2u, 5u) to Rational(-9178804929607, 44452800), - listOf(3u, 5u) to Rational(-1460114275979, 5334336), - listOf(4u, 5u) to Rational(-342533479090169, 4200789600), - listOf(5u, 5u) to Rational(20335453022963, 4200789600), - listOf(6u, 5u) to Rational(-21649775090197, 6301184400), - listOf(7u, 5u) to Rational(-197301716069, 131274675), - listOf(8u, 5u) to Rational(18711357470, 15752961), - listOf(0u, 6u) to Rational(621417991, 100800), - listOf(1u, 6u) to Rational(-159236792977, 2116800), - listOf(2u, 6u) to Rational(-6602528890883, 66679200), - listOf(3u, 6u) to Rational(-1086091664047, 19051200), - listOf(4u, 6u) to Rational(3769375009003, 1680315840), - listOf(5u, 6u) to Rational(-12920385574769, 1050197400), - listOf(6u, 6u) to Rational(-90219591809287, 6301184400), - listOf(7u, 6u) to Rational(656361553391, 1575296100), - listOf(8u, 6u) to Rational(757900793, 2250423), - listOf(0u, 7u) to Rational(-100770017, 15120), - listOf(1u, 7u) to Rational(-316364851, 17640), - listOf(2u, 7u) to Rational(-85118560057, 6667920), - listOf(3u, 7u) to Rational(6286563719, 416745), - listOf(4u, 7u) to Rational(26803885301, 1714608), - listOf(5u, 7u) to Rational(-13767154393, 4286520), - listOf(6u, 7u) to Rational(-3875138933, 1224720), - listOf(7u, 7u) to Rational(65193755, 333396), - listOf(8u, 7u) to Rational(90974351, 2500470), - listOf(0u, 8u) to Rational(-3182197, 1260), - listOf(1u, 8u) to Rational(24899923, 8820), - listOf(2u, 8u) to Rational(-19999556, 19845), - listOf(3u, 8u) to Rational(3276587, 3969), - listOf(4u, 8u) to Rational(13719549239, 5000940), - listOf(5u, 8u) to Rational(-961839938, 1250235), - listOf(6u, 8u) to Rational(-198184871, 833490), - listOf(7u, 8u) to Rational(230659711, 5000940), - listOf(8u, 8u) to Rational(292447, 35721) - ), - NumberedPolynomialAsIs( - listOf() to Rational(9, 100), - listOf(1u) to Rational(-21, 50), - listOf(2u) to Rational(293, 700), - listOf(3u) to Rational(29, 210), - listOf(4u) to Rational(3233, 8820), - listOf(5u) to Rational(-289, 441), - listOf(6u) to Rational(-1, 9), - listOf(7u) to Rational(-20, 441), - listOf(8u) to Rational(100, 441), - listOf(0u, 1u) to Rational(-57, 80), - listOf(1u, 1u) to Rational(-121, 400), - listOf(2u, 1u) to Rational(37117, 8400), - listOf(3u, 1u) to Rational(-4853, 3150), - listOf(4u, 1u) to Rational(1166203, 132300), - listOf(5u, 1u) to Rational(-2708, 567), - listOf(6u, 1u) to Rational(-287159, 416745), - listOf(7u, 1u) to Rational(-478204, 83349), - listOf(8u, 1u) to Rational(176320, 83349), - listOf(0u, 2u) to Rational(-6239, 6400), - listOf(1u, 2u) to Rational(264211, 11200), - listOf(2u, 2u) to Rational(-1591999, 100800), - listOf(3u, 2u) to Rational(12450091, 529200), - listOf(4u, 2u) to Rational(9230759, 226800), - listOf(5u, 2u) to Rational(18995554, 2083725), - listOf(6u, 2u) to Rational(136706258, 6251175), - listOf(7u, 2u) to Rational(-120907496, 3750705), - listOf(8u, 2u) to Rational(117200176, 15752961), - listOf(0u, 3u) to Rational(5653, 320), - listOf(1u, 3u) to Rational(-130853, 8400), - listOf(2u, 3u) to Rational(-20939327, 151200), - listOf(3u, 3u) to Rational(2566691, 25200), - listOf(4u, 3u) to Rational(-68441519, 476280), - listOf(5u, 3u) to Rational(2462904247, 12502350), - listOf(6u, 3u) to Rational(353667161, 18753525), - listOf(7u, 3u) to Rational(-1689134372, 26254935), - listOf(8u, 3u) to Rational(35084104, 2250423), - listOf(0u, 4u) to Rational(-3587, 300), - listOf(1u, 4u) to Rational(-10513243, 33600), - listOf(2u, 4u) to Rational(30766733, 176400), - listOf(3u, 4u) to Rational(-65680021, 198450), - listOf(4u, 4u) to Rational(-8108910547, 20003760), - listOf(5u, 4u) to Rational(2922125159, 6251175), - listOf(6u, 4u) to Rational(-4245279943, 131274675), - listOf(7u, 4u) to Rational(-371946872, 3750705), - listOf(8u, 4u) to Rational(61286752, 2250423), - listOf(0u, 5u) to Rational(-20477, 160), - listOf(1u, 5u) to Rational(215741, 1120), - listOf(2u, 5u) to Rational(30785843, 31752), - listOf(3u, 5u) to Rational(-357495959, 317520), - listOf(4u, 5u) to Rational(-1611242993, 10001880), - listOf(5u, 5u) to Rational(345925495, 500094), - listOf(6u, 5u) to Rational(-755948411, 3750705), - listOf(7u, 5u) to Rational(-108643496, 1250235), - listOf(8u, 5u) to Rational(1122512, 35721), - listOf(0u, 6u) to Rational(358037, 2880), - listOf(1u, 6u) to Rational(3895837, 3360), - listOf(2u, 6u) to Rational(359419201, 1270080), - listOf(3u, 6u) to Rational(-158522587, 105840), - listOf(4u, 6u) to Rational(10909002599, 20003760), - listOf(5u, 6u) to Rational(76846972, 138915), - listOf(6u, 6u) to Rational(-327696553, 1250235), - listOf(7u, 6u) to Rational(-1687328, 35721), - listOf(8u, 6u) to Rational(1016836, 35721), - listOf(0u, 7u) to Rational(658, 3), - listOf(1u, 7u) to Rational(48035, 168), - listOf(2u, 7u) to Rational(-5777875, 5292), - listOf(3u, 7u) to Rational(-7893899, 10584), - listOf(4u, 7u) to Rational(10191652, 11907), - listOf(5u, 7u) to Rational(2920121, 23814), - listOf(6u, 7u) to Rational(-2699780, 11907), - listOf(7u, 7u) to Rational(4556, 441), - listOf(8u, 7u) to Rational(3440, 189), - listOf(0u, 8u) to Rational(64, 1), - listOf(1u, 8u) to Rational(-808, 7), - listOf(2u, 8u) to Rational(-360895, 1764), - listOf(3u, 8u) to Rational(257657, 882), - listOf(4u, 8u) to Rational(3779917, 15876), - listOf(5u, 8u) to Rational(-610279, 3969), - listOf(6u, 8u) to Rational(-25091, 441), - listOf(7u, 8u) to Rational(9560, 567), - listOf(8u, 8u) to Rational(400, 81) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(18, 5), - listOf(1u) to Rational(-17, 5), - listOf(2u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(-5, 1), - listOf(2u, 1u) to Rational(-9, 1), - listOf(0u, 2u) to Rational(-8, 8), - listOf(1u, 2u) to Rational(2, 7), - listOf(2u, 2u) to Rational(-13, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-4, 8), - listOf(1u) to Rational(15, 9), - listOf(2u) to Rational(-10, 9), - listOf(0u, 1u) to Rational(5, 3), - listOf(1u, 1u) to Rational(4, 1), - listOf(2u, 1u) to Rational(-2, 7), - listOf(0u, 2u) to Rational(2, 2), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(-18, 9), - ) - ), - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 9), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(10, 9), - listOf(0u, 1u) to Rational(13, 3), - listOf(1u, 1u) to Rational(-12, 4), - listOf(2u, 1u) to Rational(3, 6), - listOf(0u, 2u) to Rational(2, 9), - listOf(1u, 2u) to Rational(7, 3), - listOf(2u, 2u) to Rational(16, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 2), - listOf(1u) to Rational(6, 2), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 1), - listOf(1u, 1u) to Rational(-11, 3), - listOf(2u, 1u) to Rational(7, 5), - listOf(0u, 2u) to Rational(8, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(17, 4), - ) - ) - )), - "test 3'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-66677, 3500), - listOf(1u) to Rational(-206281, 10500), - listOf(2u) to Rational(-412567, 7056), - listOf(3u) to Rational(-310081, 11025), - listOf(4u) to Rational(-575996, 15435), - listOf(0u, 1u) to Rational(-573701, 4200), - listOf(1u, 1u) to Rational(-2239001, 25200), - listOf(2u, 1u) to Rational(-8817889, 132300), - listOf(3u, 1u) to Rational(2317919, 44100), - listOf(4u, 1u) to Rational(1169471, 6615), - listOf(0u, 2u) to Rational(-4057819, 33600), - listOf(1u, 2u) to Rational(1373311, 12600), - listOf(2u, 2u) to Rational(32433493, 52920), - listOf(3u, 2u) to Rational(4998053, 33075), - listOf(4u, 2u) to Rational(-2147779, 8820), - listOf(0u, 3u) to Rational(2018481, 2240), - listOf(1u, 3u) to Rational(941713, 1440), - listOf(2u, 3u) to Rational(183749, 6615), - listOf(3u, 3u) to Rational(-4631023, 15876), - listOf(4u, 3u) to Rational(25609336, 178605), - listOf(0u, 4u) to Rational(11886431, 6720), - listOf(1u, 4u) to Rational(18433, 504), - listOf(2u, 4u) to Rational(-39613331, 45360), - listOf(3u, 4u) to Rational(681619, 5670), - listOf(4u, 4u) to Rational(-864841, 20412), - listOf(0u, 5u) to Rational(343535, 1008), - listOf(1u, 5u) to Rational(-33583, 72), - listOf(2u, 5u) to Rational(1194625, 9072), - listOf(3u, 5u) to Rational(-62917, 2268), - listOf(4u, 5u) to Rational(157645, 10206), - listOf(0u, 6u) to Rational(-1381, 3), - listOf(1u, 6u) to Rational(919, 36), - listOf(2u, 6u) to Rational(-3053, 36), - listOf(3u, 6u) to Rational(2125, 324), - listOf(4u, 6u) to Rational(-236, 243) - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(1, 4), - listOf(1u) to Rational(-5, 3), - listOf(2u) to Rational(35, 9), - listOf(3u) to Rational(-100, 27), - listOf(4u) to Rational(100, 81), - listOf(0u, 1u) to Rational(-5, 3), - listOf(1u, 1u) to Rational(14, 9), - listOf(2u, 1u) to Rational(1874, 189), - listOf(3u, 1u) to Rational(-620, 63), - listOf(4u, 1u) to Rational(40, 63), - listOf(0u, 2u) to Rational(16, 9), - listOf(1u, 2u) to Rational(365, 21), - listOf(2u, 2u) to Rational(112, 9), - listOf(3u, 2u) to Rational(-464, 63), - listOf(4u, 2u) to Rational(1996, 441), - listOf(0u, 3u) to Rational(10, 3), - listOf(1u, 3u) to Rational(118, 21), - listOf(2u, 3u) to Rational(-272, 21), - listOf(3u, 3u) to Rational(-764, 49), - listOf(4u, 3u) to Rational(8, 7), - listOf(0u, 4u) to Rational(1, 1), - listOf(1u, 4u) to Rational(-10, 7), - listOf(2u, 4u) to Rational(-171, 49), - listOf(3u, 4u) to Rational(20, 7), - listOf(4u, 4u) to Rational(4, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-66677, 3500), - listOf(1u) to Rational(-206281, 10500), - listOf(2u) to Rational(-412567, 7056), - listOf(3u) to Rational(-310081, 11025), - listOf(4u) to Rational(-575996, 15435), - listOf(0u, 1u) to Rational(-573701, 4200), - listOf(1u, 1u) to Rational(-2239001, 25200), - listOf(2u, 1u) to Rational(-8817889, 132300), - listOf(3u, 1u) to Rational(2317919, 44100), - listOf(4u, 1u) to Rational(1169471, 6615), - listOf(0u, 2u) to Rational(-4057819, 33600), - listOf(1u, 2u) to Rational(1373311, 12600), - listOf(2u, 2u) to Rational(32433493, 52920), - listOf(3u, 2u) to Rational(4998053, 33075), - listOf(4u, 2u) to Rational(-2147779, 8820), - listOf(0u, 3u) to Rational(2018481, 2240), - listOf(1u, 3u) to Rational(941713, 1440), - listOf(2u, 3u) to Rational(183749, 6615), - listOf(3u, 3u) to Rational(-4631023, 15876), - listOf(4u, 3u) to Rational(25609336, 178605), - listOf(0u, 4u) to Rational(11886431, 6720), - listOf(1u, 4u) to Rational(18433, 504), - listOf(2u, 4u) to Rational(-39613331, 45360), - listOf(3u, 4u) to Rational(681619, 5670), - listOf(4u, 4u) to Rational(-864841, 20412), - listOf(0u, 5u) to Rational(343535, 1008), - listOf(1u, 5u) to Rational(-33583, 72), - listOf(2u, 5u) to Rational(1194625, 9072), - listOf(3u, 5u) to Rational(-62917, 2268), - listOf(4u, 5u) to Rational(157645, 10206), - listOf(0u, 6u) to Rational(-1381, 3), - listOf(1u, 6u) to Rational(919, 36), - listOf(2u, 6u) to Rational(-3053, 36), - listOf(3u, 6u) to Rational(2125, 324), - listOf(4u, 6u) to Rational(-236, 243) - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(1, 4), - listOf(1u) to Rational(-5, 3), - listOf(2u) to Rational(35, 9), - listOf(3u) to Rational(-100, 27), - listOf(4u) to Rational(100, 81), - listOf(0u, 1u) to Rational(-5, 3), - listOf(1u, 1u) to Rational(14, 9), - listOf(2u, 1u) to Rational(1874, 189), - listOf(3u, 1u) to Rational(-620, 63), - listOf(4u, 1u) to Rational(40, 63), - listOf(0u, 2u) to Rational(16, 9), - listOf(1u, 2u) to Rational(365, 21), - listOf(2u, 2u) to Rational(112, 9), - listOf(3u, 2u) to Rational(-464, 63), - listOf(4u, 2u) to Rational(1996, 441), - listOf(0u, 3u) to Rational(10, 3), - listOf(1u, 3u) to Rational(118, 21), - listOf(2u, 3u) to Rational(-272, 21), - listOf(3u, 3u) to Rational(-764, 49), - listOf(4u, 3u) to Rational(8, 7), - listOf(0u, 4u) to Rational(1, 1), - listOf(1u, 4u) to Rational(-10, 7), - listOf(2u, 4u) to Rational(-171, 49), - listOf(3u, 4u) to Rational(20, 7), - listOf(4u, 4u) to Rational(4, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 9), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(10, 9), - listOf(0u, 1u) to Rational(13, 3), - listOf(1u, 1u) to Rational(-12, 4), - listOf(2u, 1u) to Rational(3, 6), - listOf(0u, 2u) to Rational(2, 9), - listOf(1u, 2u) to Rational(7, 3), - listOf(2u, 2u) to Rational(16, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 2), - listOf(1u) to Rational(6, 2), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 1), - listOf(1u, 1u) to Rational(-11, 3), - listOf(2u, 1u) to Rational(7, 5), - listOf(0u, 2u) to Rational(8, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(17, 4), - ) - ) - )), - "test 4'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(3539, 700), - listOf(1u) to Rational(-307079, 6300), - listOf(2u) to Rational(451609, 15120), - listOf(3u) to Rational(35287733, 396900), - listOf(4u) to Rational(-37242617, 396900), - listOf(5u) to Rational(382747, 19845), - listOf(6u) to Rational(-2407, 3969), - listOf(0u, 1u) to Rational(-226, 175), - listOf(1u, 1u) to Rational(-74113, 1890), - listOf(2u, 1u) to Rational(250931, 1764), - listOf(3u, 1u) to Rational(30071473, 99225), - listOf(4u, 1u) to Rational(-286466, 1323), - listOf(5u, 1u) to Rational(-2285282, 9261), - listOf(6u, 1u) to Rational(17900, 441), - listOf(0u, 2u) to Rational(3817, 3150), - listOf(1u, 2u) to Rational(577568, 11025), - listOf(2u, 2u) to Rational(9073553, 99225), - listOf(3u, 2u) to Rational(-1415849, 79380), - listOf(4u, 2u) to Rational(-124715629, 277830), - listOf(5u, 2u) to Rational(-1328953, 1890), - listOf(6u, 2u) to Rational(-297148, 1323), - listOf(0u, 3u) to Rational(6043, 945), - listOf(1u, 3u) to Rational(160381, 6615), - listOf(2u, 3u) to Rational(-673249, 13230), - listOf(3u, 3u) to Rational(-319255, 2058), - listOf(4u, 3u) to Rational(-98144, 1029), - listOf(5u, 3u) to Rational(-320239, 5145), - listOf(6u, 3u) to Rational(400, 147), - listOf(0u, 4u) to Rational(163, 63), - listOf(1u, 4u) to Rational(-25183, 4410), - listOf(2u, 4u) to Rational(-21369, 1372), - listOf(3u, 4u) to Rational(127499, 30870), - listOf(4u, 4u) to Rational(86971, 12348), - listOf(5u, 4u) to Rational(-11129, 1470), - listOf(6u, 4u) to Rational(544, 147) - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(1, 4), - listOf(1u) to Rational(-5, 3), - listOf(2u) to Rational(35, 9), - listOf(3u) to Rational(-100, 27), - listOf(4u) to Rational(100, 81), - listOf(0u, 1u) to Rational(-5, 3), - listOf(1u, 1u) to Rational(14, 9), - listOf(2u, 1u) to Rational(1874, 189), - listOf(3u, 1u) to Rational(-620, 63), - listOf(4u, 1u) to Rational(40, 63), - listOf(0u, 2u) to Rational(16, 9), - listOf(1u, 2u) to Rational(365, 21), - listOf(2u, 2u) to Rational(112, 9), - listOf(3u, 2u) to Rational(-464, 63), - listOf(4u, 2u) to Rational(1996, 441), - listOf(0u, 3u) to Rational(10, 3), - listOf(1u, 3u) to Rational(118, 21), - listOf(2u, 3u) to Rational(-272, 21), - listOf(3u, 3u) to Rational(-764, 49), - listOf(4u, 3u) to Rational(8, 7), - listOf(0u, 4u) to Rational(1, 1), - listOf(1u, 4u) to Rational(-10, 7), - listOf(2u, 4u) to Rational(-171, 49), - listOf(3u, 4u) to Rational(20, 7), - listOf(4u, 4u) to Rational(4, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(18, 5), - listOf(1u) to Rational(-17, 5), - listOf(2u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(-5, 1), - listOf(2u, 1u) to Rational(-9, 1), - listOf(0u, 2u) to Rational(-8, 8), - listOf(1u, 2u) to Rational(2, 7), - listOf(2u, 2u) to Rational(-13, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-4, 8), - listOf(1u) to Rational(15, 9), - listOf(2u) to Rational(-10, 9), - listOf(0u, 1u) to Rational(5, 3), - listOf(1u, 1u) to Rational(4, 1), - listOf(2u, 1u) to Rational(-2, 7), - listOf(0u, 2u) to Rational(2, 2), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(-18, 9), - ) - ), - )), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(3539, 700), - listOf(1u) to Rational(-307079, 6300), - listOf(2u) to Rational(451609, 15120), - listOf(3u) to Rational(35287733, 396900), - listOf(4u) to Rational(-37242617, 396900), - listOf(5u) to Rational(382747, 19845), - listOf(6u) to Rational(-2407, 3969), - listOf(0u, 1u) to Rational(-226, 175), - listOf(1u, 1u) to Rational(-74113, 1890), - listOf(2u, 1u) to Rational(250931, 1764), - listOf(3u, 1u) to Rational(30071473, 99225), - listOf(4u, 1u) to Rational(-286466, 1323), - listOf(5u, 1u) to Rational(-2285282, 9261), - listOf(6u, 1u) to Rational(17900, 441), - listOf(0u, 2u) to Rational(3817, 3150), - listOf(1u, 2u) to Rational(577568, 11025), - listOf(2u, 2u) to Rational(9073553, 99225), - listOf(3u, 2u) to Rational(-1415849, 79380), - listOf(4u, 2u) to Rational(-124715629, 277830), - listOf(5u, 2u) to Rational(-1328953, 1890), - listOf(6u, 2u) to Rational(-297148, 1323), - listOf(0u, 3u) to Rational(6043, 945), - listOf(1u, 3u) to Rational(160381, 6615), - listOf(2u, 3u) to Rational(-673249, 13230), - listOf(3u, 3u) to Rational(-319255, 2058), - listOf(4u, 3u) to Rational(-98144, 1029), - listOf(5u, 3u) to Rational(-320239, 5145), - listOf(6u, 3u) to Rational(400, 147), - listOf(0u, 4u) to Rational(163, 63), - listOf(1u, 4u) to Rational(-25183, 4410), - listOf(2u, 4u) to Rational(-21369, 1372), - listOf(3u, 4u) to Rational(127499, 30870), - listOf(4u, 4u) to Rational(86971, 12348), - listOf(5u, 4u) to Rational(-11129, 1470), - listOf(6u, 4u) to Rational(544, 147) - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(1, 4), - listOf(1u) to Rational(-5, 3), - listOf(2u) to Rational(35, 9), - listOf(3u) to Rational(-100, 27), - listOf(4u) to Rational(100, 81), - listOf(0u, 1u) to Rational(-5, 3), - listOf(1u, 1u) to Rational(14, 9), - listOf(2u, 1u) to Rational(1874, 189), - listOf(3u, 1u) to Rational(-620, 63), - listOf(4u, 1u) to Rational(40, 63), - listOf(0u, 2u) to Rational(16, 9), - listOf(1u, 2u) to Rational(365, 21), - listOf(2u, 2u) to Rational(112, 9), - listOf(3u, 2u) to Rational(-464, 63), - listOf(4u, 2u) to Rational(1996, 441), - listOf(0u, 3u) to Rational(10, 3), - listOf(1u, 3u) to Rational(118, 21), - listOf(2u, 3u) to Rational(-272, 21), - listOf(3u, 3u) to Rational(-764, 49), - listOf(4u, 3u) to Rational(8, 7), - listOf(0u, 4u) to Rational(1, 1), - listOf(1u, 4u) to Rational(-10, 7), - listOf(2u, 4u) to Rational(-171, 49), - listOf(3u, 4u) to Rational(20, 7), - listOf(4u, 4u) to Rational(4, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(18, 5), - listOf(1u) to Rational(-17, 5), - listOf(2u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(-5, 1), - listOf(2u, 1u) to Rational(-9, 1), - listOf(0u, 2u) to Rational(-8, 8), - listOf(1u, 2u) to Rational(2, 7), - listOf(2u, 2u) to Rational(-13, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-4, 8), - listOf(1u) to Rational(15, 9), - listOf(2u) to Rational(-10, 9), - listOf(0u, 1u) to Rational(5, 3), - listOf(1u, 1u) to Rational(4, 1), - listOf(2u, 1u) to Rational(-2, 7), - listOf(0u, 2u) to Rational(2, 2), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(-18, 9), - ) - ), - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 9), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(10, 9), - listOf(0u, 1u) to Rational(13, 3), - listOf(1u, 1u) to Rational(-12, 4), - listOf(2u, 1u) to Rational(3, 6), - listOf(0u, 2u) to Rational(2, 9), - listOf(1u, 2u) to Rational(7, 3), - listOf(2u, 2u) to Rational(16, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 2), - listOf(1u) to Rational(6, 2), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 1), - listOf(1u, 1u) to Rational(-11, 3), - listOf(2u, 1u) to Rational(7, 5), - listOf(0u, 2u) to Rational(8, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(17, 4), - ) - ) - )), - "test 5'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(0, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(0, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, mapOf( - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 9), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(10, 9), - listOf(0u, 1u) to Rational(13, 3), - listOf(1u, 1u) to Rational(-12, 4), - listOf(2u, 1u) to Rational(3, 6), - listOf(0u, 2u) to Rational(2, 9), - listOf(1u, 2u) to Rational(7, 3), - listOf(2u, 2u) to Rational(16, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 2), - listOf(1u) to Rational(6, 2), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 1), - listOf(1u, 1u) to Rational(-11, 3), - listOf(2u, 1u) to Rational(7, 5), - listOf(0u, 2u) to Rational(8, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(17, 4), - ) - ) - )), - "test 6'" - ) - } - @Test - fun test_RationalFunction_substitute_Double_Map() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs(emptyList() to 0.0), - NumberedPolynomialAsIs(emptyList() to 1.0), - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 1.0, - listOf(1u) to -2.0, - listOf(2u) to 1.0, - ), - NumberedPolynomialAsIs( - listOf() to 1.0, - ) - ).substitute(mapOf( - 0 to 1.0 - )), - 0.001, - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf()), - 0.001, - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 5 to 0.9211194782050933 - )), - 0.001, - "test 2'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 151.1502229133916, - listOf(0u, 1u) to -262.3790170577034, - listOf(0u, 2u) to 102.5097937392923, - ), - NumberedPolynomialAsIs( - listOf() to -367.9969733169944, - listOf(0u, 1u) to 112.4911133334554, - listOf(0u, 2u) to -469.755906895345, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 0 to -8.11707689492641, - )), - 0.001, - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 151.1502229133916, - listOf(0u, 1u) to -262.3790170577034, - listOf(0u, 2u) to 102.5097937392923, - ), - NumberedPolynomialAsIs( - listOf() to -367.9969733169944, - listOf(0u, 1u) to 112.4911133334554, - listOf(0u, 2u) to -469.755906895345, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 0 to -8.11707689492641, - 5 to 0.9211194782050933 - )), - 0.001, - "test 3'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 14.24074356896978, - listOf(1u) to -17.71987055153461, - listOf(2u) to -2.288056483312383, - ), - NumberedPolynomialAsIs( - listOf() to 7.480604285873397, - listOf(1u) to -8.43478016688617, - listOf(2u) to -9.88934943900592, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 1 to 0.795265651276015, - )), - 0.001, - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 14.24074356896978, - listOf(1u) to -17.71987055153461, - listOf(2u) to -2.288056483312383, - ), - NumberedPolynomialAsIs( - listOf() to 7.480604285873397, - listOf(1u) to -8.43478016688617, - listOf(2u) to -9.88934943900592, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 1 to 0.795265651276015, - 5 to 0.9211194782050933 - )), - 0.001, - "test 4'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 7.321261307532708, - ), - NumberedPolynomialAsIs( - listOf() to -575.6325831127576, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 0 to -8.11707689492641, - 1 to 0.795265651276015, - )), - 0.001, - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 7.321261307532708, - ), - NumberedPolynomialAsIs( - listOf() to -575.6325831127576, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(mapOf( - 0 to -8.11707689492641, - 1 to 0.795265651276015, - 5 to 0.9211194782050933 - )), - 0.001, - "test 5'" - ) - } - @Test - fun test_RationalFunction_substitute_Constant_Map() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ).substitute(RationalField, mapOf( - 0 to Rational(1) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(22047, 2450), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2204953, 147000), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 0 to Rational(7, 5), - 1 to Rational(-13, 7), - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(22047, 2450), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2204953, 147000), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 0 to Rational(7, 5), - 1 to Rational(-13, 7), - 5 to Rational(-16, 4), - )), - "test 2'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(4191, 490), - listOf(1u) to Rational(14975, 1176), - listOf(2u) to Rational(-10429, 1176) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-775, 147), - listOf(1u) to Rational(-155, 49), - listOf(2u) to Rational(-757, 280) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 1 to Rational(-13, 7), - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(4191, 490), - listOf(1u) to Rational(14975, 1176), - listOf(2u) to Rational(-10429, 1176) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-775, 147), - listOf(1u) to Rational(-155, 49), - listOf(2u) to Rational(-757, 280) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 1 to Rational(-13, 7), - 5 to Rational(-16, 4), - )), - "test 3'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-939, 200), - listOf(0u, 1u) to Rational(123, 50), - listOf(0u, 2u) to Rational(1059, 200) - ), - NumberedPolynomialAsIs( - listOf() to Rational(121, 25), - listOf(0u, 1u) to Rational(-949, 375), - listOf(0u, 2u) to Rational(-1423, 200) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 0 to Rational(7, 5), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-939, 200), - listOf(0u, 1u) to Rational(123, 50), - listOf(0u, 2u) to Rational(1059, 200) - ), - NumberedPolynomialAsIs( - listOf() to Rational(121, 25), - listOf(0u, 1u) to Rational(-949, 375), - listOf(0u, 2u) to Rational(-1423, 200) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 0 to Rational(7, 5), - 5 to Rational(-16, 4), - )), - "test 4'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf()), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, mapOf( - 5 to Rational(-16, 4), - )), - "test 5'" - ) - } - @Test - fun test_RationalFunction_substitute_Polynomial_Map() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(211, 4), - listOf(2u) to Rational(88, 3), - listOf(3u) to Rational(-63, 8), - listOf(4u) to Rational(441, 16), - listOf(0u, 1u) to Rational(-671, 15), - listOf(1u, 1u) to Rational(-551, 21), - listOf(2u, 1u) to Rational(279, 25), - listOf(3u, 1u) to Rational(231, 20), - listOf(0u, 2u) to Rational(-1436, 1575), - listOf(1u, 2u) to Rational(2471, 250), - listOf(2u, 2u) to Rational(-4919, 100), - listOf(0u, 3u) to Rational(-1464, 125), - listOf(1u, 3u) to Rational(-264, 25), - listOf(0u, 4u) to Rational(576, 25), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(-9, 4), - listOf(2u) to Rational(943, 8), - listOf(3u) to Rational(117, 8), - listOf(4u) to Rational(147, 16), - listOf(0u, 1u) to Rational(289, 90), - listOf(1u, 1u) to Rational(-2692, 15), - listOf(2u, 1u) to Rational(-1629, 140), - listOf(3u, 1u) to Rational(77, 20), - listOf(0u, 2u) to Rational(6187, 75), - listOf(1u, 2u) to Rational(-2879, 175), - listOf(2u, 2u) to Rational(-4919, 300), - listOf(0u, 3u) to Rational(336, 25), - listOf(1u, 3u) to Rational(-88, 25), - listOf(0u, 4u) to Rational(192, 25), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf(1u) to Rational(3, 2), - listOf(0u, 1u) to Rational(8, 5), - ), - 1 to NumberedPolynomialAsIs( - listOf(1u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-3, 1), - ) - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1202861, 210), - listOf(1u) to Rational(-215117, 45), - listOf(2u) to Rational(10889651, 19845), - listOf(3u) to Rational(-3503956, 6615), - listOf(4u) to Rational(809066, 2205), - listOf(5u) to Rational(-9056, 735), - listOf(6u) to Rational(5396, 315), - listOf(7u) to Rational(-752, 147), - listOf(8u) to Rational(16, 49), - listOf(0u, 1u) to Rational(1738469, 1470), - listOf(1u, 1u) to Rational(-926238703, 52920), - listOf(2u, 1u) to Rational(-44113982, 6615), - listOf(3u, 1u) to Rational(10423519, 5292), - listOf(4u, 1u) to Rational(3769712, 2205), - listOf(5u, 1u) to Rational(8905046, 6615), - listOf(6u, 1u) to Rational(1186972, 6615), - listOf(7u, 1u) to Rational(22124, 441), - listOf(8u, 1u) to Rational(-1504, 147), - listOf(0u, 2u) to Rational(-54723628, 2205), - listOf(1u, 2u) to Rational(70109407, 1323), - listOf(2u, 2u) to Rational(151072591, 17640), - listOf(3u, 2u) to Rational(1216428107, 52920), - listOf(4u, 2u) to Rational(2587873193, 317520), - listOf(5u, 2u) to Rational(393536369, 79380), - listOf(6u, 2u) to Rational(137614937, 79380), - listOf(7u, 2u) to Rational(566866, 1323), - listOf(8u, 2u) to Rational(41848, 441), - listOf(0u, 3u) to Rational(-19470406, 2205), - listOf(1u, 3u) to Rational(72514195, 882), - listOf(2u, 3u) to Rational(-78090707, 1764), - listOf(3u, 3u) to Rational(-1988237707, 26460), - listOf(4u, 3u) to Rational(-802137919, 17640), - listOf(5u, 3u) to Rational(-139989463, 5880), - listOf(6u, 3u) to Rational(-26066641, 3780), - listOf(7u, 3u) to Rational(-2363369, 1323), - listOf(8u, 3u) to Rational(-108280, 441), - listOf(0u, 4u) to Rational(14878516, 441), - listOf(1u, 4u) to Rational(-253416724, 2205), - listOf(2u, 4u) to Rational(16699157, 840), - listOf(3u, 4u) to Rational(-105220979, 13230), - listOf(4u, 4u) to Rational(208266383, 5880), - listOf(5u, 4u) to Rational(650135309, 26460), - listOf(6u, 4u) to Rational(123808663, 11760), - listOf(7u, 4u) to Rational(8563385, 2646), - listOf(8u, 4u) to Rational(19721, 49), - listOf(0u, 5u) to Rational(675645, 49), - listOf(1u, 5u) to Rational(-70554077, 588), - listOf(2u, 5u) to Rational(157884029, 980), - listOf(3u, 5u) to Rational(489548623, 4410), - listOf(4u, 5u) to Rational(148540519, 17640), - listOf(5u, 5u) to Rational(-5559551, 392), - listOf(6u, 5u) to Rational(-18335711, 1470), - listOf(7u, 5u) to Rational(-38437, 9), - listOf(8u, 5u) to Rational(-29620, 63), - listOf(0u, 6u) to Rational(-727625, 49), - listOf(1u, 6u) to Rational(7046685, 98), - listOf(2u, 6u) to Rational(-334814231, 7056), - listOf(3u, 6u) to Rational(-243971737, 17640), - listOf(4u, 6u) to Rational(-571116659, 35280), - listOf(5u, 6u) to Rational(567538, 315), - listOf(6u, 6u) to Rational(3199768, 315), - listOf(7u, 6u) to Rational(227744, 63), - listOf(8u, 6u) to Rational(23116, 63), - listOf(0u, 7u) to Rational(-27500, 7), - listOf(1u, 7u) to Rational(120125, 3), - listOf(2u, 7u) to Rational(-279200, 3), - listOf(3u, 7u) to Rational(-100160, 7), - listOf(4u, 7u) to Rational(920452, 21), - listOf(5u, 7u) to Rational(226481, 21), - listOf(6u, 7u) to Rational(-34428, 7), - listOf(7u, 7u) to Rational(-6232, 3), - listOf(8u, 7u) to Rational(-608, 3), - listOf(0u, 8u) to Rational(2500, 1), - listOf(1u, 8u) to Rational(-19000, 1), - listOf(2u, 8u) to Rational(37900, 1), - listOf(3u, 8u) to Rational(-1840, 1), - listOf(4u, 8u) to Rational(-17876, 1), - listOf(5u, 8u) to Rational(-1240, 1), - listOf(6u, 8u) to Rational(2788, 1), - listOf(7u, 8u) to Rational(800, 1), - listOf(8u, 8u) to Rational(64, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(162487, 63), - listOf(1u) to Rational(-92713, 54), - listOf(2u) to Rational(802436, 1323), - listOf(3u) to Rational(-55088, 441), - listOf(4u) to Rational(1404034, 9261), - listOf(5u) to Rational(-5804, 1029), - listOf(6u) to Rational(51556, 9261), - listOf(7u) to Rational(-752, 441), - listOf(8u) to Rational(16, 147), - listOf(0u, 1u) to Rational(296071, 441), - listOf(1u, 1u) to Rational(-4991281, 882), - listOf(2u, 1u) to Rational(-18702811, 9261), - listOf(3u, 1u) to Rational(40759043, 27783), - listOf(4u, 1u) to Rational(19768501, 27783), - listOf(5u, 1u) to Rational(14307337, 27783), - listOf(6u, 1u) to Rational(1655684, 27783), - listOf(7u, 1u) to Rational(22124, 1323), - listOf(8u, 1u) to Rational(-1504, 441), - listOf(0u, 2u) to Rational(-27667474, 3087), - listOf(1u, 2u) to Rational(265605901, 12348), - listOf(2u, 2u) to Rational(160360775, 98784), - listOf(3u, 2u) to Rational(1169992093, 148176), - listOf(4u, 2u) to Rational(3978014077, 1333584), - listOf(5u, 2u) to Rational(567058123, 333396), - listOf(6u, 2u) to Rational(205132579, 333396), - listOf(7u, 2u) to Rational(566866, 3969), - listOf(8u, 2u) to Rational(41848, 1323), - listOf(0u, 3u) to Rational(-2228822, 1029), - listOf(1u, 3u) to Rational(80179390, 3087), - listOf(2u, 3u) to Rational(-1378630487, 74088), - listOf(3u, 3u) to Rational(-3385811693, 111132), - listOf(4u, 3u) to Rational(-820686977, 49392), - listOf(5u, 3u) to Rational(-89101027, 10584), - listOf(6u, 3u) to Rational(-37847387, 15876), - listOf(7u, 3u) to Rational(-2363369, 3969), - listOf(8u, 3u) to Rational(-108280, 1323), - listOf(0u, 4u) to Rational(12619982, 1029), - listOf(1u, 4u) to Rational(-277723177, 6174), - listOf(2u, 4u) to Rational(649414169, 49392), - listOf(3u, 4u) to Rational(14457595, 63504), - listOf(4u, 4u) to Rational(139270339, 10584), - listOf(5u, 4u) to Rational(140367961, 15876), - listOf(6u, 4u) to Rational(25467083, 7056), - listOf(7u, 4u) to Rational(8563385, 7938), - listOf(8u, 4u) to Rational(19721, 147), - listOf(0u, 5u) to Rational(643850, 147), - listOf(1u, 5u) to Rational(-11818025, 294), - listOf(2u, 5u) to Rational(33963203, 588), - listOf(3u, 5u) to Rational(207216235, 5292), - listOf(4u, 5u) to Rational(2861021, 1512), - listOf(5u, 5u) to Rational(-6302335, 1176), - listOf(6u, 5u) to Rational(-3738587, 882), - listOf(7u, 5u) to Rational(-38437, 27), - listOf(8u, 5u) to Rational(-29620, 189), - listOf(0u, 6u) to Rational(-248725, 49), - listOf(1u, 6u) to Rational(2478535, 98), - listOf(2u, 6u) to Rational(-399721367, 21168), - listOf(3u, 6u) to Rational(-54309317, 10584), - listOf(4u, 6u) to Rational(-95398327, 21168), - listOf(5u, 6u) to Rational(173750, 189), - listOf(6u, 6u) to Rational(92216, 27), - listOf(7u, 6u) to Rational(227744, 189), - listOf(8u, 6u) to Rational(23116, 189), - listOf(0u, 7u) to Rational(-27500, 21), - listOf(1u, 7u) to Rational(120125, 9), - listOf(2u, 7u) to Rational(-279200, 9), - listOf(3u, 7u) to Rational(-100160, 21), - listOf(4u, 7u) to Rational(920452, 63), - listOf(5u, 7u) to Rational(226481, 63), - listOf(6u, 7u) to Rational(-11476, 7), - listOf(7u, 7u) to Rational(-6232, 9), - listOf(8u, 7u) to Rational(-608, 9), - listOf(0u, 8u) to Rational(2500, 3), - listOf(1u, 8u) to Rational(-19000, 3), - listOf(2u, 8u) to Rational(37900, 3), - listOf(3u, 8u) to Rational(-1840, 3), - listOf(4u, 8u) to Rational(-17876, 3), - listOf(5u, 8u) to Rational(-1240, 3), - listOf(6u, 8u) to Rational(2788, 3), - listOf(7u, 8u) to Rational(800, 3), - listOf(8u, 8u) to Rational(64, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - 1 to NumberedPolynomialAsIs( - listOf() to Rational(8, 2), - listOf(1u) to Rational(-15, 5), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 7), - listOf(1u, 1u) to Rational(-16, 6), - listOf(2u, 1u) to Rational(-13, 3), - listOf(0u, 2u) to Rational(-5, 1), - listOf(1u, 2u) to Rational(17, 1), - listOf(2u, 2u) to Rational(8, 2), - ), - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1202861, 210), - listOf(1u) to Rational(-215117, 45), - listOf(2u) to Rational(10889651, 19845), - listOf(3u) to Rational(-3503956, 6615), - listOf(4u) to Rational(809066, 2205), - listOf(5u) to Rational(-9056, 735), - listOf(6u) to Rational(5396, 315), - listOf(7u) to Rational(-752, 147), - listOf(8u) to Rational(16, 49), - listOf(0u, 1u) to Rational(1738469, 1470), - listOf(1u, 1u) to Rational(-926238703, 52920), - listOf(2u, 1u) to Rational(-44113982, 6615), - listOf(3u, 1u) to Rational(10423519, 5292), - listOf(4u, 1u) to Rational(3769712, 2205), - listOf(5u, 1u) to Rational(8905046, 6615), - listOf(6u, 1u) to Rational(1186972, 6615), - listOf(7u, 1u) to Rational(22124, 441), - listOf(8u, 1u) to Rational(-1504, 147), - listOf(0u, 2u) to Rational(-54723628, 2205), - listOf(1u, 2u) to Rational(70109407, 1323), - listOf(2u, 2u) to Rational(151072591, 17640), - listOf(3u, 2u) to Rational(1216428107, 52920), - listOf(4u, 2u) to Rational(2587873193, 317520), - listOf(5u, 2u) to Rational(393536369, 79380), - listOf(6u, 2u) to Rational(137614937, 79380), - listOf(7u, 2u) to Rational(566866, 1323), - listOf(8u, 2u) to Rational(41848, 441), - listOf(0u, 3u) to Rational(-19470406, 2205), - listOf(1u, 3u) to Rational(72514195, 882), - listOf(2u, 3u) to Rational(-78090707, 1764), - listOf(3u, 3u) to Rational(-1988237707, 26460), - listOf(4u, 3u) to Rational(-802137919, 17640), - listOf(5u, 3u) to Rational(-139989463, 5880), - listOf(6u, 3u) to Rational(-26066641, 3780), - listOf(7u, 3u) to Rational(-2363369, 1323), - listOf(8u, 3u) to Rational(-108280, 441), - listOf(0u, 4u) to Rational(14878516, 441), - listOf(1u, 4u) to Rational(-253416724, 2205), - listOf(2u, 4u) to Rational(16699157, 840), - listOf(3u, 4u) to Rational(-105220979, 13230), - listOf(4u, 4u) to Rational(208266383, 5880), - listOf(5u, 4u) to Rational(650135309, 26460), - listOf(6u, 4u) to Rational(123808663, 11760), - listOf(7u, 4u) to Rational(8563385, 2646), - listOf(8u, 4u) to Rational(19721, 49), - listOf(0u, 5u) to Rational(675645, 49), - listOf(1u, 5u) to Rational(-70554077, 588), - listOf(2u, 5u) to Rational(157884029, 980), - listOf(3u, 5u) to Rational(489548623, 4410), - listOf(4u, 5u) to Rational(148540519, 17640), - listOf(5u, 5u) to Rational(-5559551, 392), - listOf(6u, 5u) to Rational(-18335711, 1470), - listOf(7u, 5u) to Rational(-38437, 9), - listOf(8u, 5u) to Rational(-29620, 63), - listOf(0u, 6u) to Rational(-727625, 49), - listOf(1u, 6u) to Rational(7046685, 98), - listOf(2u, 6u) to Rational(-334814231, 7056), - listOf(3u, 6u) to Rational(-243971737, 17640), - listOf(4u, 6u) to Rational(-571116659, 35280), - listOf(5u, 6u) to Rational(567538, 315), - listOf(6u, 6u) to Rational(3199768, 315), - listOf(7u, 6u) to Rational(227744, 63), - listOf(8u, 6u) to Rational(23116, 63), - listOf(0u, 7u) to Rational(-27500, 7), - listOf(1u, 7u) to Rational(120125, 3), - listOf(2u, 7u) to Rational(-279200, 3), - listOf(3u, 7u) to Rational(-100160, 7), - listOf(4u, 7u) to Rational(920452, 21), - listOf(5u, 7u) to Rational(226481, 21), - listOf(6u, 7u) to Rational(-34428, 7), - listOf(7u, 7u) to Rational(-6232, 3), - listOf(8u, 7u) to Rational(-608, 3), - listOf(0u, 8u) to Rational(2500, 1), - listOf(1u, 8u) to Rational(-19000, 1), - listOf(2u, 8u) to Rational(37900, 1), - listOf(3u, 8u) to Rational(-1840, 1), - listOf(4u, 8u) to Rational(-17876, 1), - listOf(5u, 8u) to Rational(-1240, 1), - listOf(6u, 8u) to Rational(2788, 1), - listOf(7u, 8u) to Rational(800, 1), - listOf(8u, 8u) to Rational(64, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(162487, 63), - listOf(1u) to Rational(-92713, 54), - listOf(2u) to Rational(802436, 1323), - listOf(3u) to Rational(-55088, 441), - listOf(4u) to Rational(1404034, 9261), - listOf(5u) to Rational(-5804, 1029), - listOf(6u) to Rational(51556, 9261), - listOf(7u) to Rational(-752, 441), - listOf(8u) to Rational(16, 147), - listOf(0u, 1u) to Rational(296071, 441), - listOf(1u, 1u) to Rational(-4991281, 882), - listOf(2u, 1u) to Rational(-18702811, 9261), - listOf(3u, 1u) to Rational(40759043, 27783), - listOf(4u, 1u) to Rational(19768501, 27783), - listOf(5u, 1u) to Rational(14307337, 27783), - listOf(6u, 1u) to Rational(1655684, 27783), - listOf(7u, 1u) to Rational(22124, 1323), - listOf(8u, 1u) to Rational(-1504, 441), - listOf(0u, 2u) to Rational(-27667474, 3087), - listOf(1u, 2u) to Rational(265605901, 12348), - listOf(2u, 2u) to Rational(160360775, 98784), - listOf(3u, 2u) to Rational(1169992093, 148176), - listOf(4u, 2u) to Rational(3978014077, 1333584), - listOf(5u, 2u) to Rational(567058123, 333396), - listOf(6u, 2u) to Rational(205132579, 333396), - listOf(7u, 2u) to Rational(566866, 3969), - listOf(8u, 2u) to Rational(41848, 1323), - listOf(0u, 3u) to Rational(-2228822, 1029), - listOf(1u, 3u) to Rational(80179390, 3087), - listOf(2u, 3u) to Rational(-1378630487, 74088), - listOf(3u, 3u) to Rational(-3385811693, 111132), - listOf(4u, 3u) to Rational(-820686977, 49392), - listOf(5u, 3u) to Rational(-89101027, 10584), - listOf(6u, 3u) to Rational(-37847387, 15876), - listOf(7u, 3u) to Rational(-2363369, 3969), - listOf(8u, 3u) to Rational(-108280, 1323), - listOf(0u, 4u) to Rational(12619982, 1029), - listOf(1u, 4u) to Rational(-277723177, 6174), - listOf(2u, 4u) to Rational(649414169, 49392), - listOf(3u, 4u) to Rational(14457595, 63504), - listOf(4u, 4u) to Rational(139270339, 10584), - listOf(5u, 4u) to Rational(140367961, 15876), - listOf(6u, 4u) to Rational(25467083, 7056), - listOf(7u, 4u) to Rational(8563385, 7938), - listOf(8u, 4u) to Rational(19721, 147), - listOf(0u, 5u) to Rational(643850, 147), - listOf(1u, 5u) to Rational(-11818025, 294), - listOf(2u, 5u) to Rational(33963203, 588), - listOf(3u, 5u) to Rational(207216235, 5292), - listOf(4u, 5u) to Rational(2861021, 1512), - listOf(5u, 5u) to Rational(-6302335, 1176), - listOf(6u, 5u) to Rational(-3738587, 882), - listOf(7u, 5u) to Rational(-38437, 27), - listOf(8u, 5u) to Rational(-29620, 189), - listOf(0u, 6u) to Rational(-248725, 49), - listOf(1u, 6u) to Rational(2478535, 98), - listOf(2u, 6u) to Rational(-399721367, 21168), - listOf(3u, 6u) to Rational(-54309317, 10584), - listOf(4u, 6u) to Rational(-95398327, 21168), - listOf(5u, 6u) to Rational(173750, 189), - listOf(6u, 6u) to Rational(92216, 27), - listOf(7u, 6u) to Rational(227744, 189), - listOf(8u, 6u) to Rational(23116, 189), - listOf(0u, 7u) to Rational(-27500, 21), - listOf(1u, 7u) to Rational(120125, 9), - listOf(2u, 7u) to Rational(-279200, 9), - listOf(3u, 7u) to Rational(-100160, 21), - listOf(4u, 7u) to Rational(920452, 63), - listOf(5u, 7u) to Rational(226481, 63), - listOf(6u, 7u) to Rational(-11476, 7), - listOf(7u, 7u) to Rational(-6232, 9), - listOf(8u, 7u) to Rational(-608, 9), - listOf(0u, 8u) to Rational(2500, 3), - listOf(1u, 8u) to Rational(-19000, 3), - listOf(2u, 8u) to Rational(37900, 3), - listOf(3u, 8u) to Rational(-1840, 3), - listOf(4u, 8u) to Rational(-17876, 3), - listOf(5u, 8u) to Rational(-1240, 3), - listOf(6u, 8u) to Rational(2788, 3), - listOf(7u, 8u) to Rational(800, 3), - listOf(8u, 8u) to Rational(64, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - 1 to NumberedPolynomialAsIs( - listOf() to Rational(8, 2), - listOf(1u) to Rational(-15, 5), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 7), - listOf(1u, 1u) to Rational(-16, 6), - listOf(2u, 1u) to Rational(-13, 3), - listOf(0u, 2u) to Rational(-5, 1), - listOf(1u, 2u) to Rational(17, 1), - listOf(2u, 2u) to Rational(8, 2), - ), - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-6, 1), - listOf(1u) to Rational(-9, 8), - listOf(2u) to Rational(17, 5), - listOf(0u, 1u) to Rational(-2, 3), - listOf(1u, 1u) to Rational(1, 5), - listOf(2u, 1u) to Rational(-11, 7), - listOf(0u, 2u) to Rational(13, 6), - listOf(1u, 2u) to Rational(-15, 2), - listOf(2u, 2u) to Rational(-14, 4), - ) - )), - "test 3'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(493, 6), - listOf(1u) to Rational(-15991, 210), - listOf(2u) to Rational(2734, 63), - listOf(3u) to Rational(-8213, 245), - listOf(4u) to Rational(1843, 147), - listOf(5u) to Rational(-432, 245), - listOf(6u) to Rational(4, 49), - listOf(0u, 1u) to Rational(-66, 1), - listOf(1u, 1u) to Rational(-92924, 2205), - listOf(2u, 1u) to Rational(-257461, 2205), - listOf(3u, 1u) to Rational(58658, 2205), - listOf(4u, 1u) to Rational(-87884, 2205), - listOf(5u, 1u) to Rational(2726, 105), - listOf(6u, 1u) to Rational(-52, 21), - listOf(0u, 2u) to Rational(-17569, 147), - listOf(1u, 2u) to Rational(368819, 735), - listOf(2u, 2u) to Rational(-644626, 6615), - listOf(3u, 2u) to Rational(221738, 945), - listOf(4u, 2u) to Rational(-18022, 945), - listOf(5u, 2u) to Rational(-1201, 315), - listOf(6u, 2u) to Rational(1327, 63), - listOf(0u, 3u) to Rational(240, 7), - listOf(1u, 3u) to Rational(-868, 9), - listOf(2u, 3u) to Rational(-8936, 315), - listOf(3u, 3u) to Rational(-77146, 315), - listOf(4u, 3u) to Rational(-4072, 315), - listOf(5u, 3u) to Rational(-2218, 15), - listOf(6u, 3u) to Rational(-104, 3), - listOf(0u, 4u) to Rational(100, 3), - listOf(1u, 4u) to Rational(-725, 3), - listOf(2u, 4u) to Rational(459, 1), - listOf(3u, 4u) to Rational(-2071, 15), - listOf(4u, 4u) to Rational(2831, 15), - listOf(5u, 4u) to Rational(632, 5), - listOf(6u, 4u) to Rational(16, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1255, 9), - listOf(1u) to Rational(-24781, 126), - listOf(2u) to Rational(1195, 14), - listOf(3u) to Rational(-1931, 147), - listOf(4u) to Rational(439, 147), - listOf(5u) to Rational(-172, 343), - listOf(6u) to Rational(4, 147), - listOf(0u, 1u) to Rational(-183, 1), - listOf(1u, 1u) to Rational(-30988, 441), - listOf(2u, 1u) to Rational(-56137, 294), - listOf(3u, 1u) to Rational(204308, 1029), - listOf(4u, 1u) to Rational(-3263, 441), - listOf(5u, 1u) to Rational(2662, 441), - listOf(6u, 1u) to Rational(-52, 63), - listOf(0u, 2u) to Rational(-87119, 294), - listOf(1u, 2u) to Rational(1077919, 686), - listOf(2u, 2u) to Rational(-35209, 147), - listOf(3u, 2u) to Rational(15041, 147), - listOf(4u, 2u) to Rational(240889, 1323), - listOf(5u, 2u) to Rational(27778, 1323), - listOf(6u, 2u) to Rational(1327, 189), - listOf(0u, 3u) to Rational(1620, 7), - listOf(1u, 3u) to Rational(-25716, 49), - listOf(2u, 3u) to Rational(-32078, 49), - listOf(3u, 3u) to Rational(-704038, 441), - listOf(4u, 3u) to Rational(-30190, 63), - listOf(5u, 3u) to Rational(-5414, 63), - listOf(6u, 3u) to Rational(-104, 9), - listOf(0u, 4u) to Rational(225, 1), - listOf(1u, 4u) to Rational(-10560, 7), - listOf(2u, 4u) to Rational(44176, 21), - listOf(3u, 4u) to Rational(28996, 21), - listOf(4u, 4u) to Rational(2405, 7), - listOf(5u, 4u) to Rational(1240, 21), - listOf(6u, 4u) to Rational(16, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 1 to NumberedPolynomialAsIs( - listOf() to Rational(8, 2), - listOf(1u) to Rational(-15, 5), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 7), - listOf(1u, 1u) to Rational(-16, 6), - listOf(2u, 1u) to Rational(-13, 3), - listOf(0u, 2u) to Rational(-5, 1), - listOf(1u, 2u) to Rational(17, 1), - listOf(2u, 2u) to Rational(8, 2), - ), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(493, 6), - listOf(1u) to Rational(-15991, 210), - listOf(2u) to Rational(2734, 63), - listOf(3u) to Rational(-8213, 245), - listOf(4u) to Rational(1843, 147), - listOf(5u) to Rational(-432, 245), - listOf(6u) to Rational(4, 49), - listOf(0u, 1u) to Rational(-66, 1), - listOf(1u, 1u) to Rational(-92924, 2205), - listOf(2u, 1u) to Rational(-257461, 2205), - listOf(3u, 1u) to Rational(58658, 2205), - listOf(4u, 1u) to Rational(-87884, 2205), - listOf(5u, 1u) to Rational(2726, 105), - listOf(6u, 1u) to Rational(-52, 21), - listOf(0u, 2u) to Rational(-17569, 147), - listOf(1u, 2u) to Rational(368819, 735), - listOf(2u, 2u) to Rational(-644626, 6615), - listOf(3u, 2u) to Rational(221738, 945), - listOf(4u, 2u) to Rational(-18022, 945), - listOf(5u, 2u) to Rational(-1201, 315), - listOf(6u, 2u) to Rational(1327, 63), - listOf(0u, 3u) to Rational(240, 7), - listOf(1u, 3u) to Rational(-868, 9), - listOf(2u, 3u) to Rational(-8936, 315), - listOf(3u, 3u) to Rational(-77146, 315), - listOf(4u, 3u) to Rational(-4072, 315), - listOf(5u, 3u) to Rational(-2218, 15), - listOf(6u, 3u) to Rational(-104, 3), - listOf(0u, 4u) to Rational(100, 3), - listOf(1u, 4u) to Rational(-725, 3), - listOf(2u, 4u) to Rational(459, 1), - listOf(3u, 4u) to Rational(-2071, 15), - listOf(4u, 4u) to Rational(2831, 15), - listOf(5u, 4u) to Rational(632, 5), - listOf(6u, 4u) to Rational(16, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1255, 9), - listOf(1u) to Rational(-24781, 126), - listOf(2u) to Rational(1195, 14), - listOf(3u) to Rational(-1931, 147), - listOf(4u) to Rational(439, 147), - listOf(5u) to Rational(-172, 343), - listOf(6u) to Rational(4, 147), - listOf(0u, 1u) to Rational(-183, 1), - listOf(1u, 1u) to Rational(-30988, 441), - listOf(2u, 1u) to Rational(-56137, 294), - listOf(3u, 1u) to Rational(204308, 1029), - listOf(4u, 1u) to Rational(-3263, 441), - listOf(5u, 1u) to Rational(2662, 441), - listOf(6u, 1u) to Rational(-52, 63), - listOf(0u, 2u) to Rational(-87119, 294), - listOf(1u, 2u) to Rational(1077919, 686), - listOf(2u, 2u) to Rational(-35209, 147), - listOf(3u, 2u) to Rational(15041, 147), - listOf(4u, 2u) to Rational(240889, 1323), - listOf(5u, 2u) to Rational(27778, 1323), - listOf(6u, 2u) to Rational(1327, 189), - listOf(0u, 3u) to Rational(1620, 7), - listOf(1u, 3u) to Rational(-25716, 49), - listOf(2u, 3u) to Rational(-32078, 49), - listOf(3u, 3u) to Rational(-704038, 441), - listOf(4u, 3u) to Rational(-30190, 63), - listOf(5u, 3u) to Rational(-5414, 63), - listOf(6u, 3u) to Rational(-104, 9), - listOf(0u, 4u) to Rational(225, 1), - listOf(1u, 4u) to Rational(-10560, 7), - listOf(2u, 4u) to Rational(44176, 21), - listOf(3u, 4u) to Rational(28996, 21), - listOf(4u, 4u) to Rational(2405, 7), - listOf(5u, 4u) to Rational(1240, 21), - listOf(6u, 4u) to Rational(16, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 1 to NumberedPolynomialAsIs( - listOf() to Rational(8, 2), - listOf(1u) to Rational(-15, 5), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 7), - listOf(1u, 1u) to Rational(-16, 6), - listOf(2u, 1u) to Rational(-13, 3), - listOf(0u, 2u) to Rational(-5, 1), - listOf(1u, 2u) to Rational(17, 1), - listOf(2u, 2u) to Rational(8, 2), - ), - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-6, 1), - listOf(1u) to Rational(-9, 8), - listOf(2u) to Rational(17, 5), - listOf(0u, 1u) to Rational(-2, 3), - listOf(1u, 1u) to Rational(1, 5), - listOf(2u, 1u) to Rational(-11, 7), - listOf(0u, 2u) to Rational(13, 6), - listOf(1u, 2u) to Rational(-15, 2), - listOf(2u, 2u) to Rational(-14, 4), - ) - )), - "test 4'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-409, 6), - listOf(1u) to Rational(-376, 9), - listOf(2u) to Rational(-1781, 81), - listOf(3u) to Rational(-128, 27), - listOf(4u) to Rational(-8, 9), - listOf(0u, 1u) to Rational(18701, 210), - listOf(1u, 1u) to Rational(614183, 7560), - listOf(2u, 1u) to Rational(90941, 1890), - listOf(3u, 1u) to Rational(1802, 135), - listOf(4u, 1u) to Rational(112, 45), - listOf(0u, 2u) to Rational(181421, 315), - listOf(1u, 2u) to Rational(77813, 378), - listOf(2u, 2u) to Rational(598583, 7560), - listOf(3u, 2u) to Rational(85, 27), - listOf(4u, 2u) to Rational(2, 5), - listOf(0u, 3u) to Rational(130997, 315), - listOf(1u, 3u) to Rational(1093, 420), - listOf(2u, 3u) to Rational(9551, 2520), - listOf(3u, 3u) to Rational(-14, 45), - listOf(4u, 3u) to Rational(22, 45), - listOf(0u, 4u) to Rational(-2801, 9), - listOf(1u, 4u) to Rational(4033, 90), - listOf(2u, 4u) to Rational(6429, 80), - listOf(3u, 4u) to Rational(2851, 90), - listOf(4u, 4u) to Rational(293, 45), - listOf(0u, 5u) to Rational(-220, 1), - listOf(1u, 5u) to Rational(127, 1), - listOf(2u, 5u) to Rational(202, 5), - listOf(3u, 5u) to Rational(-63, 5), - listOf(4u, 5u) to Rational(-12, 5), - listOf(0u, 6u) to Rational(100, 1), - listOf(1u, 6u) to Rational(-80, 1), - listOf(2u, 6u) to Rational(-24, 1), - listOf(3u, 6u) to Rational(16, 1), - listOf(4u, 6u) to Rational(4, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(5407, 9), - listOf(1u) to Rational(9568, 27), - listOf(2u) to Rational(4996, 27), - listOf(3u) to Rational(352, 9), - listOf(4u) to Rational(22, 3), - listOf(0u, 1u) to Rational(104411, 126), - listOf(1u, 1u) to Rational(6001, 126), - listOf(2u, 1u) to Rational(-796, 21), - listOf(3u, 1u) to Rational(-5389, 126), - listOf(4u, 1u) to Rational(-166, 21), - listOf(0u, 2u) to Rational(-35327, 126), - listOf(1u, 2u) to Rational(53, 252), - listOf(2u, 2u) to Rational(849197, 6048), - listOf(3u, 2u) to Rational(22361, 252), - listOf(4u, 2u) to Rational(773, 42), - listOf(0u, 3u) to Rational(-6067, 21), - listOf(1u, 3u) to Rational(39049, 126), - listOf(2u, 3u) to Rational(80303, 1008), - listOf(3u, 3u) to Rational(-3035, 63), - listOf(4u, 3u) to Rational(-209, 21), - listOf(0u, 4u) to Rational(3113, 21), - listOf(1u, 4u) to Rational(-22345, 126), - listOf(2u, 4u) to Rational(-30931, 1008), - listOf(3u, 4u) to Rational(5837, 126), - listOf(4u, 4u) to Rational(229, 21), - listOf(0u, 5u) to Rational(-2120, 21), - listOf(1u, 5u) to Rational(451, 7), - listOf(2u, 5u) to Rational(422, 21), - listOf(3u, 5u) to Rational(-181, 21), - listOf(4u, 5u) to Rational(-40, 21), - listOf(0u, 6u) to Rational(100, 3), - listOf(1u, 6u) to Rational(-80, 3), - listOf(2u, 6u) to Rational(-8, 1), - listOf(3u, 6u) to Rational(16, 3), - listOf(4u, 6u) to Rational(4, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - )), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-409, 6), - listOf(1u) to Rational(-376, 9), - listOf(2u) to Rational(-1781, 81), - listOf(3u) to Rational(-128, 27), - listOf(4u) to Rational(-8, 9), - listOf(0u, 1u) to Rational(18701, 210), - listOf(1u, 1u) to Rational(614183, 7560), - listOf(2u, 1u) to Rational(90941, 1890), - listOf(3u, 1u) to Rational(1802, 135), - listOf(4u, 1u) to Rational(112, 45), - listOf(0u, 2u) to Rational(181421, 315), - listOf(1u, 2u) to Rational(77813, 378), - listOf(2u, 2u) to Rational(598583, 7560), - listOf(3u, 2u) to Rational(85, 27), - listOf(4u, 2u) to Rational(2, 5), - listOf(0u, 3u) to Rational(130997, 315), - listOf(1u, 3u) to Rational(1093, 420), - listOf(2u, 3u) to Rational(9551, 2520), - listOf(3u, 3u) to Rational(-14, 45), - listOf(4u, 3u) to Rational(22, 45), - listOf(0u, 4u) to Rational(-2801, 9), - listOf(1u, 4u) to Rational(4033, 90), - listOf(2u, 4u) to Rational(6429, 80), - listOf(3u, 4u) to Rational(2851, 90), - listOf(4u, 4u) to Rational(293, 45), - listOf(0u, 5u) to Rational(-220, 1), - listOf(1u, 5u) to Rational(127, 1), - listOf(2u, 5u) to Rational(202, 5), - listOf(3u, 5u) to Rational(-63, 5), - listOf(4u, 5u) to Rational(-12, 5), - listOf(0u, 6u) to Rational(100, 1), - listOf(1u, 6u) to Rational(-80, 1), - listOf(2u, 6u) to Rational(-24, 1), - listOf(3u, 6u) to Rational(16, 1), - listOf(4u, 6u) to Rational(4, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(5407, 9), - listOf(1u) to Rational(9568, 27), - listOf(2u) to Rational(4996, 27), - listOf(3u) to Rational(352, 9), - listOf(4u) to Rational(22, 3), - listOf(0u, 1u) to Rational(104411, 126), - listOf(1u, 1u) to Rational(6001, 126), - listOf(2u, 1u) to Rational(-796, 21), - listOf(3u, 1u) to Rational(-5389, 126), - listOf(4u, 1u) to Rational(-166, 21), - listOf(0u, 2u) to Rational(-35327, 126), - listOf(1u, 2u) to Rational(53, 252), - listOf(2u, 2u) to Rational(849197, 6048), - listOf(3u, 2u) to Rational(22361, 252), - listOf(4u, 2u) to Rational(773, 42), - listOf(0u, 3u) to Rational(-6067, 21), - listOf(1u, 3u) to Rational(39049, 126), - listOf(2u, 3u) to Rational(80303, 1008), - listOf(3u, 3u) to Rational(-3035, 63), - listOf(4u, 3u) to Rational(-209, 21), - listOf(0u, 4u) to Rational(3113, 21), - listOf(1u, 4u) to Rational(-22345, 126), - listOf(2u, 4u) to Rational(-30931, 1008), - listOf(3u, 4u) to Rational(5837, 126), - listOf(4u, 4u) to Rational(229, 21), - listOf(0u, 5u) to Rational(-2120, 21), - listOf(1u, 5u) to Rational(451, 7), - listOf(2u, 5u) to Rational(422, 21), - listOf(3u, 5u) to Rational(-181, 21), - listOf(4u, 5u) to Rational(-40, 21), - listOf(0u, 6u) to Rational(100, 3), - listOf(1u, 6u) to Rational(-80, 3), - listOf(2u, 6u) to Rational(-8, 1), - listOf(3u, 6u) to Rational(16, 3), - listOf(4u, 6u) to Rational(4, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-6, 1), - listOf(1u) to Rational(-9, 8), - listOf(2u) to Rational(17, 5), - listOf(0u, 1u) to Rational(-2, 3), - listOf(1u, 1u) to Rational(1, 5), - listOf(2u, 1u) to Rational(-11, 7), - listOf(0u, 2u) to Rational(13, 6), - listOf(1u, 2u) to Rational(-15, 2), - listOf(2u, 2u) to Rational(-14, 4), - ) - )), - "test 5'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, mapOf( - 5 to NumberedPolynomialAsIs( - listOf() to Rational(-6, 1), - listOf(1u) to Rational(-9, 8), - listOf(2u) to Rational(17, 5), - listOf(0u, 1u) to Rational(-2, 3), - listOf(1u, 1u) to Rational(1, 5), - listOf(2u, 1u) to Rational(-11, 7), - listOf(0u, 2u) to Rational(13, 6), - listOf(1u, 2u) to Rational(-15, 2), - listOf(2u, 2u) to Rational(-14, 4), - ) - )), - "test 6'" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_RationalFunction_substitute_RationalFunction_Map() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ), - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(4u) to Rational(-17166109, 793800), - listOf(3u, 1u) to Rational(-930960143, 5556600), - listOf(2u, 2u) to Rational(-144665109691, 350065800), - listOf(1u, 3u) to Rational(-17232577, 52920), - listOf(0u, 4u) to Rational(-68141, 1323), - ), - NumberedPolynomialAsIs( - listOf(4u) to Rational(-57522533, 14288400), - listOf(3u, 1u) to Rational(-13085162953, 300056400), - listOf(2u, 2u) to Rational(-92093367341, 525098700), - listOf(1u, 3u) to Rational(-1979342797, 6667920), - listOf(0u, 4u) to Rational(-3082727, 21168), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(11, 5), - listOf(0u, 1u) to Rational(8, 4), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(1, 9), - listOf(0u, 1u) to Rational(11, 7), - ) - ), - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(-4, 3), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(3, 6), - listOf(0u, 1u) to Rational(12, 8), - ) - ), - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-130778291, 76800), - listOf(1u) to Rational(-445270919, 230400), - listOf(2u) to Rational(44578444937, 14515200), - listOf(3u) to Rational(17329402153, 1555200), - listOf(4u) to Rational(89239926809, 2332800), - listOf(5u) to Rational(2808812267, 145152), - listOf(6u) to Rational(-21362661007, 725760), - listOf(7u) to Rational(-258455443, 2016), - listOf(8u) to Rational(-21454693, 96), - listOf(0u, 1u) to Rational(-1002137, 15360), - listOf(1u, 1u) to Rational(-1704849697, 430080), - listOf(2u, 1u) to Rational(-57657676789, 4838400), - listOf(3u, 1u) to Rational(-101331731, 89600), - listOf(4u, 1u) to Rational(5362280079329, 130636800), - listOf(5u, 1u) to Rational(4069896167053, 130636800), - listOf(6u, 1u) to Rational(12011514569, 544320), - listOf(7u, 1u) to Rational(138293195623, 725760), - listOf(8u, 1u) to Rational(6228779419, 48384), - listOf(0u, 2u) to Rational(-32395872823, 8064000), - listOf(1u, 2u) to Rational(-7398505523, 2304000), - listOf(2u, 2u) to Rational(95217051699521, 3048192000), - listOf(3u, 2u) to Rational(198026968812079, 3657830400), - listOf(4u, 2u) to Rational(4291645618499, 228614400), - listOf(5u, 2u) to Rational(-33211690942439, 914457600), - listOf(6u, 2u) to Rational(-637385538163153, 1371686400), - listOf(7u, 2u) to Rational(-138671528276273, 182891520), - listOf(8u, 2u) to Rational(-14566368751, 217728), - listOf(0u, 3u) to Rational(-10538718719, 2016000), - listOf(1u, 3u) to Rational(-1844485375199, 84672000), - listOf(2u, 3u) to Rational(103968665891, 12096000), - listOf(3u, 3u) to Rational(175402107278351, 1828915200), - listOf(4u, 3u) to Rational(8020699588879, 114307200), - listOf(5u, 3u) to Rational(3414841894991, 38102400), - listOf(6u, 3u) to Rational(1848405591611, 4665600), - listOf(7u, 3u) to Rational(39486708738989, 137168640), - listOf(8u, 3u) to Rational(255926289517, 9144576), - listOf(0u, 4u) to Rational(-655379564629, 105840000), - listOf(1u, 4u) to Rational(-208336039441, 127008000), - listOf(2u, 4u) to Rational(40173146771411, 1143072000), - listOf(3u, 4u) to Rational(150473493581239, 2667168000), - listOf(4u, 4u) to Rational(38833783990483, 1143072000), - listOf(5u, 4u) to Rational(-1963676248203053, 4800902400), - listOf(6u, 4u) to Rational(-2598759412825747, 3200601600), - listOf(7u, 4u) to Rational(-192895352019667, 1280240640), - listOf(8u, 4u) to Rational(3737382679, 6858432), - listOf(0u, 5u) to Rational(-16959378721, 1890000), - listOf(1u, 5u) to Rational(-1864802244743, 79380000), - listOf(2u, 5u) to Rational(13449261536489, 666792000), - listOf(3u, 5u) to Rational(215272234137329, 2667168000), - listOf(4u, 5u) to Rational(6040691379277, 83349000), - listOf(5u, 5u) to Rational(153687143525887, 800150400), - listOf(6u, 5u) to Rational(475602854903563, 2400451200), - listOf(7u, 5u) to Rational(27315599358749, 640120320), - listOf(8u, 5u) to Rational(-2630413357, 10668672), - listOf(0u, 6u) to Rational(-6654999511, 2646000), - listOf(1u, 6u) to Rational(-67885252327, 15876000), - listOf(2u, 6u) to Rational(5786776220983, 2667168000), - listOf(3u, 6u) to Rational(60615922629083, 1143072000), - listOf(4u, 6u) to Rational(-34703539637627407, 672126336000), - listOf(5u, 6u) to Rational(-744694192134101, 2240421120), - listOf(6u, 6u) to Rational(-1782470617231, 14817600), - listOf(7u, 6u) to Rational(59123208433, 8890560), - listOf(8u, 6u) to Rational(-141653, 5292), - listOf(0u, 7u) to Rational(-338051969, 441000), - listOf(1u, 7u) to Rational(468850013, 1764000), - listOf(2u, 7u) to Rational(2102343426101, 222264000), - listOf(3u, 7u) to Rational(7836130602007, 1333584000), - listOf(4u, 7u) to Rational(16239111865997, 746807040), - listOf(5u, 7u) to Rational(3824649185383, 88905600), - listOf(6u, 7u) to Rational(56058614459, 3457440), - listOf(7u, 7u) to Rational(-396766339, 493920), - listOf(8u, 7u) to Rational(-165147, 2744), - listOf(0u, 8u) to Rational(-3088619, 58800), - listOf(1u, 8u) to Rational(155343347, 88200), - listOf(2u, 8u) to Rational(100098736469, 7408800), - listOf(3u, 8u) to Rational(109725511381, 7408800), - listOf(4u, 8u) to Rational(-2431199641013, 59270400), - listOf(5u, 8u) to Rational(-102872383249, 3457440), - listOf(6u, 8u) to Rational(1449461309, 576240), - listOf(7u, 8u) to Rational(812775, 1372), - listOf(8u, 8u) to Rational(-16461, 343) - ), - NumberedPolynomialAsIs( - listOf() to Rational(164202773, 230400), - listOf(1u) to Rational(-70345303, 518400), - listOf(2u) to Rational(-4229702731, 4665600), - listOf(3u) to Rational(3262171027, 6998400), - listOf(4u) to Rational(-25423104169, 13996800), - listOf(5u) to Rational(64061869, 349920), - listOf(6u) to Rational(-1655878091, 116640), - listOf(7u) to Rational(-7991441, 648), - listOf(8u) to Rational(-502591, 18), - listOf(0u, 1u) to Rational(-8780429, 3840), - listOf(1u, 1u) to Rational(434272361, 115200), - listOf(2u, 1u) to Rational(429825727, 41472), - listOf(3u, 1u) to Rational(-10066790339, 6998400), - listOf(4u, 1u) to Rational(70022035471, 20995200), - listOf(5u, 1u) to Rational(-32070283493, 1399680), - listOf(6u, 1u) to Rational(-22051101001, 1399680), - listOf(7u, 1u) to Rational(-126493427, 12960), - listOf(8u, 1u) to Rational(3050245, 864), - listOf(0u, 2u) to Rational(-1194654631, 345600), - listOf(1u, 2u) to Rational(-542961452671, 31104000), - listOf(2u, 2u) to Rational(-234000873607, 48988800), - listOf(3u, 2u) to Rational(140520538087, 3628800), - listOf(4u, 2u) to Rational(9215088876563, 130636800), - listOf(5u, 2u) to Rational(27590569647253, 293932800), - listOf(6u, 2u) to Rational(5129057792891, 97977600), - listOf(7u, 2u) to Rational(-106334191, 5103), - listOf(8u, 2u) to Rational(-1024113911, 435456), - listOf(0u, 3u) to Rational(76223843, 6000), - listOf(1u, 3u) to Rational(57425857357, 2592000), - listOf(2u, 3u) to Rational(-2044736497573, 46656000), - listOf(3u, 3u) to Rational(-26155810120031, 293932800), - listOf(4u, 3u) to Rational(-1064419459813, 6998400), - listOf(5u, 3u) to Rational(-753782018389, 4082400), - listOf(6u, 3u) to Rational(-291973360873, 2799360), - listOf(7u, 3u) to Rational(-46372122599, 816480), - listOf(8u, 3u) to Rational(3579859657, 653184), - listOf(0u, 4u) to Rational(-13374241901, 4320000), - listOf(1u, 4u) to Rational(306606499811, 54432000), - listOf(2u, 4u) to Rational(964267124745437, 13716864000), - listOf(3u, 4u) to Rational(21603809415373, 182891520), - listOf(4u, 4u) to Rational(1097860214654027, 6858432000), - listOf(5u, 4u) to Rational(161615254570669, 914457600), - listOf(6u, 4u) to Rational(758415239461, 22861440), - listOf(7u, 4u) to Rational(2585568355471, 274337280), - listOf(8u, 4u) to Rational(-70433747863, 9144576), - listOf(0u, 5u) to Rational(-9582586217, 2520000), - listOf(1u, 5u) to Rational(-19093471394171, 635040000), - listOf(2u, 5u) to Rational(-13010261944411, 381024000), - listOf(3u, 5u) to Rational(-259039825301861, 4572288000), - listOf(4u, 5u) to Rational(-305081119071079, 2286144000), - listOf(5u, 5u) to Rational(-1923114383311, 19595520), - listOf(6u, 5u) to Rational(-14181787253231, 228614400), - listOf(7u, 5u) to Rational(-3959584789, 4354560), - listOf(8u, 5u) to Rational(4691742523, 762048), - listOf(0u, 6u) to Rational(-588323437, 180000), - listOf(1u, 6u) to Rational(5952234691, 52920000), - listOf(2u, 6u) to Rational(21001851056959, 1088640000), - listOf(3u, 6u) to Rational(84668034357563, 2133734400), - listOf(4u, 6u) to Rational(2029754605811557, 25604812800), - listOf(5u, 6u) to Rational(11721216739823, 426746880), - listOf(6u, 6u) to Rational(-8275903187003, 2133734400), - listOf(7u, 6u) to Rational(-4730447299, 2540160), - listOf(8u, 6u) to Rational(-46069985, 21168), - listOf(0u, 7u) to Rational(-75711301, 117600), - listOf(1u, 7u) to Rational(32430417413, 7056000), - listOf(2u, 7u) to Rational(677988533153, 98784000), - listOf(3u, 7u) to Rational(-948417645827, 71124480), - listOf(4u, 7u) to Rational(-11320265215207, 711244800), - listOf(5u, 7u) to Rational(-676438627783, 50803200), - listOf(6u, 7u) to Rational(-7382274253, 1975680), - listOf(7u, 7u) to Rational(6505733, 2205), - listOf(8u, 7u) to Rational(450137, 882), - listOf(0u, 8u) to Rational(-8368253, 78400), - listOf(1u, 8u) to Rational(6833783, 117600), - listOf(2u, 8u) to Rational(4528971133, 5927040), - listOf(3u, 8u) to Rational(146252636617, 29635200), - listOf(4u, 8u) to Rational(8321882556889, 1659571200), - listOf(5u, 8u) to Rational(-4686033011, 1975680), - listOf(6u, 8u) to Rational(-1074445963, 987840), - listOf(7u, 8u) to Rational(-142313, 588), - listOf(8u, 8u) to Rational(-4281, 49) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(14, 4), - listOf(1u) to Rational(7, 6), - listOf(2u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-15, 2), - listOf(1u, 1u) to Rational(-13, 8), - listOf(2u, 1u) to Rational(-14, 3), - listOf(0u, 2u) to Rational(-7, 6), - listOf(1u, 2u) to Rational(7, 4), - listOf(2u, 2u) to Rational(9, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-7, 4), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(-16, 2), - listOf(0u, 1u) to Rational(-15, 5), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(5, 4), - listOf(0u, 2u) to Rational(-12, 5), - listOf(1u, 2u) to Rational(-18, 2), - listOf(2u, 2u) to Rational(6, 7), - ) - ), - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-130778291, 76800), - listOf(1u) to Rational(-445270919, 230400), - listOf(2u) to Rational(44578444937, 14515200), - listOf(3u) to Rational(17329402153, 1555200), - listOf(4u) to Rational(89239926809, 2332800), - listOf(5u) to Rational(2808812267, 145152), - listOf(6u) to Rational(-21362661007, 725760), - listOf(7u) to Rational(-258455443, 2016), - listOf(8u) to Rational(-21454693, 96), - listOf(0u, 1u) to Rational(-1002137, 15360), - listOf(1u, 1u) to Rational(-1704849697, 430080), - listOf(2u, 1u) to Rational(-57657676789, 4838400), - listOf(3u, 1u) to Rational(-101331731, 89600), - listOf(4u, 1u) to Rational(5362280079329, 130636800), - listOf(5u, 1u) to Rational(4069896167053, 130636800), - listOf(6u, 1u) to Rational(12011514569, 544320), - listOf(7u, 1u) to Rational(138293195623, 725760), - listOf(8u, 1u) to Rational(6228779419, 48384), - listOf(0u, 2u) to Rational(-32395872823, 8064000), - listOf(1u, 2u) to Rational(-7398505523, 2304000), - listOf(2u, 2u) to Rational(95217051699521, 3048192000), - listOf(3u, 2u) to Rational(198026968812079, 3657830400), - listOf(4u, 2u) to Rational(4291645618499, 228614400), - listOf(5u, 2u) to Rational(-33211690942439, 914457600), - listOf(6u, 2u) to Rational(-637385538163153, 1371686400), - listOf(7u, 2u) to Rational(-138671528276273, 182891520), - listOf(8u, 2u) to Rational(-14566368751, 217728), - listOf(0u, 3u) to Rational(-10538718719, 2016000), - listOf(1u, 3u) to Rational(-1844485375199, 84672000), - listOf(2u, 3u) to Rational(103968665891, 12096000), - listOf(3u, 3u) to Rational(175402107278351, 1828915200), - listOf(4u, 3u) to Rational(8020699588879, 114307200), - listOf(5u, 3u) to Rational(3414841894991, 38102400), - listOf(6u, 3u) to Rational(1848405591611, 4665600), - listOf(7u, 3u) to Rational(39486708738989, 137168640), - listOf(8u, 3u) to Rational(255926289517, 9144576), - listOf(0u, 4u) to Rational(-655379564629, 105840000), - listOf(1u, 4u) to Rational(-208336039441, 127008000), - listOf(2u, 4u) to Rational(40173146771411, 1143072000), - listOf(3u, 4u) to Rational(150473493581239, 2667168000), - listOf(4u, 4u) to Rational(38833783990483, 1143072000), - listOf(5u, 4u) to Rational(-1963676248203053, 4800902400), - listOf(6u, 4u) to Rational(-2598759412825747, 3200601600), - listOf(7u, 4u) to Rational(-192895352019667, 1280240640), - listOf(8u, 4u) to Rational(3737382679, 6858432), - listOf(0u, 5u) to Rational(-16959378721, 1890000), - listOf(1u, 5u) to Rational(-1864802244743, 79380000), - listOf(2u, 5u) to Rational(13449261536489, 666792000), - listOf(3u, 5u) to Rational(215272234137329, 2667168000), - listOf(4u, 5u) to Rational(6040691379277, 83349000), - listOf(5u, 5u) to Rational(153687143525887, 800150400), - listOf(6u, 5u) to Rational(475602854903563, 2400451200), - listOf(7u, 5u) to Rational(27315599358749, 640120320), - listOf(8u, 5u) to Rational(-2630413357, 10668672), - listOf(0u, 6u) to Rational(-6654999511, 2646000), - listOf(1u, 6u) to Rational(-67885252327, 15876000), - listOf(2u, 6u) to Rational(5786776220983, 2667168000), - listOf(3u, 6u) to Rational(60615922629083, 1143072000), - listOf(4u, 6u) to Rational(-34703539637627407, 672126336000), - listOf(5u, 6u) to Rational(-744694192134101, 2240421120), - listOf(6u, 6u) to Rational(-1782470617231, 14817600), - listOf(7u, 6u) to Rational(59123208433, 8890560), - listOf(8u, 6u) to Rational(-141653, 5292), - listOf(0u, 7u) to Rational(-338051969, 441000), - listOf(1u, 7u) to Rational(468850013, 1764000), - listOf(2u, 7u) to Rational(2102343426101, 222264000), - listOf(3u, 7u) to Rational(7836130602007, 1333584000), - listOf(4u, 7u) to Rational(16239111865997, 746807040), - listOf(5u, 7u) to Rational(3824649185383, 88905600), - listOf(6u, 7u) to Rational(56058614459, 3457440), - listOf(7u, 7u) to Rational(-396766339, 493920), - listOf(8u, 7u) to Rational(-165147, 2744), - listOf(0u, 8u) to Rational(-3088619, 58800), - listOf(1u, 8u) to Rational(155343347, 88200), - listOf(2u, 8u) to Rational(100098736469, 7408800), - listOf(3u, 8u) to Rational(109725511381, 7408800), - listOf(4u, 8u) to Rational(-2431199641013, 59270400), - listOf(5u, 8u) to Rational(-102872383249, 3457440), - listOf(6u, 8u) to Rational(1449461309, 576240), - listOf(7u, 8u) to Rational(812775, 1372), - listOf(8u, 8u) to Rational(-16461, 343) - ), - NumberedPolynomialAsIs( - listOf() to Rational(164202773, 230400), - listOf(1u) to Rational(-70345303, 518400), - listOf(2u) to Rational(-4229702731, 4665600), - listOf(3u) to Rational(3262171027, 6998400), - listOf(4u) to Rational(-25423104169, 13996800), - listOf(5u) to Rational(64061869, 349920), - listOf(6u) to Rational(-1655878091, 116640), - listOf(7u) to Rational(-7991441, 648), - listOf(8u) to Rational(-502591, 18), - listOf(0u, 1u) to Rational(-8780429, 3840), - listOf(1u, 1u) to Rational(434272361, 115200), - listOf(2u, 1u) to Rational(429825727, 41472), - listOf(3u, 1u) to Rational(-10066790339, 6998400), - listOf(4u, 1u) to Rational(70022035471, 20995200), - listOf(5u, 1u) to Rational(-32070283493, 1399680), - listOf(6u, 1u) to Rational(-22051101001, 1399680), - listOf(7u, 1u) to Rational(-126493427, 12960), - listOf(8u, 1u) to Rational(3050245, 864), - listOf(0u, 2u) to Rational(-1194654631, 345600), - listOf(1u, 2u) to Rational(-542961452671, 31104000), - listOf(2u, 2u) to Rational(-234000873607, 48988800), - listOf(3u, 2u) to Rational(140520538087, 3628800), - listOf(4u, 2u) to Rational(9215088876563, 130636800), - listOf(5u, 2u) to Rational(27590569647253, 293932800), - listOf(6u, 2u) to Rational(5129057792891, 97977600), - listOf(7u, 2u) to Rational(-106334191, 5103), - listOf(8u, 2u) to Rational(-1024113911, 435456), - listOf(0u, 3u) to Rational(76223843, 6000), - listOf(1u, 3u) to Rational(57425857357, 2592000), - listOf(2u, 3u) to Rational(-2044736497573, 46656000), - listOf(3u, 3u) to Rational(-26155810120031, 293932800), - listOf(4u, 3u) to Rational(-1064419459813, 6998400), - listOf(5u, 3u) to Rational(-753782018389, 4082400), - listOf(6u, 3u) to Rational(-291973360873, 2799360), - listOf(7u, 3u) to Rational(-46372122599, 816480), - listOf(8u, 3u) to Rational(3579859657, 653184), - listOf(0u, 4u) to Rational(-13374241901, 4320000), - listOf(1u, 4u) to Rational(306606499811, 54432000), - listOf(2u, 4u) to Rational(964267124745437, 13716864000), - listOf(3u, 4u) to Rational(21603809415373, 182891520), - listOf(4u, 4u) to Rational(1097860214654027, 6858432000), - listOf(5u, 4u) to Rational(161615254570669, 914457600), - listOf(6u, 4u) to Rational(758415239461, 22861440), - listOf(7u, 4u) to Rational(2585568355471, 274337280), - listOf(8u, 4u) to Rational(-70433747863, 9144576), - listOf(0u, 5u) to Rational(-9582586217, 2520000), - listOf(1u, 5u) to Rational(-19093471394171, 635040000), - listOf(2u, 5u) to Rational(-13010261944411, 381024000), - listOf(3u, 5u) to Rational(-259039825301861, 4572288000), - listOf(4u, 5u) to Rational(-305081119071079, 2286144000), - listOf(5u, 5u) to Rational(-1923114383311, 19595520), - listOf(6u, 5u) to Rational(-14181787253231, 228614400), - listOf(7u, 5u) to Rational(-3959584789, 4354560), - listOf(8u, 5u) to Rational(4691742523, 762048), - listOf(0u, 6u) to Rational(-588323437, 180000), - listOf(1u, 6u) to Rational(5952234691, 52920000), - listOf(2u, 6u) to Rational(21001851056959, 1088640000), - listOf(3u, 6u) to Rational(84668034357563, 2133734400), - listOf(4u, 6u) to Rational(2029754605811557, 25604812800), - listOf(5u, 6u) to Rational(11721216739823, 426746880), - listOf(6u, 6u) to Rational(-8275903187003, 2133734400), - listOf(7u, 6u) to Rational(-4730447299, 2540160), - listOf(8u, 6u) to Rational(-46069985, 21168), - listOf(0u, 7u) to Rational(-75711301, 117600), - listOf(1u, 7u) to Rational(32430417413, 7056000), - listOf(2u, 7u) to Rational(677988533153, 98784000), - listOf(3u, 7u) to Rational(-948417645827, 71124480), - listOf(4u, 7u) to Rational(-11320265215207, 711244800), - listOf(5u, 7u) to Rational(-676438627783, 50803200), - listOf(6u, 7u) to Rational(-7382274253, 1975680), - listOf(7u, 7u) to Rational(6505733, 2205), - listOf(8u, 7u) to Rational(450137, 882), - listOf(0u, 8u) to Rational(-8368253, 78400), - listOf(1u, 8u) to Rational(6833783, 117600), - listOf(2u, 8u) to Rational(4528971133, 5927040), - listOf(3u, 8u) to Rational(146252636617, 29635200), - listOf(4u, 8u) to Rational(8321882556889, 1659571200), - listOf(5u, 8u) to Rational(-4686033011, 1975680), - listOf(6u, 8u) to Rational(-1074445963, 987840), - listOf(7u, 8u) to Rational(-142313, 588), - listOf(8u, 8u) to Rational(-4281, 49) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(14, 4), - listOf(1u) to Rational(7, 6), - listOf(2u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-15, 2), - listOf(1u, 1u) to Rational(-13, 8), - listOf(2u, 1u) to Rational(-14, 3), - listOf(0u, 2u) to Rational(-7, 6), - listOf(1u, 2u) to Rational(7, 4), - listOf(2u, 2u) to Rational(9, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-7, 4), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(-16, 2), - listOf(0u, 1u) to Rational(-15, 5), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(5, 4), - listOf(0u, 2u) to Rational(-12, 5), - listOf(1u, 2u) to Rational(-18, 2), - listOf(2u, 2u) to Rational(6, 7), - ) - ), - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 8), - listOf(1u) to Rational(-12, 6), - listOf(2u) to Rational(7, 6), - listOf(0u, 1u) to Rational(-10, 4), - listOf(1u, 1u) to Rational(-7, 6), - listOf(2u, 1u) to Rational(8, 9), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-13, 4), - listOf(2u, 2u) to Rational(5, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(10, 6), - listOf(1u) to Rational(-18, 6), - listOf(2u) to Rational(5, 1), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(8, 4), - listOf(2u, 1u) to Rational(-4, 9), - listOf(0u, 2u) to Rational(-6, 5), - listOf(1u, 2u) to Rational(-15, 8), - listOf(2u, 2u) to Rational(-18, 5), - ) - ), - )), - "test 3'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(2303, 64), - listOf(1u) to Rational(31843, 192), - listOf(2u) to Rational(118891, 576), - listOf(3u) to Rational(94453, 168), - listOf(4u) to Rational(-179203, 1512), - listOf(5u) to Rational(-16979, 126), - listOf(6u) to Rational(-13499, 12), - listOf(0u, 1u) to Rational(-4767, 64), - listOf(1u, 1u) to Rational(-58689, 256), - listOf(2u, 1u) to Rational(-757333, 4032), - listOf(3u, 1u) to Rational(-4921205, 4032), - listOf(4u, 1u) to Rational(-2930815, 4032), - listOf(5u, 1u) to Rational(-398803, 1512), - listOf(6u, 1u) to Rational(18835, 36), - listOf(0u, 2u) to Rational(224101, 960), - listOf(1u, 2u) to Rational(9139699, 40320), - listOf(2u, 2u) to Rational(3848803, 5760), - listOf(3u, 2u) to Rational(93102371, 241920), - listOf(4u, 2u) to Rational(-65821229, 141120), - listOf(5u, 2u) to Rational(-15675899, 7056), - listOf(6u, 2u) to Rational(10459, 189), - listOf(0u, 3u) to Rational(2411, 16), - listOf(1u, 3u) to Rational(1294543, 10080), - listOf(2u, 3u) to Rational(-1740199, 1440), - listOf(3u, 3u) to Rational(-266994841, 282240), - listOf(4u, 3u) to Rational(-41261893, 211680), - listOf(5u, 3u) to Rational(1717357, 3528), - listOf(6u, 3u) to Rational(69, 14), - listOf(0u, 4u) to Rational(13231, 360), - listOf(1u, 4u) to Rational(4858831, 25200), - listOf(2u, 4u) to Rational(15565759, 75600), - listOf(3u, 4u) to Rational(-15583391, 35280), - listOf(4u, 4u) to Rational(-13345747, 11760), - listOf(5u, 4u) to Rational(140103, 686), - listOf(6u, 4u) to Rational(-765, 49) - ), - NumberedPolynomialAsIs( - listOf() to Rational(31409, 576), - listOf(1u) to Rational(-337099, 1728), - listOf(2u) to Rational(-211429, 1728), - listOf(3u) to Rational(-259241, 432), - listOf(4u) to Rational(-13777, 36), - listOf(5u) to Rational(-41389, 72), - listOf(6u) to Rational(-7679, 48), - listOf(0u, 1u) to Rational(-3269, 12), - listOf(1u, 1u) to Rational(629569, 864), - listOf(2u, 1u) to Rational(53867, 324), - listOf(3u, 1u) to Rational(2290577, 1728), - listOf(4u, 1u) to Rational(101507, 216), - listOf(5u, 1u) to Rational(213109, 288), - listOf(6u, 1u) to Rational(17927, 144), - listOf(0u, 2u) to Rational(314587, 1080), - listOf(1u, 2u) to Rational(-109771, 144), - listOf(2u, 2u) to Rational(-6469, 16), - listOf(3u, 2u) to Rational(-298291681, 181440), - listOf(4u, 2u) to Rational(-59147357, 48384), - listOf(5u, 2u) to Rational(-4982365, 6048), - listOf(6u, 2u) to Rational(-18727, 576), - listOf(0u, 3u) to Rational(12379, 90), - listOf(1u, 3u) to Rational(-542911, 1620), - listOf(2u, 3u) to Rational(143123, 1260), - listOf(3u, 3u) to Rational(9859177, 30240), - listOf(4u, 3u) to Rational(9312529, 20160), - listOf(5u, 3u) to Rational(207001, 672), - listOf(6u, 3u) to Rational(203, 24), - listOf(0u, 4u) to Rational(9442, 675), - listOf(1u, 4u) to Rational(-13729, 300), - listOf(2u, 4u) to Rational(-3490471, 25200), - listOf(3u, 4u) to Rational(-333031, 840), - listOf(4u, 4u) to Rational(-7572211, 47040), - listOf(5u, 4u) to Rational(-1189, 56), - listOf(6u, 4u) to Rational(-405, 196) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(14, 4), - listOf(1u) to Rational(7, 6), - listOf(2u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-15, 2), - listOf(1u, 1u) to Rational(-13, 8), - listOf(2u, 1u) to Rational(-14, 3), - listOf(0u, 2u) to Rational(-7, 6), - listOf(1u, 2u) to Rational(7, 4), - listOf(2u, 2u) to Rational(9, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-7, 4), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(-16, 2), - listOf(0u, 1u) to Rational(-15, 5), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(5, 4), - listOf(0u, 2u) to Rational(-12, 5), - listOf(1u, 2u) to Rational(-18, 2), - listOf(2u, 2u) to Rational(6, 7), - ) - ), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(2303, 64), - listOf(1u) to Rational(31843, 192), - listOf(2u) to Rational(118891, 576), - listOf(3u) to Rational(94453, 168), - listOf(4u) to Rational(-179203, 1512), - listOf(5u) to Rational(-16979, 126), - listOf(6u) to Rational(-13499, 12), - listOf(0u, 1u) to Rational(-4767, 64), - listOf(1u, 1u) to Rational(-58689, 256), - listOf(2u, 1u) to Rational(-757333, 4032), - listOf(3u, 1u) to Rational(-4921205, 4032), - listOf(4u, 1u) to Rational(-2930815, 4032), - listOf(5u, 1u) to Rational(-398803, 1512), - listOf(6u, 1u) to Rational(18835, 36), - listOf(0u, 2u) to Rational(224101, 960), - listOf(1u, 2u) to Rational(9139699, 40320), - listOf(2u, 2u) to Rational(3848803, 5760), - listOf(3u, 2u) to Rational(93102371, 241920), - listOf(4u, 2u) to Rational(-65821229, 141120), - listOf(5u, 2u) to Rational(-15675899, 7056), - listOf(6u, 2u) to Rational(10459, 189), - listOf(0u, 3u) to Rational(2411, 16), - listOf(1u, 3u) to Rational(1294543, 10080), - listOf(2u, 3u) to Rational(-1740199, 1440), - listOf(3u, 3u) to Rational(-266994841, 282240), - listOf(4u, 3u) to Rational(-41261893, 211680), - listOf(5u, 3u) to Rational(1717357, 3528), - listOf(6u, 3u) to Rational(69, 14), - listOf(0u, 4u) to Rational(13231, 360), - listOf(1u, 4u) to Rational(4858831, 25200), - listOf(2u, 4u) to Rational(15565759, 75600), - listOf(3u, 4u) to Rational(-15583391, 35280), - listOf(4u, 4u) to Rational(-13345747, 11760), - listOf(5u, 4u) to Rational(140103, 686), - listOf(6u, 4u) to Rational(-765, 49) - ), - NumberedPolynomialAsIs( - listOf() to Rational(31409, 576), - listOf(1u) to Rational(-337099, 1728), - listOf(2u) to Rational(-211429, 1728), - listOf(3u) to Rational(-259241, 432), - listOf(4u) to Rational(-13777, 36), - listOf(5u) to Rational(-41389, 72), - listOf(6u) to Rational(-7679, 48), - listOf(0u, 1u) to Rational(-3269, 12), - listOf(1u, 1u) to Rational(629569, 864), - listOf(2u, 1u) to Rational(53867, 324), - listOf(3u, 1u) to Rational(2290577, 1728), - listOf(4u, 1u) to Rational(101507, 216), - listOf(5u, 1u) to Rational(213109, 288), - listOf(6u, 1u) to Rational(17927, 144), - listOf(0u, 2u) to Rational(314587, 1080), - listOf(1u, 2u) to Rational(-109771, 144), - listOf(2u, 2u) to Rational(-6469, 16), - listOf(3u, 2u) to Rational(-298291681, 181440), - listOf(4u, 2u) to Rational(-59147357, 48384), - listOf(5u, 2u) to Rational(-4982365, 6048), - listOf(6u, 2u) to Rational(-18727, 576), - listOf(0u, 3u) to Rational(12379, 90), - listOf(1u, 3u) to Rational(-542911, 1620), - listOf(2u, 3u) to Rational(143123, 1260), - listOf(3u, 3u) to Rational(9859177, 30240), - listOf(4u, 3u) to Rational(9312529, 20160), - listOf(5u, 3u) to Rational(207001, 672), - listOf(6u, 3u) to Rational(203, 24), - listOf(0u, 4u) to Rational(9442, 675), - listOf(1u, 4u) to Rational(-13729, 300), - listOf(2u, 4u) to Rational(-3490471, 25200), - listOf(3u, 4u) to Rational(-333031, 840), - listOf(4u, 4u) to Rational(-7572211, 47040), - listOf(5u, 4u) to Rational(-1189, 56), - listOf(6u, 4u) to Rational(-405, 196) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 1 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(14, 4), - listOf(1u) to Rational(7, 6), - listOf(2u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-15, 2), - listOf(1u, 1u) to Rational(-13, 8), - listOf(2u, 1u) to Rational(-14, 3), - listOf(0u, 2u) to Rational(-7, 6), - listOf(1u, 2u) to Rational(7, 4), - listOf(2u, 2u) to Rational(9, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-7, 4), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(-16, 2), - listOf(0u, 1u) to Rational(-15, 5), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(5, 4), - listOf(0u, 2u) to Rational(-12, 5), - listOf(1u, 2u) to Rational(-18, 2), - listOf(2u, 2u) to Rational(6, 7), - ) - ), - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 8), - listOf(1u) to Rational(-12, 6), - listOf(2u) to Rational(7, 6), - listOf(0u, 1u) to Rational(-10, 4), - listOf(1u, 1u) to Rational(-7, 6), - listOf(2u, 1u) to Rational(8, 9), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-13, 4), - listOf(2u, 2u) to Rational(5, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(10, 6), - listOf(1u) to Rational(-18, 6), - listOf(2u) to Rational(5, 1), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(8, 4), - listOf(2u, 1u) to Rational(-4, 9), - listOf(0u, 2u) to Rational(-6, 5), - listOf(1u, 2u) to Rational(-15, 8), - listOf(2u, 2u) to Rational(-18, 5), - ) - ), - )), - "test 4'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-506213, 2800), - listOf(1u) to Rational(9859, 315), - listOf(2u) to Rational(17384377, 11340), - listOf(3u) to Rational(-9662, 63), - listOf(4u) to Rational(-12563, 4), - listOf(0u, 1u) to Rational(-486293, 22400), - listOf(1u, 1u) to Rational(-6530947, 25200), - listOf(2u, 1u) to Rational(866125, 18144), - listOf(3u, 1u) to Rational(2948747, 2520), - listOf(4u, 1u) to Rational(1196611, 2016), - listOf(0u, 2u) to Rational(-20266021, 117600), - listOf(1u, 2u) to Rational(26656339, 44100), - listOf(2u, 2u) to Rational(19499183, 18144), - listOf(3u, 2u) to Rational(-19801849, 7560), - listOf(4u, 2u) to Rational(-2639635, 1296), - listOf(0u, 3u) to Rational(-5017697, 29400), - listOf(1u, 3u) to Rational(-606007, 1575), - listOf(2u, 3u) to Rational(127494487, 132300), - listOf(3u, 3u) to Rational(166567, 105), - listOf(4u, 3u) to Rational(486403, 18144), - listOf(0u, 4u) to Rational(-32182, 735), - listOf(1u, 4u) to Rational(2420671, 8820), - listOf(2u, 4u) to Rational(-12619193, 26460), - listOf(3u, 4u) to Rational(-6823067, 5670), - listOf(4u, 4u) to Rational(-2311693, 13608), - listOf(0u, 5u) to Rational(-13324, 245), - listOf(1u, 5u) to Rational(1966, 35), - listOf(2u, 5u) to Rational(1052719, 2520), - listOf(3u, 5u) to Rational(19153, 270), - listOf(4u, 5u) to Rational(701, 54), - listOf(0u, 6u) to Rational(4647, 196), - listOf(1u, 6u) to Rational(2197, 28), - listOf(2u, 6u) to Rational(-43853, 336), - listOf(3u, 6u) to Rational(-301, 3), - listOf(4u, 6u) to Rational(34, 3) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2843, 1600), - listOf(1u) to Rational(-1483, 240), - listOf(2u) to Rational(110623, 1296), - listOf(3u) to Rational(1265, 72), - listOf(4u) to Rational(-5011, 16), - listOf(0u, 1u) to Rational(47743, 1800), - listOf(1u, 1u) to Rational(619229, 32400), - listOf(2u, 1u) to Rational(-5978369, 58320), - listOf(3u, 1u) to Rational(-86081, 1620), - listOf(4u, 1u) to Rational(6325, 72), - listOf(0u, 2u) to Rational(110951, 3360), - listOf(1u, 2u) to Rational(-9550649, 302400), - listOf(2u, 2u) to Rational(6542933, 85050), - listOf(3u, 2u) to Rational(4708291, 38880), - listOf(4u, 2u) to Rational(-433327, 1296), - listOf(0u, 3u) to Rational(56143, 600), - listOf(1u, 3u) to Rational(94243, 720), - listOf(2u, 3u) to Rational(-46779139, 226800), - listOf(3u, 3u) to Rational(-6948253, 12960), - listOf(4u, 3u) to Rational(-260261, 486), - listOf(0u, 4u) to Rational(-3205317, 19600), - listOf(1u, 4u) to Rational(-201253, 1050), - listOf(2u, 4u) to Rational(332192677, 302400), - listOf(3u, 4u) to Rational(351511, 360), - listOf(4u, 4u) to Rational(-40547, 81), - listOf(0u, 5u) to Rational(-65421, 1960), - listOf(1u, 5u) to Rational(-10118, 35), - listOf(2u, 5u) to Rational(-4341709, 10080), - listOf(3u, 5u) to Rational(-91703, 360), - listOf(4u, 5u) to Rational(-85, 9), - listOf(0u, 6u) to Rational(-25965, 784), - listOf(1u, 6u) to Rational(3351, 16), - listOf(2u, 6u) to Rational(595159, 1344), - listOf(3u, 6u) to Rational(-1381, 12), - listOf(4u, 6u) to Rational(-155, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - )), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-506213, 2800), - listOf(1u) to Rational(9859, 315), - listOf(2u) to Rational(17384377, 11340), - listOf(3u) to Rational(-9662, 63), - listOf(4u) to Rational(-12563, 4), - listOf(0u, 1u) to Rational(-486293, 22400), - listOf(1u, 1u) to Rational(-6530947, 25200), - listOf(2u, 1u) to Rational(866125, 18144), - listOf(3u, 1u) to Rational(2948747, 2520), - listOf(4u, 1u) to Rational(1196611, 2016), - listOf(0u, 2u) to Rational(-20266021, 117600), - listOf(1u, 2u) to Rational(26656339, 44100), - listOf(2u, 2u) to Rational(19499183, 18144), - listOf(3u, 2u) to Rational(-19801849, 7560), - listOf(4u, 2u) to Rational(-2639635, 1296), - listOf(0u, 3u) to Rational(-5017697, 29400), - listOf(1u, 3u) to Rational(-606007, 1575), - listOf(2u, 3u) to Rational(127494487, 132300), - listOf(3u, 3u) to Rational(166567, 105), - listOf(4u, 3u) to Rational(486403, 18144), - listOf(0u, 4u) to Rational(-32182, 735), - listOf(1u, 4u) to Rational(2420671, 8820), - listOf(2u, 4u) to Rational(-12619193, 26460), - listOf(3u, 4u) to Rational(-6823067, 5670), - listOf(4u, 4u) to Rational(-2311693, 13608), - listOf(0u, 5u) to Rational(-13324, 245), - listOf(1u, 5u) to Rational(1966, 35), - listOf(2u, 5u) to Rational(1052719, 2520), - listOf(3u, 5u) to Rational(19153, 270), - listOf(4u, 5u) to Rational(701, 54), - listOf(0u, 6u) to Rational(4647, 196), - listOf(1u, 6u) to Rational(2197, 28), - listOf(2u, 6u) to Rational(-43853, 336), - listOf(3u, 6u) to Rational(-301, 3), - listOf(4u, 6u) to Rational(34, 3) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2843, 1600), - listOf(1u) to Rational(-1483, 240), - listOf(2u) to Rational(110623, 1296), - listOf(3u) to Rational(1265, 72), - listOf(4u) to Rational(-5011, 16), - listOf(0u, 1u) to Rational(47743, 1800), - listOf(1u, 1u) to Rational(619229, 32400), - listOf(2u, 1u) to Rational(-5978369, 58320), - listOf(3u, 1u) to Rational(-86081, 1620), - listOf(4u, 1u) to Rational(6325, 72), - listOf(0u, 2u) to Rational(110951, 3360), - listOf(1u, 2u) to Rational(-9550649, 302400), - listOf(2u, 2u) to Rational(6542933, 85050), - listOf(3u, 2u) to Rational(4708291, 38880), - listOf(4u, 2u) to Rational(-433327, 1296), - listOf(0u, 3u) to Rational(56143, 600), - listOf(1u, 3u) to Rational(94243, 720), - listOf(2u, 3u) to Rational(-46779139, 226800), - listOf(3u, 3u) to Rational(-6948253, 12960), - listOf(4u, 3u) to Rational(-260261, 486), - listOf(0u, 4u) to Rational(-3205317, 19600), - listOf(1u, 4u) to Rational(-201253, 1050), - listOf(2u, 4u) to Rational(332192677, 302400), - listOf(3u, 4u) to Rational(351511, 360), - listOf(4u, 4u) to Rational(-40547, 81), - listOf(0u, 5u) to Rational(-65421, 1960), - listOf(1u, 5u) to Rational(-10118, 35), - listOf(2u, 5u) to Rational(-4341709, 10080), - listOf(3u, 5u) to Rational(-91703, 360), - listOf(4u, 5u) to Rational(-85, 9), - listOf(0u, 6u) to Rational(-25965, 784), - listOf(1u, 6u) to Rational(3351, 16), - listOf(2u, 6u) to Rational(595159, 1344), - listOf(3u, 6u) to Rational(-1381, 12), - listOf(4u, 6u) to Rational(-155, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 0 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 8), - listOf(1u) to Rational(-12, 6), - listOf(2u) to Rational(7, 6), - listOf(0u, 1u) to Rational(-10, 4), - listOf(1u, 1u) to Rational(-7, 6), - listOf(2u, 1u) to Rational(8, 9), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-13, 4), - listOf(2u, 2u) to Rational(5, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(10, 6), - listOf(1u) to Rational(-18, 6), - listOf(2u) to Rational(5, 1), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(8, 4), - listOf(2u, 1u) to Rational(-4, 9), - listOf(0u, 2u) to Rational(-6, 5), - listOf(1u, 2u) to Rational(-15, 8), - listOf(2u, 2u) to Rational(-18, 5), - ) - ), - )), - "test 5'" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf>()), - "test 6" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, mapOf( - 5 to NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 8), - listOf(1u) to Rational(-12, 6), - listOf(2u) to Rational(7, 6), - listOf(0u, 1u) to Rational(-10, 4), - listOf(1u, 1u) to Rational(-7, 6), - listOf(2u, 1u) to Rational(8, 9), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-13, 4), - listOf(2u, 2u) to Rational(5, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(10, 6), - listOf(1u) to Rational(-18, 6), - listOf(2u) to Rational(5, 1), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(8, 4), - listOf(2u, 1u) to Rational(-4, 9), - listOf(0u, 2u) to Rational(-6, 5), - listOf(1u, 2u) to Rational(-15, 8), - listOf(2u, 2u) to Rational(-18, 5), - ) - ), - )), - "test 6'" - ) - } - @Test - fun test_Polynomial_substitute_Double_Buffer() { - assertEquals( - NumberedPolynomialAsIs(emptyList() to 0.0), - NumberedPolynomialAsIs( - listOf() to 1.0, - listOf(1u) to -2.0, - listOf(2u) to 1.0, - ).substitute(bufferOf( - 1.0 - )), - 0.001, - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(bufferOf()), - 0.001, - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(0u, 1u) to 0.4561746111587508, - listOf(0u, 2u) to 0.2700930201481795, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(bufferOf( - 0.0, - )), - 0.001, - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.047895694399743, - listOf(0u, 1u) to 0.859913883275481, - listOf(0u, 2u) to 0.2327806735363575, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(bufferOf( - 0.4846192734143442, - )), - 0.001, - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.934530767358133, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(bufferOf( - 0.4846192734143442, - 0.8400458576651112, - )), - 0.001, - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.934530767358133, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(bufferOf( - 0.4846192734143442, - 0.8400458576651112, - 0.9211194782050933 - )), - 0.001, - "test 6" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to 1.934530767358133, - ), - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substitute(bufferOf( - 0.4846192734143442, - 0.8400458576651112, - 0.9211194782050933, - 0.4752854632152105 - )), - 0.001, - "test 7" - ) - } - @Test - fun test_Polynomial_substitute_Constant_Buffer() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substitute(RationalField, bufferOf( - Rational(1) - )), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf()), - "test 2" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-83, 50), - listOf(0u, 1u) to Rational(29, 25), - listOf(0u, 2u) to Rational(3, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - Rational(-2, 5), - )), - "test 3" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(143, 150) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - Rational(-2, 5), - Rational(12, 9), - )), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(143, 150) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - Rational(-2, 5), - Rational(12, 9), - Rational(57, 179), - )), - "test 5" - ) - // https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(47639065216, 2562890625) - ), - NumberedPolynomialAsIs( - listOf(8u) to Rational(-3, 2), - listOf(7u, 1u) to Rational(8, 6), - listOf(6u, 2u) to Rational(14, 6), - listOf(5u, 3u) to Rational(-3, 1), - listOf(4u, 4u) to Rational(-19, 2), - listOf(3u, 5u) to Rational(9, 4), - listOf(2u, 6u) to Rational(5, 5), - listOf(1u, 7u) to Rational(18, 9), - listOf(0u, 8u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - Rational(-2, 5), - Rational(12, 9), - )), - "test 6" - ) - } - @Test - fun test_Polynomial_substitute_Polynomial_Buffer() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - )), - "test 1" - ) - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-5%2F1+s+%2B+2%2F8+t%2C+y+%3D+11%2F7+t - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(0u, 1u) to Rational(-92, 21), - listOf(0u, 2u) to Rational(-2627, 2352), - listOf(0u, 3u) to Rational(4565, 3136), - listOf(0u, 4u) to Rational(605, 1568), - listOf(1u) to Rational(-20, 3), - listOf(1u, 1u) to Rational(1445, 21), - listOf(1u, 2u) to Rational(-13145, 392), - listOf(1u, 3u) to Rational(-3025, 196), - listOf(2u) to Rational(175, 3), - listOf(2u, 1u) to Rational(2475, 28), - listOf(2u, 2u) to Rational(15125, 98), - listOf(3u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf(1u) to Rational(-5, 1), - listOf(0u, 1u) to Rational(2, 8), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(0, 5), - listOf(0u, 1u) to Rational(11, 7), - ), - )), - "test 2" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = (0/6 + 14/8 s + -14/2 s^2) + (-3/5 + 11/1 s + 3/7 s^2) t + (-3/7 + -18/5 s + -9/1 s^2) t^2, y = (-9/2 + 2/7 s + 9/1 s^2) + (13/1 + -1/8 s + 2/8 s^2) t + (19/4 + 15/7 s + -19/4 s^2) t^2 - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(129, 4), - listOf(1u) to Rational(48583, 336), - listOf(2u) to Rational(-913477, 1568), - listOf(3u) to Rational(-967567, 672), - listOf(4u) to Rational(4722043, 1344), - listOf(5u) to Rational(8855, 2), - listOf(6u) to Rational(-311971, 32), - listOf(7u) to Rational(-17325, 4), - listOf(8u) to Rational(19845, 2), - listOf(0u, 1u) to Rational(-827, 4), - listOf(1u, 1u) to Rational(191927, 840), - listOf(2u, 1u) to Rational(9592627, 2352), - listOf(3u, 1u) to Rational(-105400711, 53760), - listOf(4u, 1u) to Rational(-10054101459, 439040), - listOf(5u, 1u) to Rational(2127351, 128), - listOf(6u, 1u) to Rational(116680973, 3136), - listOf(7u, 1u) to Rational(-220445, 7), - listOf(8u, 1u) to Rational(-2655, 4), - listOf(0u, 2u) to Rational(30567, 100), - listOf(1u, 2u) to Rational(-156284953, 39200), - listOf(2u, 2u) to Rational(-57661541711, 6585600), - listOf(3u, 2u) to Rational(131931579, 3136), - listOf(4u, 2u) to Rational(98818124791, 3512320), - listOf(5u, 2u) to Rational(-94458855053, 878080), - listOf(6u, 2u) to Rational(13937705305, 1229312), - listOf(7u, 2u) to Rational(335706887, 21952), - listOf(8u, 2u) to Rational(23549165, 1568), - listOf(0u, 3u) to Rational(111367, 1400), - listOf(1u, 3u) to Rational(4937369, 700), - listOf(2u, 3u) to Rational(-4449423711, 274400), - listOf(3u, 3u) to Rational(-351873325703, 4390400), - listOf(4u, 3u) to Rational(23495875029, 307328), - listOf(5u, 3u) to Rational(17576300919, 878080), - listOf(6u, 3u) to Rational(230316993, 12544), - listOf(7u, 3u) to Rational(-191130515, 21952), - listOf(8u, 3u) to Rational(332435, 392), - listOf(0u, 4u) to Rational(-275084, 1225), - listOf(1u, 4u) to Rational(-266774603, 137200), - listOf(2u, 4u) to Rational(2176279167121, 30732800), - listOf(3u, 4u) to Rational(10904913303, 2195200), - listOf(4u, 4u) to Rational(-10769286147, 2195200), - listOf(5u, 4u) to Rational(-26277119793, 439040), - listOf(6u, 4u) to Rational(25859735869, 6146560), - listOf(7u, 4u) to Rational(38906289, 2744), - listOf(8u, 4u) to Rational(-3072025, 392), - listOf(0u, 5u) to Rational(9573, 98), - listOf(1u, 5u) to Rational(-4154651399, 548800), - listOf(2u, 5u) to Rational(3446069019, 548800), - listOf(3u, 5u) to Rational(-7851500623, 137200), - listOf(4u, 5u) to Rational(-53205142903, 1920800), - listOf(5u, 5u) to Rational(-31953611, 3430), - listOf(6u, 5u) to Rational(1447380313, 109760), - listOf(7u, 5u) to Rational(764158625, 21952), - listOf(8u, 5u) to Rational(1153515, 784), - listOf(0u, 6u) to Rational(1722351, 7840), - listOf(1u, 6u) to Rational(-164554821, 109760), - listOf(2u, 6u) to Rational(-79096147243, 7683200), - listOf(3u, 6u) to Rational(-624721089, 15680), - listOf(4u, 6u) to Rational(11147305567, 548800), - listOf(5u, 6u) to Rational(8318333679, 109760), - listOf(6u, 6u) to Rational(32981871553, 1536640), - listOf(7u, 6u) to Rational(-225359619, 21952), - listOf(8u, 6u) to Rational(-3973995, 392), - listOf(0u, 7u) to Rational(67203, 784), - listOf(1u, 7u) to Rational(39281469, 54880), - listOf(2u, 7u) to Rational(70162551, 27440), - listOf(3u, 7u) to Rational(413630709, 54880), - listOf(4u, 7u) to Rational(4640410269, 192080), - listOf(5u, 7u) to Rational(802712247, 54880), - listOf(6u, 7u) to Rational(-473517603, 27440), - listOf(7u, 7u) to Rational(-17055459, 1568), - listOf(8u, 7u) to Rational(-12825, 14), - listOf(0u, 8u) to Rational(16245, 1568), - listOf(1u, 8u) to Rational(503253, 2744), - listOf(2u, 8u) to Rational(125292591, 96040), - listOf(3u, 8u) to Rational(12033171, 2744), - listOf(4u, 8u) to Rational(154352673, 27440), - listOf(5u, 8u) to Rational(-1302291, 392), - listOf(6u, 8u) to Rational(-20265741, 1960), - listOf(7u, 8u) to Rational(-26163, 56), - listOf(8u, 8u) to Rational(146205, 32), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-9, 2), - listOf(1u) to Rational(2, 7), - listOf(2u) to Rational(9, 1), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-1, 8), - listOf(2u, 1u) to Rational(2, 8), - listOf(0u, 2u) to Rational(19, 4), - listOf(1u, 2u) to Rational(15, 7), - listOf(2u, 2u) to Rational(-19, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 3), - listOf(1u) to Rational(5, 2), - listOf(2u) to Rational(13, 7), - listOf(0u, 1u) to Rational(16, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(6, 1), - listOf(0u, 2u) to Rational(-14, 3), - listOf(1u, 2u) to Rational(-2, 7), - listOf(2u, 2u) to Rational(-10, 8), - ) - )), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(129, 4), - listOf(1u) to Rational(48583, 336), - listOf(2u) to Rational(-913477, 1568), - listOf(3u) to Rational(-967567, 672), - listOf(4u) to Rational(4722043, 1344), - listOf(5u) to Rational(8855, 2), - listOf(6u) to Rational(-311971, 32), - listOf(7u) to Rational(-17325, 4), - listOf(8u) to Rational(19845, 2), - listOf(0u, 1u) to Rational(-827, 4), - listOf(1u, 1u) to Rational(191927, 840), - listOf(2u, 1u) to Rational(9592627, 2352), - listOf(3u, 1u) to Rational(-105400711, 53760), - listOf(4u, 1u) to Rational(-10054101459, 439040), - listOf(5u, 1u) to Rational(2127351, 128), - listOf(6u, 1u) to Rational(116680973, 3136), - listOf(7u, 1u) to Rational(-220445, 7), - listOf(8u, 1u) to Rational(-2655, 4), - listOf(0u, 2u) to Rational(30567, 100), - listOf(1u, 2u) to Rational(-156284953, 39200), - listOf(2u, 2u) to Rational(-57661541711, 6585600), - listOf(3u, 2u) to Rational(131931579, 3136), - listOf(4u, 2u) to Rational(98818124791, 3512320), - listOf(5u, 2u) to Rational(-94458855053, 878080), - listOf(6u, 2u) to Rational(13937705305, 1229312), - listOf(7u, 2u) to Rational(335706887, 21952), - listOf(8u, 2u) to Rational(23549165, 1568), - listOf(0u, 3u) to Rational(111367, 1400), - listOf(1u, 3u) to Rational(4937369, 700), - listOf(2u, 3u) to Rational(-4449423711, 274400), - listOf(3u, 3u) to Rational(-351873325703, 4390400), - listOf(4u, 3u) to Rational(23495875029, 307328), - listOf(5u, 3u) to Rational(17576300919, 878080), - listOf(6u, 3u) to Rational(230316993, 12544), - listOf(7u, 3u) to Rational(-191130515, 21952), - listOf(8u, 3u) to Rational(332435, 392), - listOf(0u, 4u) to Rational(-275084, 1225), - listOf(1u, 4u) to Rational(-266774603, 137200), - listOf(2u, 4u) to Rational(2176279167121, 30732800), - listOf(3u, 4u) to Rational(10904913303, 2195200), - listOf(4u, 4u) to Rational(-10769286147, 2195200), - listOf(5u, 4u) to Rational(-26277119793, 439040), - listOf(6u, 4u) to Rational(25859735869, 6146560), - listOf(7u, 4u) to Rational(38906289, 2744), - listOf(8u, 4u) to Rational(-3072025, 392), - listOf(0u, 5u) to Rational(9573, 98), - listOf(1u, 5u) to Rational(-4154651399, 548800), - listOf(2u, 5u) to Rational(3446069019, 548800), - listOf(3u, 5u) to Rational(-7851500623, 137200), - listOf(4u, 5u) to Rational(-53205142903, 1920800), - listOf(5u, 5u) to Rational(-31953611, 3430), - listOf(6u, 5u) to Rational(1447380313, 109760), - listOf(7u, 5u) to Rational(764158625, 21952), - listOf(8u, 5u) to Rational(1153515, 784), - listOf(0u, 6u) to Rational(1722351, 7840), - listOf(1u, 6u) to Rational(-164554821, 109760), - listOf(2u, 6u) to Rational(-79096147243, 7683200), - listOf(3u, 6u) to Rational(-624721089, 15680), - listOf(4u, 6u) to Rational(11147305567, 548800), - listOf(5u, 6u) to Rational(8318333679, 109760), - listOf(6u, 6u) to Rational(32981871553, 1536640), - listOf(7u, 6u) to Rational(-225359619, 21952), - listOf(8u, 6u) to Rational(-3973995, 392), - listOf(0u, 7u) to Rational(67203, 784), - listOf(1u, 7u) to Rational(39281469, 54880), - listOf(2u, 7u) to Rational(70162551, 27440), - listOf(3u, 7u) to Rational(413630709, 54880), - listOf(4u, 7u) to Rational(4640410269, 192080), - listOf(5u, 7u) to Rational(802712247, 54880), - listOf(6u, 7u) to Rational(-473517603, 27440), - listOf(7u, 7u) to Rational(-17055459, 1568), - listOf(8u, 7u) to Rational(-12825, 14), - listOf(0u, 8u) to Rational(16245, 1568), - listOf(1u, 8u) to Rational(503253, 2744), - listOf(2u, 8u) to Rational(125292591, 96040), - listOf(3u, 8u) to Rational(12033171, 2744), - listOf(4u, 8u) to Rational(154352673, 27440), - listOf(5u, 8u) to Rational(-1302291, 392), - listOf(6u, 8u) to Rational(-20265741, 1960), - listOf(7u, 8u) to Rational(-26163, 56), - listOf(8u, 8u) to Rational(146205, 32), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-9, 2), - listOf(1u) to Rational(2, 7), - listOf(2u) to Rational(9, 1), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-1, 8), - listOf(2u, 1u) to Rational(2, 8), - listOf(0u, 2u) to Rational(19, 4), - listOf(1u, 2u) to Rational(15, 7), - listOf(2u, 2u) to Rational(-19, 4), - ), - )), - "test 4" - ) - // (-3/2 + 8/6 x + 14/6 x^2) + (-3/1 + -19/2 x + 9/4 x^2) y + (5/5 + 18/9 x + 5/2 x^2) y^2 where x = (0/6 + 14/8 s + -14/2 s^2) + (-3/5 + 11/1 s + 3/7 s^2) t + (-3/7 + -18/5 s + -9/1 s^2) t^2, y = t - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(7, 3), - listOf(2u) to Rational(-35, 16), - listOf(3u) to Rational(-343, 6), - listOf(4u) to Rational(343, 3), - listOf(0u, 1u) to Rational(-19, 5), - listOf(1u, 1u) to Rational(-823, 120), - listOf(2u, 1u) to Rational(1232417, 6720), - listOf(3u, 1u) to Rational(-9863, 24), - listOf(4u, 1u) to Rational(385, 4), - listOf(0u, 2u) to Rational(2439, 350), - listOf(1u, 2u) to Rational(-5793, 40), - listOf(2u, 2u) to Rational(1172113, 3360), - listOf(3u, 2u) to Rational(-13531, 40), - listOf(4u, 2u) to Rational(2824, 7), - listOf(0u, 3u) to Rational(3417, 700), - listOf(1u, 3u) to Rational(1191, 200), - listOf(2u, 3u) to Rational(8383, 28), - listOf(3u, 3u) to Rational(-220279, 280), - listOf(4u, 3u) to Rational(49179, 196), - listOf(0u, 4u) to Rational(57, 35), - listOf(1u, 4u) to Rational(-33771, 700), - listOf(2u, 4u) to Rational(196279, 1225), - listOf(3u, 4u) to Rational(-32259, 140), - listOf(4u, 4u) to Rational(23868, 49), - listOf(0u, 5u) to Rational(333, 196), - listOf(1u, 5u) to Rational(-204, 35), - listOf(2u, 5u) to Rational(-307233, 2450), - listOf(3u, 5u) to Rational(-12492, 35), - listOf(4u, 5u) to Rational(4563, 28), - listOf(0u, 6u) to Rational(45, 98), - listOf(1u, 6u) to Rational(54, 7), - listOf(2u, 6u) to Rational(1809, 35), - listOf(3u, 6u) to Rational(162), - listOf(4u, 6u) to Rational(405, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(0, 6), - listOf(1u) to Rational(14, 8), - listOf(2u) to Rational(-14, 2), - listOf(0u, 1u) to Rational(-3, 5), - listOf(1u, 1u) to Rational(11, 1), - listOf(2u, 1u) to Rational(3, 7), - listOf(0u, 2u) to Rational(-3, 7), - listOf(1u, 2u) to Rational(-18, 5), - listOf(2u, 2u) to Rational(-9, 1), - ), - )), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substitute(RationalField, bufferOf>()), - "test 6" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_Polynomial_substitute_RationalFunction_Buffer() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(4u) to Rational(-194071, 4900), - listOf(3u, 1u) to Rational(394811, 225), - listOf(2u, 2u) to Rational(-444183161, 66150), - listOf(1u, 3u) to Rational(70537618, 59535), - listOf(0u, 4u) to Rational(9655504, 2835), - ), - NumberedPolynomialAsIs( - listOf(4u) to Rational(9, 1), - listOf(3u, 1u) to Rational(61, 1), - listOf(2u, 2u) to Rational(2137, 36), - listOf(1u, 3u) to Rational(-1342, 9), - listOf(0u, 4u) to Rational(484, 9), - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(17, 7), - listOf(0u, 1u) to Rational(-13, 1), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(-18, 6), - listOf(0u, 1u) to Rational(11, 6), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(18, 5), - listOf(0u, 1u) to Rational(-16, 3), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(-1, 1), - listOf(0u, 1u) to Rational(-4, 1), - ) - ), - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-6443599, 10000), - listOf(1u) to Rational(166251223, 210000), - listOf(2u) to Rational(-4606805099, 3528000), - listOf(3u) to Rational(51204379, 19600), - listOf(4u) to Rational(-529045460659, 277830000), - listOf(5u) to Rational(2630836709, 1488375), - listOf(6u) to Rational(-42675691369, 25004700), - listOf(7u) to Rational(495825223, 1250235), - listOf(8u) to Rational(-22531756, 1750329), - listOf(0u, 1u) to Rational(-2526552797, 420000), - listOf(1u, 1u) to Rational(31108840471, 2520000), - listOf(2u, 1u) to Rational(-4789740847, 1102500), - listOf(3u, 1u) to Rational(186594307807, 11340000), - listOf(4u, 1u) to Rational(-11677815943, 1488375), - listOf(5u, 1u) to Rational(-181118486447, 27783000), - listOf(6u, 1u) to Rational(-16123292162, 14586075), - listOf(7u, 1u) to Rational(-140339343808, 26254935), - listOf(8u, 1u) to Rational(4570171616, 5250987), - listOf(0u, 2u) to Rational(-181436530573, 10080000), - listOf(1u, 2u) to Rational(6700437957491, 105840000), - listOf(2u, 2u) to Rational(-3527267461, 1417500), - listOf(3u, 2u) to Rational(-38084563451, 5556600), - listOf(4u, 2u) to Rational(-565662040631, 13891500), - listOf(5u, 2u) to Rational(-35479071126397, 583443000), - listOf(6u, 2u) to Rational(-11717559078469, 525098700), - listOf(7u, 2u) to Rational(-2043385293517, 225042300), - listOf(8u, 2u) to Rational(-3644439630451, 551353635), - listOf(0u, 3u) to Rational(-1760423269, 126000), - listOf(1u, 3u) to Rational(310176758299, 2352000), - listOf(2u, 3u) to Rational(-907229584837, 21168000), - listOf(3u, 3u) to Rational(-16717135885963, 95256000), - listOf(4u, 3u) to Rational(-43762928025353, 333396000), - listOf(5u, 3u) to Rational(-328427480571607, 3000564000), - listOf(6u, 3u) to Rational(-7722675917197, 210039480), - listOf(7u, 3u) to Rational(1713350137019, 1225230300), - listOf(8u, 3u) to Rational(156695935643, 31505922), - listOf(0u, 4u) to Rational(18362364269, 1008000), - listOf(1u, 4u) to Rational(955674858553, 10584000), - listOf(2u, 4u) to Rational(-71937470607371, 444528000), - listOf(3u, 4u) to Rational(-34097985615163, 95256000), - listOf(4u, 4u) to Rational(-340736178775883, 2000376000), - listOf(5u, 4u) to Rational(-511324523441897, 10501974000), - listOf(6u, 4u) to Rational(-125375649409151, 8821658160), - listOf(7u, 4u) to Rational(-2813518533421, 1575296100), - listOf(8u, 4u) to Rational(-17044089109, 5250987), - listOf(0u, 5u) to Rational(600086461, 20160), - listOf(1u, 5u) to Rational(-18959931367, 423360), - listOf(2u, 5u) to Rational(-9178804929607, 44452800), - listOf(3u, 5u) to Rational(-1460114275979, 5334336), - listOf(4u, 5u) to Rational(-342533479090169, 4200789600), - listOf(5u, 5u) to Rational(20335453022963, 4200789600), - listOf(6u, 5u) to Rational(-21649775090197, 6301184400), - listOf(7u, 5u) to Rational(-197301716069, 131274675), - listOf(8u, 5u) to Rational(18711357470, 15752961), - listOf(0u, 6u) to Rational(621417991, 100800), - listOf(1u, 6u) to Rational(-159236792977, 2116800), - listOf(2u, 6u) to Rational(-6602528890883, 66679200), - listOf(3u, 6u) to Rational(-1086091664047, 19051200), - listOf(4u, 6u) to Rational(3769375009003, 1680315840), - listOf(5u, 6u) to Rational(-12920385574769, 1050197400), - listOf(6u, 6u) to Rational(-90219591809287, 6301184400), - listOf(7u, 6u) to Rational(656361553391, 1575296100), - listOf(8u, 6u) to Rational(757900793, 2250423), - listOf(0u, 7u) to Rational(-100770017, 15120), - listOf(1u, 7u) to Rational(-316364851, 17640), - listOf(2u, 7u) to Rational(-85118560057, 6667920), - listOf(3u, 7u) to Rational(6286563719, 416745), - listOf(4u, 7u) to Rational(26803885301, 1714608), - listOf(5u, 7u) to Rational(-13767154393, 4286520), - listOf(6u, 7u) to Rational(-3875138933, 1224720), - listOf(7u, 7u) to Rational(65193755, 333396), - listOf(8u, 7u) to Rational(90974351, 2500470), - listOf(0u, 8u) to Rational(-3182197, 1260), - listOf(1u, 8u) to Rational(24899923, 8820), - listOf(2u, 8u) to Rational(-19999556, 19845), - listOf(3u, 8u) to Rational(3276587, 3969), - listOf(4u, 8u) to Rational(13719549239, 5000940), - listOf(5u, 8u) to Rational(-961839938, 1250235), - listOf(6u, 8u) to Rational(-198184871, 833490), - listOf(7u, 8u) to Rational(230659711, 5000940), - listOf(8u, 8u) to Rational(292447, 35721) - ), - NumberedPolynomialAsIs( - listOf() to Rational(9, 100), - listOf(1u) to Rational(-21, 50), - listOf(2u) to Rational(293, 700), - listOf(3u) to Rational(29, 210), - listOf(4u) to Rational(3233, 8820), - listOf(5u) to Rational(-289, 441), - listOf(6u) to Rational(-1, 9), - listOf(7u) to Rational(-20, 441), - listOf(8u) to Rational(100, 441), - listOf(0u, 1u) to Rational(-57, 80), - listOf(1u, 1u) to Rational(-121, 400), - listOf(2u, 1u) to Rational(37117, 8400), - listOf(3u, 1u) to Rational(-4853, 3150), - listOf(4u, 1u) to Rational(1166203, 132300), - listOf(5u, 1u) to Rational(-2708, 567), - listOf(6u, 1u) to Rational(-287159, 416745), - listOf(7u, 1u) to Rational(-478204, 83349), - listOf(8u, 1u) to Rational(176320, 83349), - listOf(0u, 2u) to Rational(-6239, 6400), - listOf(1u, 2u) to Rational(264211, 11200), - listOf(2u, 2u) to Rational(-1591999, 100800), - listOf(3u, 2u) to Rational(12450091, 529200), - listOf(4u, 2u) to Rational(9230759, 226800), - listOf(5u, 2u) to Rational(18995554, 2083725), - listOf(6u, 2u) to Rational(136706258, 6251175), - listOf(7u, 2u) to Rational(-120907496, 3750705), - listOf(8u, 2u) to Rational(117200176, 15752961), - listOf(0u, 3u) to Rational(5653, 320), - listOf(1u, 3u) to Rational(-130853, 8400), - listOf(2u, 3u) to Rational(-20939327, 151200), - listOf(3u, 3u) to Rational(2566691, 25200), - listOf(4u, 3u) to Rational(-68441519, 476280), - listOf(5u, 3u) to Rational(2462904247, 12502350), - listOf(6u, 3u) to Rational(353667161, 18753525), - listOf(7u, 3u) to Rational(-1689134372, 26254935), - listOf(8u, 3u) to Rational(35084104, 2250423), - listOf(0u, 4u) to Rational(-3587, 300), - listOf(1u, 4u) to Rational(-10513243, 33600), - listOf(2u, 4u) to Rational(30766733, 176400), - listOf(3u, 4u) to Rational(-65680021, 198450), - listOf(4u, 4u) to Rational(-8108910547, 20003760), - listOf(5u, 4u) to Rational(2922125159, 6251175), - listOf(6u, 4u) to Rational(-4245279943, 131274675), - listOf(7u, 4u) to Rational(-371946872, 3750705), - listOf(8u, 4u) to Rational(61286752, 2250423), - listOf(0u, 5u) to Rational(-20477, 160), - listOf(1u, 5u) to Rational(215741, 1120), - listOf(2u, 5u) to Rational(30785843, 31752), - listOf(3u, 5u) to Rational(-357495959, 317520), - listOf(4u, 5u) to Rational(-1611242993, 10001880), - listOf(5u, 5u) to Rational(345925495, 500094), - listOf(6u, 5u) to Rational(-755948411, 3750705), - listOf(7u, 5u) to Rational(-108643496, 1250235), - listOf(8u, 5u) to Rational(1122512, 35721), - listOf(0u, 6u) to Rational(358037, 2880), - listOf(1u, 6u) to Rational(3895837, 3360), - listOf(2u, 6u) to Rational(359419201, 1270080), - listOf(3u, 6u) to Rational(-158522587, 105840), - listOf(4u, 6u) to Rational(10909002599, 20003760), - listOf(5u, 6u) to Rational(76846972, 138915), - listOf(6u, 6u) to Rational(-327696553, 1250235), - listOf(7u, 6u) to Rational(-1687328, 35721), - listOf(8u, 6u) to Rational(1016836, 35721), - listOf(0u, 7u) to Rational(658, 3), - listOf(1u, 7u) to Rational(48035, 168), - listOf(2u, 7u) to Rational(-5777875, 5292), - listOf(3u, 7u) to Rational(-7893899, 10584), - listOf(4u, 7u) to Rational(10191652, 11907), - listOf(5u, 7u) to Rational(2920121, 23814), - listOf(6u, 7u) to Rational(-2699780, 11907), - listOf(7u, 7u) to Rational(4556, 441), - listOf(8u, 7u) to Rational(3440, 189), - listOf(0u, 8u) to Rational(64, 1), - listOf(1u, 8u) to Rational(-808, 7), - listOf(2u, 8u) to Rational(-360895, 1764), - listOf(3u, 8u) to Rational(257657, 882), - listOf(4u, 8u) to Rational(3779917, 15876), - listOf(5u, 8u) to Rational(-610279, 3969), - listOf(6u, 8u) to Rational(-25091, 441), - listOf(7u, 8u) to Rational(9560, 567), - listOf(8u, 8u) to Rational(400, 81) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(18, 5), - listOf(1u) to Rational(-17, 5), - listOf(2u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(-5, 1), - listOf(2u, 1u) to Rational(-9, 1), - listOf(0u, 2u) to Rational(-8, 8), - listOf(1u, 2u) to Rational(2, 7), - listOf(2u, 2u) to Rational(-13, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-4, 8), - listOf(1u) to Rational(15, 9), - listOf(2u) to Rational(-10, 9), - listOf(0u, 1u) to Rational(5, 3), - listOf(1u, 1u) to Rational(4, 1), - listOf(2u, 1u) to Rational(-2, 7), - listOf(0u, 2u) to Rational(2, 2), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(-18, 9), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 9), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(10, 9), - listOf(0u, 1u) to Rational(13, 3), - listOf(1u, 1u) to Rational(-12, 4), - listOf(2u, 1u) to Rational(3, 6), - listOf(0u, 2u) to Rational(2, 9), - listOf(1u, 2u) to Rational(7, 3), - listOf(2u, 2u) to Rational(16, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 2), - listOf(1u) to Rational(6, 2), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 1), - listOf(1u, 1u) to Rational(-11, 3), - listOf(2u, 1u) to Rational(7, 5), - listOf(0u, 2u) to Rational(8, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(17, 4), - ) - ) - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-6443599, 10000), - listOf(1u) to Rational(166251223, 210000), - listOf(2u) to Rational(-4606805099, 3528000), - listOf(3u) to Rational(51204379, 19600), - listOf(4u) to Rational(-529045460659, 277830000), - listOf(5u) to Rational(2630836709, 1488375), - listOf(6u) to Rational(-42675691369, 25004700), - listOf(7u) to Rational(495825223, 1250235), - listOf(8u) to Rational(-22531756, 1750329), - listOf(0u, 1u) to Rational(-2526552797, 420000), - listOf(1u, 1u) to Rational(31108840471, 2520000), - listOf(2u, 1u) to Rational(-4789740847, 1102500), - listOf(3u, 1u) to Rational(186594307807, 11340000), - listOf(4u, 1u) to Rational(-11677815943, 1488375), - listOf(5u, 1u) to Rational(-181118486447, 27783000), - listOf(6u, 1u) to Rational(-16123292162, 14586075), - listOf(7u, 1u) to Rational(-140339343808, 26254935), - listOf(8u, 1u) to Rational(4570171616, 5250987), - listOf(0u, 2u) to Rational(-181436530573, 10080000), - listOf(1u, 2u) to Rational(6700437957491, 105840000), - listOf(2u, 2u) to Rational(-3527267461, 1417500), - listOf(3u, 2u) to Rational(-38084563451, 5556600), - listOf(4u, 2u) to Rational(-565662040631, 13891500), - listOf(5u, 2u) to Rational(-35479071126397, 583443000), - listOf(6u, 2u) to Rational(-11717559078469, 525098700), - listOf(7u, 2u) to Rational(-2043385293517, 225042300), - listOf(8u, 2u) to Rational(-3644439630451, 551353635), - listOf(0u, 3u) to Rational(-1760423269, 126000), - listOf(1u, 3u) to Rational(310176758299, 2352000), - listOf(2u, 3u) to Rational(-907229584837, 21168000), - listOf(3u, 3u) to Rational(-16717135885963, 95256000), - listOf(4u, 3u) to Rational(-43762928025353, 333396000), - listOf(5u, 3u) to Rational(-328427480571607, 3000564000), - listOf(6u, 3u) to Rational(-7722675917197, 210039480), - listOf(7u, 3u) to Rational(1713350137019, 1225230300), - listOf(8u, 3u) to Rational(156695935643, 31505922), - listOf(0u, 4u) to Rational(18362364269, 1008000), - listOf(1u, 4u) to Rational(955674858553, 10584000), - listOf(2u, 4u) to Rational(-71937470607371, 444528000), - listOf(3u, 4u) to Rational(-34097985615163, 95256000), - listOf(4u, 4u) to Rational(-340736178775883, 2000376000), - listOf(5u, 4u) to Rational(-511324523441897, 10501974000), - listOf(6u, 4u) to Rational(-125375649409151, 8821658160), - listOf(7u, 4u) to Rational(-2813518533421, 1575296100), - listOf(8u, 4u) to Rational(-17044089109, 5250987), - listOf(0u, 5u) to Rational(600086461, 20160), - listOf(1u, 5u) to Rational(-18959931367, 423360), - listOf(2u, 5u) to Rational(-9178804929607, 44452800), - listOf(3u, 5u) to Rational(-1460114275979, 5334336), - listOf(4u, 5u) to Rational(-342533479090169, 4200789600), - listOf(5u, 5u) to Rational(20335453022963, 4200789600), - listOf(6u, 5u) to Rational(-21649775090197, 6301184400), - listOf(7u, 5u) to Rational(-197301716069, 131274675), - listOf(8u, 5u) to Rational(18711357470, 15752961), - listOf(0u, 6u) to Rational(621417991, 100800), - listOf(1u, 6u) to Rational(-159236792977, 2116800), - listOf(2u, 6u) to Rational(-6602528890883, 66679200), - listOf(3u, 6u) to Rational(-1086091664047, 19051200), - listOf(4u, 6u) to Rational(3769375009003, 1680315840), - listOf(5u, 6u) to Rational(-12920385574769, 1050197400), - listOf(6u, 6u) to Rational(-90219591809287, 6301184400), - listOf(7u, 6u) to Rational(656361553391, 1575296100), - listOf(8u, 6u) to Rational(757900793, 2250423), - listOf(0u, 7u) to Rational(-100770017, 15120), - listOf(1u, 7u) to Rational(-316364851, 17640), - listOf(2u, 7u) to Rational(-85118560057, 6667920), - listOf(3u, 7u) to Rational(6286563719, 416745), - listOf(4u, 7u) to Rational(26803885301, 1714608), - listOf(5u, 7u) to Rational(-13767154393, 4286520), - listOf(6u, 7u) to Rational(-3875138933, 1224720), - listOf(7u, 7u) to Rational(65193755, 333396), - listOf(8u, 7u) to Rational(90974351, 2500470), - listOf(0u, 8u) to Rational(-3182197, 1260), - listOf(1u, 8u) to Rational(24899923, 8820), - listOf(2u, 8u) to Rational(-19999556, 19845), - listOf(3u, 8u) to Rational(3276587, 3969), - listOf(4u, 8u) to Rational(13719549239, 5000940), - listOf(5u, 8u) to Rational(-961839938, 1250235), - listOf(6u, 8u) to Rational(-198184871, 833490), - listOf(7u, 8u) to Rational(230659711, 5000940), - listOf(8u, 8u) to Rational(292447, 35721) - ), - NumberedPolynomialAsIs( - listOf() to Rational(9, 100), - listOf(1u) to Rational(-21, 50), - listOf(2u) to Rational(293, 700), - listOf(3u) to Rational(29, 210), - listOf(4u) to Rational(3233, 8820), - listOf(5u) to Rational(-289, 441), - listOf(6u) to Rational(-1, 9), - listOf(7u) to Rational(-20, 441), - listOf(8u) to Rational(100, 441), - listOf(0u, 1u) to Rational(-57, 80), - listOf(1u, 1u) to Rational(-121, 400), - listOf(2u, 1u) to Rational(37117, 8400), - listOf(3u, 1u) to Rational(-4853, 3150), - listOf(4u, 1u) to Rational(1166203, 132300), - listOf(5u, 1u) to Rational(-2708, 567), - listOf(6u, 1u) to Rational(-287159, 416745), - listOf(7u, 1u) to Rational(-478204, 83349), - listOf(8u, 1u) to Rational(176320, 83349), - listOf(0u, 2u) to Rational(-6239, 6400), - listOf(1u, 2u) to Rational(264211, 11200), - listOf(2u, 2u) to Rational(-1591999, 100800), - listOf(3u, 2u) to Rational(12450091, 529200), - listOf(4u, 2u) to Rational(9230759, 226800), - listOf(5u, 2u) to Rational(18995554, 2083725), - listOf(6u, 2u) to Rational(136706258, 6251175), - listOf(7u, 2u) to Rational(-120907496, 3750705), - listOf(8u, 2u) to Rational(117200176, 15752961), - listOf(0u, 3u) to Rational(5653, 320), - listOf(1u, 3u) to Rational(-130853, 8400), - listOf(2u, 3u) to Rational(-20939327, 151200), - listOf(3u, 3u) to Rational(2566691, 25200), - listOf(4u, 3u) to Rational(-68441519, 476280), - listOf(5u, 3u) to Rational(2462904247, 12502350), - listOf(6u, 3u) to Rational(353667161, 18753525), - listOf(7u, 3u) to Rational(-1689134372, 26254935), - listOf(8u, 3u) to Rational(35084104, 2250423), - listOf(0u, 4u) to Rational(-3587, 300), - listOf(1u, 4u) to Rational(-10513243, 33600), - listOf(2u, 4u) to Rational(30766733, 176400), - listOf(3u, 4u) to Rational(-65680021, 198450), - listOf(4u, 4u) to Rational(-8108910547, 20003760), - listOf(5u, 4u) to Rational(2922125159, 6251175), - listOf(6u, 4u) to Rational(-4245279943, 131274675), - listOf(7u, 4u) to Rational(-371946872, 3750705), - listOf(8u, 4u) to Rational(61286752, 2250423), - listOf(0u, 5u) to Rational(-20477, 160), - listOf(1u, 5u) to Rational(215741, 1120), - listOf(2u, 5u) to Rational(30785843, 31752), - listOf(3u, 5u) to Rational(-357495959, 317520), - listOf(4u, 5u) to Rational(-1611242993, 10001880), - listOf(5u, 5u) to Rational(345925495, 500094), - listOf(6u, 5u) to Rational(-755948411, 3750705), - listOf(7u, 5u) to Rational(-108643496, 1250235), - listOf(8u, 5u) to Rational(1122512, 35721), - listOf(0u, 6u) to Rational(358037, 2880), - listOf(1u, 6u) to Rational(3895837, 3360), - listOf(2u, 6u) to Rational(359419201, 1270080), - listOf(3u, 6u) to Rational(-158522587, 105840), - listOf(4u, 6u) to Rational(10909002599, 20003760), - listOf(5u, 6u) to Rational(76846972, 138915), - listOf(6u, 6u) to Rational(-327696553, 1250235), - listOf(7u, 6u) to Rational(-1687328, 35721), - listOf(8u, 6u) to Rational(1016836, 35721), - listOf(0u, 7u) to Rational(658, 3), - listOf(1u, 7u) to Rational(48035, 168), - listOf(2u, 7u) to Rational(-5777875, 5292), - listOf(3u, 7u) to Rational(-7893899, 10584), - listOf(4u, 7u) to Rational(10191652, 11907), - listOf(5u, 7u) to Rational(2920121, 23814), - listOf(6u, 7u) to Rational(-2699780, 11907), - listOf(7u, 7u) to Rational(4556, 441), - listOf(8u, 7u) to Rational(3440, 189), - listOf(0u, 8u) to Rational(64, 1), - listOf(1u, 8u) to Rational(-808, 7), - listOf(2u, 8u) to Rational(-360895, 1764), - listOf(3u, 8u) to Rational(257657, 882), - listOf(4u, 8u) to Rational(3779917, 15876), - listOf(5u, 8u) to Rational(-610279, 3969), - listOf(6u, 8u) to Rational(-25091, 441), - listOf(7u, 8u) to Rational(9560, 567), - listOf(8u, 8u) to Rational(400, 81) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(18, 5), - listOf(1u) to Rational(-17, 5), - listOf(2u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(-5, 1), - listOf(2u, 1u) to Rational(-9, 1), - listOf(0u, 2u) to Rational(-8, 8), - listOf(1u, 2u) to Rational(2, 7), - listOf(2u, 2u) to Rational(-13, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-4, 8), - listOf(1u) to Rational(15, 9), - listOf(2u) to Rational(-10, 9), - listOf(0u, 1u) to Rational(5, 3), - listOf(1u, 1u) to Rational(4, 1), - listOf(2u, 1u) to Rational(-2, 7), - listOf(0u, 2u) to Rational(2, 2), - listOf(1u, 2u) to Rational(-5, 7), - listOf(2u, 2u) to Rational(-18, 9), - ) - ), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-66677, 3500), - listOf(1u) to Rational(-206281, 10500), - listOf(2u) to Rational(-412567, 7056), - listOf(3u) to Rational(-310081, 11025), - listOf(4u) to Rational(-575996, 15435), - listOf(0u, 1u) to Rational(-573701, 4200), - listOf(1u, 1u) to Rational(-2239001, 25200), - listOf(2u, 1u) to Rational(-8817889, 132300), - listOf(3u, 1u) to Rational(2317919, 44100), - listOf(4u, 1u) to Rational(1169471, 6615), - listOf(0u, 2u) to Rational(-4057819, 33600), - listOf(1u, 2u) to Rational(1373311, 12600), - listOf(2u, 2u) to Rational(32433493, 52920), - listOf(3u, 2u) to Rational(4998053, 33075), - listOf(4u, 2u) to Rational(-2147779, 8820), - listOf(0u, 3u) to Rational(2018481, 2240), - listOf(1u, 3u) to Rational(941713, 1440), - listOf(2u, 3u) to Rational(183749, 6615), - listOf(3u, 3u) to Rational(-4631023, 15876), - listOf(4u, 3u) to Rational(25609336, 178605), - listOf(0u, 4u) to Rational(11886431, 6720), - listOf(1u, 4u) to Rational(18433, 504), - listOf(2u, 4u) to Rational(-39613331, 45360), - listOf(3u, 4u) to Rational(681619, 5670), - listOf(4u, 4u) to Rational(-864841, 20412), - listOf(0u, 5u) to Rational(343535, 1008), - listOf(1u, 5u) to Rational(-33583, 72), - listOf(2u, 5u) to Rational(1194625, 9072), - listOf(3u, 5u) to Rational(-62917, 2268), - listOf(4u, 5u) to Rational(157645, 10206), - listOf(0u, 6u) to Rational(-1381, 3), - listOf(1u, 6u) to Rational(919, 36), - listOf(2u, 6u) to Rational(-3053, 36), - listOf(3u, 6u) to Rational(2125, 324), - listOf(4u, 6u) to Rational(-236, 243) - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(1, 4), - listOf(1u) to Rational(-5, 3), - listOf(2u) to Rational(35, 9), - listOf(3u) to Rational(-100, 27), - listOf(4u) to Rational(100, 81), - listOf(0u, 1u) to Rational(-5, 3), - listOf(1u, 1u) to Rational(14, 9), - listOf(2u, 1u) to Rational(1874, 189), - listOf(3u, 1u) to Rational(-620, 63), - listOf(4u, 1u) to Rational(40, 63), - listOf(0u, 2u) to Rational(16, 9), - listOf(1u, 2u) to Rational(365, 21), - listOf(2u, 2u) to Rational(112, 9), - listOf(3u, 2u) to Rational(-464, 63), - listOf(4u, 2u) to Rational(1996, 441), - listOf(0u, 3u) to Rational(10, 3), - listOf(1u, 3u) to Rational(118, 21), - listOf(2u, 3u) to Rational(-272, 21), - listOf(3u, 3u) to Rational(-764, 49), - listOf(4u, 3u) to Rational(8, 7), - listOf(0u, 4u) to Rational(1, 1), - listOf(1u, 4u) to Rational(-10, 7), - listOf(2u, 4u) to Rational(-171, 49), - listOf(3u, 4u) to Rational(20, 7), - listOf(4u, 4u) to Rational(4, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(17, 5), - listOf(1u) to Rational(11, 6), - listOf(2u) to Rational(14, 3), - listOf(0u, 1u) to Rational(17, 1), - listOf(1u, 1u) to Rational(12, 3), - listOf(2u, 1u) to Rational(-6, 2), - listOf(0u, 2u) to Rational(17, 1), - listOf(1u, 2u) to Rational(-4, 3), - listOf(2u, 2u) to Rational(2, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(3, 5), - listOf(1u) to Rational(3, 5), - listOf(2u) to Rational(3, 7), - listOf(0u, 1u) to Rational(-3, 8), - listOf(1u, 1u) to Rational(-1, 1), - listOf(2u, 1u) to Rational(17, 9), - listOf(0u, 2u) to Rational(-8, 1), - listOf(1u, 2u) to Rational(6, 4), - listOf(2u, 2u) to Rational(10, 9), - ) - ), - )), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ), - NumberedPolynomialAsIs(listOf() to Rational(0, 1), - listOf() to Rational(0, 1) - ) - ), - NumberedPolynomialAsIs( - listOf() to Rational(15, 7), - listOf(1u) to Rational(1, 5), - listOf(2u) to Rational(-7, 4), - listOf(0u, 1u) to Rational(-1, 9), - listOf(1u, 1u) to Rational(-2, 7), - listOf(2u, 1u) to Rational(17, 3), - listOf(0u, 2u) to Rational(2, 6), - listOf(1u, 2u) to Rational(-17, 6), - listOf(2u, 2u) to Rational(-6, 2), - ).substitute(RationalField, bufferOf>()), - "test 6" - ) - } - @Test - fun test_RationalFunction_substitute_Double_Buffer() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs(emptyList() to 0.0), - NumberedPolynomialAsIs(emptyList() to 1.0), - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 1.0, - listOf(1u) to -2.0, - listOf(2u) to 1.0, - ), - NumberedPolynomialAsIs( - listOf() to 1.0, - ) - ).substitute(bufferOf( - 1.0 - )), - 0.001, - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(bufferOf()), - 0.001, - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 151.1502229133916, - listOf(0u, 1u) to -262.3790170577034, - listOf(0u, 2u) to 102.5097937392923, - ), - NumberedPolynomialAsIs( - listOf() to -367.9969733169944, - listOf(0u, 1u) to 112.4911133334554, - listOf(0u, 2u) to -469.755906895345, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(bufferOf( - -8.11707689492641, - )), - 0.001, - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 7.321261307532708, - ), - NumberedPolynomialAsIs( - listOf() to -575.6325831127576, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(bufferOf( - -8.11707689492641, - 0.795265651276015, - )), - 0.001, - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 7.321261307532708, - ), - NumberedPolynomialAsIs( - listOf() to -575.6325831127576, - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substitute(bufferOf( - -8.11707689492641, - 0.795265651276015, - 0.9211194782050933 - )), - 0.001, - "test 5" - ) - } - @Test - fun test_RationalFunction_substitute_Constant_Buffer() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ).substitute(RationalField, bufferOf( - Rational(1) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(22047, 2450), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2204953, 147000), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, bufferOf( - Rational(7, 5), - Rational(-13, 7), - Rational(-16, 4), - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(22047, 2450), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2204953, 147000), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, bufferOf( - Rational(7, 5), - Rational(-13, 7), - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-939, 200), - listOf(0u, 1u) to Rational(123, 50), - listOf(0u, 2u) to Rational(1059, 200) - ), - NumberedPolynomialAsIs( - listOf() to Rational(121, 25), - listOf(0u, 1u) to Rational(-949, 375), - listOf(0u, 2u) to Rational(-1423, 200) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, bufferOf( - Rational(7, 5), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substitute(RationalField, bufferOf()), - "test 5" - ) - } - @Test - fun test_RationalFunction_substitute_Polynomial_Buffer() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(211, 4), - listOf(2u) to Rational(88, 3), - listOf(3u) to Rational(-63, 8), - listOf(4u) to Rational(441, 16), - listOf(0u, 1u) to Rational(-671, 15), - listOf(1u, 1u) to Rational(-551, 21), - listOf(2u, 1u) to Rational(279, 25), - listOf(3u, 1u) to Rational(231, 20), - listOf(0u, 2u) to Rational(-1436, 1575), - listOf(1u, 2u) to Rational(2471, 250), - listOf(2u, 2u) to Rational(-4919, 100), - listOf(0u, 3u) to Rational(-1464, 125), - listOf(1u, 3u) to Rational(-264, 25), - listOf(0u, 4u) to Rational(576, 25), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(-9, 4), - listOf(2u) to Rational(943, 8), - listOf(3u) to Rational(117, 8), - listOf(4u) to Rational(147, 16), - listOf(0u, 1u) to Rational(289, 90), - listOf(1u, 1u) to Rational(-2692, 15), - listOf(2u, 1u) to Rational(-1629, 140), - listOf(3u, 1u) to Rational(77, 20), - listOf(0u, 2u) to Rational(6187, 75), - listOf(1u, 2u) to Rational(-2879, 175), - listOf(2u, 2u) to Rational(-4919, 300), - listOf(0u, 3u) to Rational(336, 25), - listOf(1u, 3u) to Rational(-88, 25), - listOf(0u, 4u) to Rational(192, 25), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf(1u) to Rational(3, 2), - listOf(0u, 1u) to Rational(8, 5), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-3, 1), - ) - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1202861, 210), - listOf(1u) to Rational(-215117, 45), - listOf(2u) to Rational(10889651, 19845), - listOf(3u) to Rational(-3503956, 6615), - listOf(4u) to Rational(809066, 2205), - listOf(5u) to Rational(-9056, 735), - listOf(6u) to Rational(5396, 315), - listOf(7u) to Rational(-752, 147), - listOf(8u) to Rational(16, 49), - listOf(0u, 1u) to Rational(1738469, 1470), - listOf(1u, 1u) to Rational(-926238703, 52920), - listOf(2u, 1u) to Rational(-44113982, 6615), - listOf(3u, 1u) to Rational(10423519, 5292), - listOf(4u, 1u) to Rational(3769712, 2205), - listOf(5u, 1u) to Rational(8905046, 6615), - listOf(6u, 1u) to Rational(1186972, 6615), - listOf(7u, 1u) to Rational(22124, 441), - listOf(8u, 1u) to Rational(-1504, 147), - listOf(0u, 2u) to Rational(-54723628, 2205), - listOf(1u, 2u) to Rational(70109407, 1323), - listOf(2u, 2u) to Rational(151072591, 17640), - listOf(3u, 2u) to Rational(1216428107, 52920), - listOf(4u, 2u) to Rational(2587873193, 317520), - listOf(5u, 2u) to Rational(393536369, 79380), - listOf(6u, 2u) to Rational(137614937, 79380), - listOf(7u, 2u) to Rational(566866, 1323), - listOf(8u, 2u) to Rational(41848, 441), - listOf(0u, 3u) to Rational(-19470406, 2205), - listOf(1u, 3u) to Rational(72514195, 882), - listOf(2u, 3u) to Rational(-78090707, 1764), - listOf(3u, 3u) to Rational(-1988237707, 26460), - listOf(4u, 3u) to Rational(-802137919, 17640), - listOf(5u, 3u) to Rational(-139989463, 5880), - listOf(6u, 3u) to Rational(-26066641, 3780), - listOf(7u, 3u) to Rational(-2363369, 1323), - listOf(8u, 3u) to Rational(-108280, 441), - listOf(0u, 4u) to Rational(14878516, 441), - listOf(1u, 4u) to Rational(-253416724, 2205), - listOf(2u, 4u) to Rational(16699157, 840), - listOf(3u, 4u) to Rational(-105220979, 13230), - listOf(4u, 4u) to Rational(208266383, 5880), - listOf(5u, 4u) to Rational(650135309, 26460), - listOf(6u, 4u) to Rational(123808663, 11760), - listOf(7u, 4u) to Rational(8563385, 2646), - listOf(8u, 4u) to Rational(19721, 49), - listOf(0u, 5u) to Rational(675645, 49), - listOf(1u, 5u) to Rational(-70554077, 588), - listOf(2u, 5u) to Rational(157884029, 980), - listOf(3u, 5u) to Rational(489548623, 4410), - listOf(4u, 5u) to Rational(148540519, 17640), - listOf(5u, 5u) to Rational(-5559551, 392), - listOf(6u, 5u) to Rational(-18335711, 1470), - listOf(7u, 5u) to Rational(-38437, 9), - listOf(8u, 5u) to Rational(-29620, 63), - listOf(0u, 6u) to Rational(-727625, 49), - listOf(1u, 6u) to Rational(7046685, 98), - listOf(2u, 6u) to Rational(-334814231, 7056), - listOf(3u, 6u) to Rational(-243971737, 17640), - listOf(4u, 6u) to Rational(-571116659, 35280), - listOf(5u, 6u) to Rational(567538, 315), - listOf(6u, 6u) to Rational(3199768, 315), - listOf(7u, 6u) to Rational(227744, 63), - listOf(8u, 6u) to Rational(23116, 63), - listOf(0u, 7u) to Rational(-27500, 7), - listOf(1u, 7u) to Rational(120125, 3), - listOf(2u, 7u) to Rational(-279200, 3), - listOf(3u, 7u) to Rational(-100160, 7), - listOf(4u, 7u) to Rational(920452, 21), - listOf(5u, 7u) to Rational(226481, 21), - listOf(6u, 7u) to Rational(-34428, 7), - listOf(7u, 7u) to Rational(-6232, 3), - listOf(8u, 7u) to Rational(-608, 3), - listOf(0u, 8u) to Rational(2500, 1), - listOf(1u, 8u) to Rational(-19000, 1), - listOf(2u, 8u) to Rational(37900, 1), - listOf(3u, 8u) to Rational(-1840, 1), - listOf(4u, 8u) to Rational(-17876, 1), - listOf(5u, 8u) to Rational(-1240, 1), - listOf(6u, 8u) to Rational(2788, 1), - listOf(7u, 8u) to Rational(800, 1), - listOf(8u, 8u) to Rational(64, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(162487, 63), - listOf(1u) to Rational(-92713, 54), - listOf(2u) to Rational(802436, 1323), - listOf(3u) to Rational(-55088, 441), - listOf(4u) to Rational(1404034, 9261), - listOf(5u) to Rational(-5804, 1029), - listOf(6u) to Rational(51556, 9261), - listOf(7u) to Rational(-752, 441), - listOf(8u) to Rational(16, 147), - listOf(0u, 1u) to Rational(296071, 441), - listOf(1u, 1u) to Rational(-4991281, 882), - listOf(2u, 1u) to Rational(-18702811, 9261), - listOf(3u, 1u) to Rational(40759043, 27783), - listOf(4u, 1u) to Rational(19768501, 27783), - listOf(5u, 1u) to Rational(14307337, 27783), - listOf(6u, 1u) to Rational(1655684, 27783), - listOf(7u, 1u) to Rational(22124, 1323), - listOf(8u, 1u) to Rational(-1504, 441), - listOf(0u, 2u) to Rational(-27667474, 3087), - listOf(1u, 2u) to Rational(265605901, 12348), - listOf(2u, 2u) to Rational(160360775, 98784), - listOf(3u, 2u) to Rational(1169992093, 148176), - listOf(4u, 2u) to Rational(3978014077, 1333584), - listOf(5u, 2u) to Rational(567058123, 333396), - listOf(6u, 2u) to Rational(205132579, 333396), - listOf(7u, 2u) to Rational(566866, 3969), - listOf(8u, 2u) to Rational(41848, 1323), - listOf(0u, 3u) to Rational(-2228822, 1029), - listOf(1u, 3u) to Rational(80179390, 3087), - listOf(2u, 3u) to Rational(-1378630487, 74088), - listOf(3u, 3u) to Rational(-3385811693, 111132), - listOf(4u, 3u) to Rational(-820686977, 49392), - listOf(5u, 3u) to Rational(-89101027, 10584), - listOf(6u, 3u) to Rational(-37847387, 15876), - listOf(7u, 3u) to Rational(-2363369, 3969), - listOf(8u, 3u) to Rational(-108280, 1323), - listOf(0u, 4u) to Rational(12619982, 1029), - listOf(1u, 4u) to Rational(-277723177, 6174), - listOf(2u, 4u) to Rational(649414169, 49392), - listOf(3u, 4u) to Rational(14457595, 63504), - listOf(4u, 4u) to Rational(139270339, 10584), - listOf(5u, 4u) to Rational(140367961, 15876), - listOf(6u, 4u) to Rational(25467083, 7056), - listOf(7u, 4u) to Rational(8563385, 7938), - listOf(8u, 4u) to Rational(19721, 147), - listOf(0u, 5u) to Rational(643850, 147), - listOf(1u, 5u) to Rational(-11818025, 294), - listOf(2u, 5u) to Rational(33963203, 588), - listOf(3u, 5u) to Rational(207216235, 5292), - listOf(4u, 5u) to Rational(2861021, 1512), - listOf(5u, 5u) to Rational(-6302335, 1176), - listOf(6u, 5u) to Rational(-3738587, 882), - listOf(7u, 5u) to Rational(-38437, 27), - listOf(8u, 5u) to Rational(-29620, 189), - listOf(0u, 6u) to Rational(-248725, 49), - listOf(1u, 6u) to Rational(2478535, 98), - listOf(2u, 6u) to Rational(-399721367, 21168), - listOf(3u, 6u) to Rational(-54309317, 10584), - listOf(4u, 6u) to Rational(-95398327, 21168), - listOf(5u, 6u) to Rational(173750, 189), - listOf(6u, 6u) to Rational(92216, 27), - listOf(7u, 6u) to Rational(227744, 189), - listOf(8u, 6u) to Rational(23116, 189), - listOf(0u, 7u) to Rational(-27500, 21), - listOf(1u, 7u) to Rational(120125, 9), - listOf(2u, 7u) to Rational(-279200, 9), - listOf(3u, 7u) to Rational(-100160, 21), - listOf(4u, 7u) to Rational(920452, 63), - listOf(5u, 7u) to Rational(226481, 63), - listOf(6u, 7u) to Rational(-11476, 7), - listOf(7u, 7u) to Rational(-6232, 9), - listOf(8u, 7u) to Rational(-608, 9), - listOf(0u, 8u) to Rational(2500, 3), - listOf(1u, 8u) to Rational(-19000, 3), - listOf(2u, 8u) to Rational(37900, 3), - listOf(3u, 8u) to Rational(-1840, 3), - listOf(4u, 8u) to Rational(-17876, 3), - listOf(5u, 8u) to Rational(-1240, 3), - listOf(6u, 8u) to Rational(2788, 3), - listOf(7u, 8u) to Rational(800, 3), - listOf(8u, 8u) to Rational(64, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(8, 2), - listOf(1u) to Rational(-15, 5), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 7), - listOf(1u, 1u) to Rational(-16, 6), - listOf(2u, 1u) to Rational(-13, 3), - listOf(0u, 2u) to Rational(-5, 1), - listOf(1u, 2u) to Rational(17, 1), - listOf(2u, 2u) to Rational(8, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 1), - listOf(1u) to Rational(-9, 8), - listOf(2u) to Rational(17, 5), - listOf(0u, 1u) to Rational(-2, 3), - listOf(1u, 1u) to Rational(1, 5), - listOf(2u, 1u) to Rational(-11, 7), - listOf(0u, 2u) to Rational(13, 6), - listOf(1u, 2u) to Rational(-15, 2), - listOf(2u, 2u) to Rational(-14, 4), - ) - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1202861, 210), - listOf(1u) to Rational(-215117, 45), - listOf(2u) to Rational(10889651, 19845), - listOf(3u) to Rational(-3503956, 6615), - listOf(4u) to Rational(809066, 2205), - listOf(5u) to Rational(-9056, 735), - listOf(6u) to Rational(5396, 315), - listOf(7u) to Rational(-752, 147), - listOf(8u) to Rational(16, 49), - listOf(0u, 1u) to Rational(1738469, 1470), - listOf(1u, 1u) to Rational(-926238703, 52920), - listOf(2u, 1u) to Rational(-44113982, 6615), - listOf(3u, 1u) to Rational(10423519, 5292), - listOf(4u, 1u) to Rational(3769712, 2205), - listOf(5u, 1u) to Rational(8905046, 6615), - listOf(6u, 1u) to Rational(1186972, 6615), - listOf(7u, 1u) to Rational(22124, 441), - listOf(8u, 1u) to Rational(-1504, 147), - listOf(0u, 2u) to Rational(-54723628, 2205), - listOf(1u, 2u) to Rational(70109407, 1323), - listOf(2u, 2u) to Rational(151072591, 17640), - listOf(3u, 2u) to Rational(1216428107, 52920), - listOf(4u, 2u) to Rational(2587873193, 317520), - listOf(5u, 2u) to Rational(393536369, 79380), - listOf(6u, 2u) to Rational(137614937, 79380), - listOf(7u, 2u) to Rational(566866, 1323), - listOf(8u, 2u) to Rational(41848, 441), - listOf(0u, 3u) to Rational(-19470406, 2205), - listOf(1u, 3u) to Rational(72514195, 882), - listOf(2u, 3u) to Rational(-78090707, 1764), - listOf(3u, 3u) to Rational(-1988237707, 26460), - listOf(4u, 3u) to Rational(-802137919, 17640), - listOf(5u, 3u) to Rational(-139989463, 5880), - listOf(6u, 3u) to Rational(-26066641, 3780), - listOf(7u, 3u) to Rational(-2363369, 1323), - listOf(8u, 3u) to Rational(-108280, 441), - listOf(0u, 4u) to Rational(14878516, 441), - listOf(1u, 4u) to Rational(-253416724, 2205), - listOf(2u, 4u) to Rational(16699157, 840), - listOf(3u, 4u) to Rational(-105220979, 13230), - listOf(4u, 4u) to Rational(208266383, 5880), - listOf(5u, 4u) to Rational(650135309, 26460), - listOf(6u, 4u) to Rational(123808663, 11760), - listOf(7u, 4u) to Rational(8563385, 2646), - listOf(8u, 4u) to Rational(19721, 49), - listOf(0u, 5u) to Rational(675645, 49), - listOf(1u, 5u) to Rational(-70554077, 588), - listOf(2u, 5u) to Rational(157884029, 980), - listOf(3u, 5u) to Rational(489548623, 4410), - listOf(4u, 5u) to Rational(148540519, 17640), - listOf(5u, 5u) to Rational(-5559551, 392), - listOf(6u, 5u) to Rational(-18335711, 1470), - listOf(7u, 5u) to Rational(-38437, 9), - listOf(8u, 5u) to Rational(-29620, 63), - listOf(0u, 6u) to Rational(-727625, 49), - listOf(1u, 6u) to Rational(7046685, 98), - listOf(2u, 6u) to Rational(-334814231, 7056), - listOf(3u, 6u) to Rational(-243971737, 17640), - listOf(4u, 6u) to Rational(-571116659, 35280), - listOf(5u, 6u) to Rational(567538, 315), - listOf(6u, 6u) to Rational(3199768, 315), - listOf(7u, 6u) to Rational(227744, 63), - listOf(8u, 6u) to Rational(23116, 63), - listOf(0u, 7u) to Rational(-27500, 7), - listOf(1u, 7u) to Rational(120125, 3), - listOf(2u, 7u) to Rational(-279200, 3), - listOf(3u, 7u) to Rational(-100160, 7), - listOf(4u, 7u) to Rational(920452, 21), - listOf(5u, 7u) to Rational(226481, 21), - listOf(6u, 7u) to Rational(-34428, 7), - listOf(7u, 7u) to Rational(-6232, 3), - listOf(8u, 7u) to Rational(-608, 3), - listOf(0u, 8u) to Rational(2500, 1), - listOf(1u, 8u) to Rational(-19000, 1), - listOf(2u, 8u) to Rational(37900, 1), - listOf(3u, 8u) to Rational(-1840, 1), - listOf(4u, 8u) to Rational(-17876, 1), - listOf(5u, 8u) to Rational(-1240, 1), - listOf(6u, 8u) to Rational(2788, 1), - listOf(7u, 8u) to Rational(800, 1), - listOf(8u, 8u) to Rational(64, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(162487, 63), - listOf(1u) to Rational(-92713, 54), - listOf(2u) to Rational(802436, 1323), - listOf(3u) to Rational(-55088, 441), - listOf(4u) to Rational(1404034, 9261), - listOf(5u) to Rational(-5804, 1029), - listOf(6u) to Rational(51556, 9261), - listOf(7u) to Rational(-752, 441), - listOf(8u) to Rational(16, 147), - listOf(0u, 1u) to Rational(296071, 441), - listOf(1u, 1u) to Rational(-4991281, 882), - listOf(2u, 1u) to Rational(-18702811, 9261), - listOf(3u, 1u) to Rational(40759043, 27783), - listOf(4u, 1u) to Rational(19768501, 27783), - listOf(5u, 1u) to Rational(14307337, 27783), - listOf(6u, 1u) to Rational(1655684, 27783), - listOf(7u, 1u) to Rational(22124, 1323), - listOf(8u, 1u) to Rational(-1504, 441), - listOf(0u, 2u) to Rational(-27667474, 3087), - listOf(1u, 2u) to Rational(265605901, 12348), - listOf(2u, 2u) to Rational(160360775, 98784), - listOf(3u, 2u) to Rational(1169992093, 148176), - listOf(4u, 2u) to Rational(3978014077, 1333584), - listOf(5u, 2u) to Rational(567058123, 333396), - listOf(6u, 2u) to Rational(205132579, 333396), - listOf(7u, 2u) to Rational(566866, 3969), - listOf(8u, 2u) to Rational(41848, 1323), - listOf(0u, 3u) to Rational(-2228822, 1029), - listOf(1u, 3u) to Rational(80179390, 3087), - listOf(2u, 3u) to Rational(-1378630487, 74088), - listOf(3u, 3u) to Rational(-3385811693, 111132), - listOf(4u, 3u) to Rational(-820686977, 49392), - listOf(5u, 3u) to Rational(-89101027, 10584), - listOf(6u, 3u) to Rational(-37847387, 15876), - listOf(7u, 3u) to Rational(-2363369, 3969), - listOf(8u, 3u) to Rational(-108280, 1323), - listOf(0u, 4u) to Rational(12619982, 1029), - listOf(1u, 4u) to Rational(-277723177, 6174), - listOf(2u, 4u) to Rational(649414169, 49392), - listOf(3u, 4u) to Rational(14457595, 63504), - listOf(4u, 4u) to Rational(139270339, 10584), - listOf(5u, 4u) to Rational(140367961, 15876), - listOf(6u, 4u) to Rational(25467083, 7056), - listOf(7u, 4u) to Rational(8563385, 7938), - listOf(8u, 4u) to Rational(19721, 147), - listOf(0u, 5u) to Rational(643850, 147), - listOf(1u, 5u) to Rational(-11818025, 294), - listOf(2u, 5u) to Rational(33963203, 588), - listOf(3u, 5u) to Rational(207216235, 5292), - listOf(4u, 5u) to Rational(2861021, 1512), - listOf(5u, 5u) to Rational(-6302335, 1176), - listOf(6u, 5u) to Rational(-3738587, 882), - listOf(7u, 5u) to Rational(-38437, 27), - listOf(8u, 5u) to Rational(-29620, 189), - listOf(0u, 6u) to Rational(-248725, 49), - listOf(1u, 6u) to Rational(2478535, 98), - listOf(2u, 6u) to Rational(-399721367, 21168), - listOf(3u, 6u) to Rational(-54309317, 10584), - listOf(4u, 6u) to Rational(-95398327, 21168), - listOf(5u, 6u) to Rational(173750, 189), - listOf(6u, 6u) to Rational(92216, 27), - listOf(7u, 6u) to Rational(227744, 189), - listOf(8u, 6u) to Rational(23116, 189), - listOf(0u, 7u) to Rational(-27500, 21), - listOf(1u, 7u) to Rational(120125, 9), - listOf(2u, 7u) to Rational(-279200, 9), - listOf(3u, 7u) to Rational(-100160, 21), - listOf(4u, 7u) to Rational(920452, 63), - listOf(5u, 7u) to Rational(226481, 63), - listOf(6u, 7u) to Rational(-11476, 7), - listOf(7u, 7u) to Rational(-6232, 9), - listOf(8u, 7u) to Rational(-608, 9), - listOf(0u, 8u) to Rational(2500, 3), - listOf(1u, 8u) to Rational(-19000, 3), - listOf(2u, 8u) to Rational(37900, 3), - listOf(3u, 8u) to Rational(-1840, 3), - listOf(4u, 8u) to Rational(-17876, 3), - listOf(5u, 8u) to Rational(-1240, 3), - listOf(6u, 8u) to Rational(2788, 3), - listOf(7u, 8u) to Rational(800, 3), - listOf(8u, 8u) to Rational(64, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(8, 2), - listOf(1u) to Rational(-15, 5), - listOf(2u) to Rational(2, 7), - listOf(0u, 1u) to Rational(-18, 7), - listOf(1u, 1u) to Rational(-16, 6), - listOf(2u, 1u) to Rational(-13, 3), - listOf(0u, 2u) to Rational(-5, 1), - listOf(1u, 2u) to Rational(17, 1), - listOf(2u, 2u) to Rational(8, 2), - ), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-409, 6), - listOf(1u) to Rational(-376, 9), - listOf(2u) to Rational(-1781, 81), - listOf(3u) to Rational(-128, 27), - listOf(4u) to Rational(-8, 9), - listOf(0u, 1u) to Rational(18701, 210), - listOf(1u, 1u) to Rational(614183, 7560), - listOf(2u, 1u) to Rational(90941, 1890), - listOf(3u, 1u) to Rational(1802, 135), - listOf(4u, 1u) to Rational(112, 45), - listOf(0u, 2u) to Rational(181421, 315), - listOf(1u, 2u) to Rational(77813, 378), - listOf(2u, 2u) to Rational(598583, 7560), - listOf(3u, 2u) to Rational(85, 27), - listOf(4u, 2u) to Rational(2, 5), - listOf(0u, 3u) to Rational(130997, 315), - listOf(1u, 3u) to Rational(1093, 420), - listOf(2u, 3u) to Rational(9551, 2520), - listOf(3u, 3u) to Rational(-14, 45), - listOf(4u, 3u) to Rational(22, 45), - listOf(0u, 4u) to Rational(-2801, 9), - listOf(1u, 4u) to Rational(4033, 90), - listOf(2u, 4u) to Rational(6429, 80), - listOf(3u, 4u) to Rational(2851, 90), - listOf(4u, 4u) to Rational(293, 45), - listOf(0u, 5u) to Rational(-220, 1), - listOf(1u, 5u) to Rational(127, 1), - listOf(2u, 5u) to Rational(202, 5), - listOf(3u, 5u) to Rational(-63, 5), - listOf(4u, 5u) to Rational(-12, 5), - listOf(0u, 6u) to Rational(100, 1), - listOf(1u, 6u) to Rational(-80, 1), - listOf(2u, 6u) to Rational(-24, 1), - listOf(3u, 6u) to Rational(16, 1), - listOf(4u, 6u) to Rational(4, 1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(5407, 9), - listOf(1u) to Rational(9568, 27), - listOf(2u) to Rational(4996, 27), - listOf(3u) to Rational(352, 9), - listOf(4u) to Rational(22, 3), - listOf(0u, 1u) to Rational(104411, 126), - listOf(1u, 1u) to Rational(6001, 126), - listOf(2u, 1u) to Rational(-796, 21), - listOf(3u, 1u) to Rational(-5389, 126), - listOf(4u, 1u) to Rational(-166, 21), - listOf(0u, 2u) to Rational(-35327, 126), - listOf(1u, 2u) to Rational(53, 252), - listOf(2u, 2u) to Rational(849197, 6048), - listOf(3u, 2u) to Rational(22361, 252), - listOf(4u, 2u) to Rational(773, 42), - listOf(0u, 3u) to Rational(-6067, 21), - listOf(1u, 3u) to Rational(39049, 126), - listOf(2u, 3u) to Rational(80303, 1008), - listOf(3u, 3u) to Rational(-3035, 63), - listOf(4u, 3u) to Rational(-209, 21), - listOf(0u, 4u) to Rational(3113, 21), - listOf(1u, 4u) to Rational(-22345, 126), - listOf(2u, 4u) to Rational(-30931, 1008), - listOf(3u, 4u) to Rational(5837, 126), - listOf(4u, 4u) to Rational(229, 21), - listOf(0u, 5u) to Rational(-2120, 21), - listOf(1u, 5u) to Rational(451, 7), - listOf(2u, 5u) to Rational(422, 21), - listOf(3u, 5u) to Rational(-181, 21), - listOf(4u, 5u) to Rational(-40, 21), - listOf(0u, 6u) to Rational(100, 3), - listOf(1u, 6u) to Rational(-80, 3), - listOf(2u, 6u) to Rational(-8, 1), - listOf(3u, 6u) to Rational(16, 3), - listOf(4u, 6u) to Rational(4, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, bufferOf( - NumberedPolynomialAsIs( - listOf() to Rational(18, 1), - listOf(1u) to Rational(16, 3), - listOf(2u) to Rational(12, 6), - listOf(0u, 1u) to Rational(13, 1), - listOf(1u, 1u) to Rational(-11, 4), - listOf(2u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(-10, 1), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(2, 1), - ), - )), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 6), - listOf(1u) to Rational(1, 6), - listOf(2u) to Rational(-2, 9), - listOf(0u, 1u) to Rational(15, 1), - listOf(1u, 1u) to Rational(18, 7), - listOf(2u, 1u) to Rational(2, 5), - listOf(0u, 2u) to Rational(12, 9), - listOf(1u, 2u) to Rational(-3, 5), - listOf(2u, 2u) to Rational(4, 4), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-11, 9), - listOf(1u) to Rational(4, 9), - listOf(2u) to Rational(11, 6), - listOf(0u, 1u) to Rational(-5, 6), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(-1, 7), - listOf(0u, 2u) to Rational(9, 1), - listOf(1u, 2u) to Rational(6, 7), - listOf(2u, 2u) to Rational(1, 3), - ) - ).substitute(RationalField, bufferOf>()), - "test 6" - ) - } - @Test - @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not. - // Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p), - // not r^(deg(p)(deg(p)+1)/2) as it is now. - fun test_RationalFunction_substitute_RationalFunction_Buffer() { - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(0) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ), - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ) - )), - "test 1" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(4u) to Rational(-17166109, 793800), - listOf(3u, 1u) to Rational(-930960143, 5556600), - listOf(2u, 2u) to Rational(-144665109691, 350065800), - listOf(1u, 3u) to Rational(-17232577, 52920), - listOf(0u, 4u) to Rational(-68141, 1323), - ), - NumberedPolynomialAsIs( - listOf(4u) to Rational(-57522533, 14288400), - listOf(3u, 1u) to Rational(-13085162953, 300056400), - listOf(2u, 2u) to Rational(-92093367341, 525098700), - listOf(1u, 3u) to Rational(-1979342797, 6667920), - listOf(0u, 4u) to Rational(-3082727, 21168), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(11, 5), - listOf(0u, 1u) to Rational(8, 4), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(1, 9), - listOf(0u, 1u) to Rational(11, 7), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf(1u) to Rational(-2, 7), - listOf(0u, 1u) to Rational(-4, 3), - ), - NumberedPolynomialAsIs( - listOf(1u) to Rational(3, 6), - listOf(0u, 1u) to Rational(12, 8), - ) - ), - )), - "test 2" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-130778291, 76800), - listOf(1u) to Rational(-445270919, 230400), - listOf(2u) to Rational(44578444937, 14515200), - listOf(3u) to Rational(17329402153, 1555200), - listOf(4u) to Rational(89239926809, 2332800), - listOf(5u) to Rational(2808812267, 145152), - listOf(6u) to Rational(-21362661007, 725760), - listOf(7u) to Rational(-258455443, 2016), - listOf(8u) to Rational(-21454693, 96), - listOf(0u, 1u) to Rational(-1002137, 15360), - listOf(1u, 1u) to Rational(-1704849697, 430080), - listOf(2u, 1u) to Rational(-57657676789, 4838400), - listOf(3u, 1u) to Rational(-101331731, 89600), - listOf(4u, 1u) to Rational(5362280079329, 130636800), - listOf(5u, 1u) to Rational(4069896167053, 130636800), - listOf(6u, 1u) to Rational(12011514569, 544320), - listOf(7u, 1u) to Rational(138293195623, 725760), - listOf(8u, 1u) to Rational(6228779419, 48384), - listOf(0u, 2u) to Rational(-32395872823, 8064000), - listOf(1u, 2u) to Rational(-7398505523, 2304000), - listOf(2u, 2u) to Rational(95217051699521, 3048192000), - listOf(3u, 2u) to Rational(198026968812079, 3657830400), - listOf(4u, 2u) to Rational(4291645618499, 228614400), - listOf(5u, 2u) to Rational(-33211690942439, 914457600), - listOf(6u, 2u) to Rational(-637385538163153, 1371686400), - listOf(7u, 2u) to Rational(-138671528276273, 182891520), - listOf(8u, 2u) to Rational(-14566368751, 217728), - listOf(0u, 3u) to Rational(-10538718719, 2016000), - listOf(1u, 3u) to Rational(-1844485375199, 84672000), - listOf(2u, 3u) to Rational(103968665891, 12096000), - listOf(3u, 3u) to Rational(175402107278351, 1828915200), - listOf(4u, 3u) to Rational(8020699588879, 114307200), - listOf(5u, 3u) to Rational(3414841894991, 38102400), - listOf(6u, 3u) to Rational(1848405591611, 4665600), - listOf(7u, 3u) to Rational(39486708738989, 137168640), - listOf(8u, 3u) to Rational(255926289517, 9144576), - listOf(0u, 4u) to Rational(-655379564629, 105840000), - listOf(1u, 4u) to Rational(-208336039441, 127008000), - listOf(2u, 4u) to Rational(40173146771411, 1143072000), - listOf(3u, 4u) to Rational(150473493581239, 2667168000), - listOf(4u, 4u) to Rational(38833783990483, 1143072000), - listOf(5u, 4u) to Rational(-1963676248203053, 4800902400), - listOf(6u, 4u) to Rational(-2598759412825747, 3200601600), - listOf(7u, 4u) to Rational(-192895352019667, 1280240640), - listOf(8u, 4u) to Rational(3737382679, 6858432), - listOf(0u, 5u) to Rational(-16959378721, 1890000), - listOf(1u, 5u) to Rational(-1864802244743, 79380000), - listOf(2u, 5u) to Rational(13449261536489, 666792000), - listOf(3u, 5u) to Rational(215272234137329, 2667168000), - listOf(4u, 5u) to Rational(6040691379277, 83349000), - listOf(5u, 5u) to Rational(153687143525887, 800150400), - listOf(6u, 5u) to Rational(475602854903563, 2400451200), - listOf(7u, 5u) to Rational(27315599358749, 640120320), - listOf(8u, 5u) to Rational(-2630413357, 10668672), - listOf(0u, 6u) to Rational(-6654999511, 2646000), - listOf(1u, 6u) to Rational(-67885252327, 15876000), - listOf(2u, 6u) to Rational(5786776220983, 2667168000), - listOf(3u, 6u) to Rational(60615922629083, 1143072000), - listOf(4u, 6u) to Rational(-34703539637627407, 672126336000), - listOf(5u, 6u) to Rational(-744694192134101, 2240421120), - listOf(6u, 6u) to Rational(-1782470617231, 14817600), - listOf(7u, 6u) to Rational(59123208433, 8890560), - listOf(8u, 6u) to Rational(-141653, 5292), - listOf(0u, 7u) to Rational(-338051969, 441000), - listOf(1u, 7u) to Rational(468850013, 1764000), - listOf(2u, 7u) to Rational(2102343426101, 222264000), - listOf(3u, 7u) to Rational(7836130602007, 1333584000), - listOf(4u, 7u) to Rational(16239111865997, 746807040), - listOf(5u, 7u) to Rational(3824649185383, 88905600), - listOf(6u, 7u) to Rational(56058614459, 3457440), - listOf(7u, 7u) to Rational(-396766339, 493920), - listOf(8u, 7u) to Rational(-165147, 2744), - listOf(0u, 8u) to Rational(-3088619, 58800), - listOf(1u, 8u) to Rational(155343347, 88200), - listOf(2u, 8u) to Rational(100098736469, 7408800), - listOf(3u, 8u) to Rational(109725511381, 7408800), - listOf(4u, 8u) to Rational(-2431199641013, 59270400), - listOf(5u, 8u) to Rational(-102872383249, 3457440), - listOf(6u, 8u) to Rational(1449461309, 576240), - listOf(7u, 8u) to Rational(812775, 1372), - listOf(8u, 8u) to Rational(-16461, 343) - ), - NumberedPolynomialAsIs( - listOf() to Rational(164202773, 230400), - listOf(1u) to Rational(-70345303, 518400), - listOf(2u) to Rational(-4229702731, 4665600), - listOf(3u) to Rational(3262171027, 6998400), - listOf(4u) to Rational(-25423104169, 13996800), - listOf(5u) to Rational(64061869, 349920), - listOf(6u) to Rational(-1655878091, 116640), - listOf(7u) to Rational(-7991441, 648), - listOf(8u) to Rational(-502591, 18), - listOf(0u, 1u) to Rational(-8780429, 3840), - listOf(1u, 1u) to Rational(434272361, 115200), - listOf(2u, 1u) to Rational(429825727, 41472), - listOf(3u, 1u) to Rational(-10066790339, 6998400), - listOf(4u, 1u) to Rational(70022035471, 20995200), - listOf(5u, 1u) to Rational(-32070283493, 1399680), - listOf(6u, 1u) to Rational(-22051101001, 1399680), - listOf(7u, 1u) to Rational(-126493427, 12960), - listOf(8u, 1u) to Rational(3050245, 864), - listOf(0u, 2u) to Rational(-1194654631, 345600), - listOf(1u, 2u) to Rational(-542961452671, 31104000), - listOf(2u, 2u) to Rational(-234000873607, 48988800), - listOf(3u, 2u) to Rational(140520538087, 3628800), - listOf(4u, 2u) to Rational(9215088876563, 130636800), - listOf(5u, 2u) to Rational(27590569647253, 293932800), - listOf(6u, 2u) to Rational(5129057792891, 97977600), - listOf(7u, 2u) to Rational(-106334191, 5103), - listOf(8u, 2u) to Rational(-1024113911, 435456), - listOf(0u, 3u) to Rational(76223843, 6000), - listOf(1u, 3u) to Rational(57425857357, 2592000), - listOf(2u, 3u) to Rational(-2044736497573, 46656000), - listOf(3u, 3u) to Rational(-26155810120031, 293932800), - listOf(4u, 3u) to Rational(-1064419459813, 6998400), - listOf(5u, 3u) to Rational(-753782018389, 4082400), - listOf(6u, 3u) to Rational(-291973360873, 2799360), - listOf(7u, 3u) to Rational(-46372122599, 816480), - listOf(8u, 3u) to Rational(3579859657, 653184), - listOf(0u, 4u) to Rational(-13374241901, 4320000), - listOf(1u, 4u) to Rational(306606499811, 54432000), - listOf(2u, 4u) to Rational(964267124745437, 13716864000), - listOf(3u, 4u) to Rational(21603809415373, 182891520), - listOf(4u, 4u) to Rational(1097860214654027, 6858432000), - listOf(5u, 4u) to Rational(161615254570669, 914457600), - listOf(6u, 4u) to Rational(758415239461, 22861440), - listOf(7u, 4u) to Rational(2585568355471, 274337280), - listOf(8u, 4u) to Rational(-70433747863, 9144576), - listOf(0u, 5u) to Rational(-9582586217, 2520000), - listOf(1u, 5u) to Rational(-19093471394171, 635040000), - listOf(2u, 5u) to Rational(-13010261944411, 381024000), - listOf(3u, 5u) to Rational(-259039825301861, 4572288000), - listOf(4u, 5u) to Rational(-305081119071079, 2286144000), - listOf(5u, 5u) to Rational(-1923114383311, 19595520), - listOf(6u, 5u) to Rational(-14181787253231, 228614400), - listOf(7u, 5u) to Rational(-3959584789, 4354560), - listOf(8u, 5u) to Rational(4691742523, 762048), - listOf(0u, 6u) to Rational(-588323437, 180000), - listOf(1u, 6u) to Rational(5952234691, 52920000), - listOf(2u, 6u) to Rational(21001851056959, 1088640000), - listOf(3u, 6u) to Rational(84668034357563, 2133734400), - listOf(4u, 6u) to Rational(2029754605811557, 25604812800), - listOf(5u, 6u) to Rational(11721216739823, 426746880), - listOf(6u, 6u) to Rational(-8275903187003, 2133734400), - listOf(7u, 6u) to Rational(-4730447299, 2540160), - listOf(8u, 6u) to Rational(-46069985, 21168), - listOf(0u, 7u) to Rational(-75711301, 117600), - listOf(1u, 7u) to Rational(32430417413, 7056000), - listOf(2u, 7u) to Rational(677988533153, 98784000), - listOf(3u, 7u) to Rational(-948417645827, 71124480), - listOf(4u, 7u) to Rational(-11320265215207, 711244800), - listOf(5u, 7u) to Rational(-676438627783, 50803200), - listOf(6u, 7u) to Rational(-7382274253, 1975680), - listOf(7u, 7u) to Rational(6505733, 2205), - listOf(8u, 7u) to Rational(450137, 882), - listOf(0u, 8u) to Rational(-8368253, 78400), - listOf(1u, 8u) to Rational(6833783, 117600), - listOf(2u, 8u) to Rational(4528971133, 5927040), - listOf(3u, 8u) to Rational(146252636617, 29635200), - listOf(4u, 8u) to Rational(8321882556889, 1659571200), - listOf(5u, 8u) to Rational(-4686033011, 1975680), - listOf(6u, 8u) to Rational(-1074445963, 987840), - listOf(7u, 8u) to Rational(-142313, 588), - listOf(8u, 8u) to Rational(-4281, 49) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(14, 4), - listOf(1u) to Rational(7, 6), - listOf(2u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-15, 2), - listOf(1u, 1u) to Rational(-13, 8), - listOf(2u, 1u) to Rational(-14, 3), - listOf(0u, 2u) to Rational(-7, 6), - listOf(1u, 2u) to Rational(7, 4), - listOf(2u, 2u) to Rational(9, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-7, 4), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(-16, 2), - listOf(0u, 1u) to Rational(-15, 5), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(5, 4), - listOf(0u, 2u) to Rational(-12, 5), - listOf(1u, 2u) to Rational(-18, 2), - listOf(2u, 2u) to Rational(6, 7), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(5, 8), - listOf(1u) to Rational(-12, 6), - listOf(2u) to Rational(7, 6), - listOf(0u, 1u) to Rational(-10, 4), - listOf(1u, 1u) to Rational(-7, 6), - listOf(2u, 1u) to Rational(8, 9), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-13, 4), - listOf(2u, 2u) to Rational(5, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(10, 6), - listOf(1u) to Rational(-18, 6), - listOf(2u) to Rational(5, 1), - listOf(0u, 1u) to Rational(17, 7), - listOf(1u, 1u) to Rational(8, 4), - listOf(2u, 1u) to Rational(-4, 9), - listOf(0u, 2u) to Rational(-6, 5), - listOf(1u, 2u) to Rational(-15, 8), - listOf(2u, 2u) to Rational(-18, 5), - ) - ), - )), - "test 3" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-130778291, 76800), - listOf(1u) to Rational(-445270919, 230400), - listOf(2u) to Rational(44578444937, 14515200), - listOf(3u) to Rational(17329402153, 1555200), - listOf(4u) to Rational(89239926809, 2332800), - listOf(5u) to Rational(2808812267, 145152), - listOf(6u) to Rational(-21362661007, 725760), - listOf(7u) to Rational(-258455443, 2016), - listOf(8u) to Rational(-21454693, 96), - listOf(0u, 1u) to Rational(-1002137, 15360), - listOf(1u, 1u) to Rational(-1704849697, 430080), - listOf(2u, 1u) to Rational(-57657676789, 4838400), - listOf(3u, 1u) to Rational(-101331731, 89600), - listOf(4u, 1u) to Rational(5362280079329, 130636800), - listOf(5u, 1u) to Rational(4069896167053, 130636800), - listOf(6u, 1u) to Rational(12011514569, 544320), - listOf(7u, 1u) to Rational(138293195623, 725760), - listOf(8u, 1u) to Rational(6228779419, 48384), - listOf(0u, 2u) to Rational(-32395872823, 8064000), - listOf(1u, 2u) to Rational(-7398505523, 2304000), - listOf(2u, 2u) to Rational(95217051699521, 3048192000), - listOf(3u, 2u) to Rational(198026968812079, 3657830400), - listOf(4u, 2u) to Rational(4291645618499, 228614400), - listOf(5u, 2u) to Rational(-33211690942439, 914457600), - listOf(6u, 2u) to Rational(-637385538163153, 1371686400), - listOf(7u, 2u) to Rational(-138671528276273, 182891520), - listOf(8u, 2u) to Rational(-14566368751, 217728), - listOf(0u, 3u) to Rational(-10538718719, 2016000), - listOf(1u, 3u) to Rational(-1844485375199, 84672000), - listOf(2u, 3u) to Rational(103968665891, 12096000), - listOf(3u, 3u) to Rational(175402107278351, 1828915200), - listOf(4u, 3u) to Rational(8020699588879, 114307200), - listOf(5u, 3u) to Rational(3414841894991, 38102400), - listOf(6u, 3u) to Rational(1848405591611, 4665600), - listOf(7u, 3u) to Rational(39486708738989, 137168640), - listOf(8u, 3u) to Rational(255926289517, 9144576), - listOf(0u, 4u) to Rational(-655379564629, 105840000), - listOf(1u, 4u) to Rational(-208336039441, 127008000), - listOf(2u, 4u) to Rational(40173146771411, 1143072000), - listOf(3u, 4u) to Rational(150473493581239, 2667168000), - listOf(4u, 4u) to Rational(38833783990483, 1143072000), - listOf(5u, 4u) to Rational(-1963676248203053, 4800902400), - listOf(6u, 4u) to Rational(-2598759412825747, 3200601600), - listOf(7u, 4u) to Rational(-192895352019667, 1280240640), - listOf(8u, 4u) to Rational(3737382679, 6858432), - listOf(0u, 5u) to Rational(-16959378721, 1890000), - listOf(1u, 5u) to Rational(-1864802244743, 79380000), - listOf(2u, 5u) to Rational(13449261536489, 666792000), - listOf(3u, 5u) to Rational(215272234137329, 2667168000), - listOf(4u, 5u) to Rational(6040691379277, 83349000), - listOf(5u, 5u) to Rational(153687143525887, 800150400), - listOf(6u, 5u) to Rational(475602854903563, 2400451200), - listOf(7u, 5u) to Rational(27315599358749, 640120320), - listOf(8u, 5u) to Rational(-2630413357, 10668672), - listOf(0u, 6u) to Rational(-6654999511, 2646000), - listOf(1u, 6u) to Rational(-67885252327, 15876000), - listOf(2u, 6u) to Rational(5786776220983, 2667168000), - listOf(3u, 6u) to Rational(60615922629083, 1143072000), - listOf(4u, 6u) to Rational(-34703539637627407, 672126336000), - listOf(5u, 6u) to Rational(-744694192134101, 2240421120), - listOf(6u, 6u) to Rational(-1782470617231, 14817600), - listOf(7u, 6u) to Rational(59123208433, 8890560), - listOf(8u, 6u) to Rational(-141653, 5292), - listOf(0u, 7u) to Rational(-338051969, 441000), - listOf(1u, 7u) to Rational(468850013, 1764000), - listOf(2u, 7u) to Rational(2102343426101, 222264000), - listOf(3u, 7u) to Rational(7836130602007, 1333584000), - listOf(4u, 7u) to Rational(16239111865997, 746807040), - listOf(5u, 7u) to Rational(3824649185383, 88905600), - listOf(6u, 7u) to Rational(56058614459, 3457440), - listOf(7u, 7u) to Rational(-396766339, 493920), - listOf(8u, 7u) to Rational(-165147, 2744), - listOf(0u, 8u) to Rational(-3088619, 58800), - listOf(1u, 8u) to Rational(155343347, 88200), - listOf(2u, 8u) to Rational(100098736469, 7408800), - listOf(3u, 8u) to Rational(109725511381, 7408800), - listOf(4u, 8u) to Rational(-2431199641013, 59270400), - listOf(5u, 8u) to Rational(-102872383249, 3457440), - listOf(6u, 8u) to Rational(1449461309, 576240), - listOf(7u, 8u) to Rational(812775, 1372), - listOf(8u, 8u) to Rational(-16461, 343) - ), - NumberedPolynomialAsIs( - listOf() to Rational(164202773, 230400), - listOf(1u) to Rational(-70345303, 518400), - listOf(2u) to Rational(-4229702731, 4665600), - listOf(3u) to Rational(3262171027, 6998400), - listOf(4u) to Rational(-25423104169, 13996800), - listOf(5u) to Rational(64061869, 349920), - listOf(6u) to Rational(-1655878091, 116640), - listOf(7u) to Rational(-7991441, 648), - listOf(8u) to Rational(-502591, 18), - listOf(0u, 1u) to Rational(-8780429, 3840), - listOf(1u, 1u) to Rational(434272361, 115200), - listOf(2u, 1u) to Rational(429825727, 41472), - listOf(3u, 1u) to Rational(-10066790339, 6998400), - listOf(4u, 1u) to Rational(70022035471, 20995200), - listOf(5u, 1u) to Rational(-32070283493, 1399680), - listOf(6u, 1u) to Rational(-22051101001, 1399680), - listOf(7u, 1u) to Rational(-126493427, 12960), - listOf(8u, 1u) to Rational(3050245, 864), - listOf(0u, 2u) to Rational(-1194654631, 345600), - listOf(1u, 2u) to Rational(-542961452671, 31104000), - listOf(2u, 2u) to Rational(-234000873607, 48988800), - listOf(3u, 2u) to Rational(140520538087, 3628800), - listOf(4u, 2u) to Rational(9215088876563, 130636800), - listOf(5u, 2u) to Rational(27590569647253, 293932800), - listOf(6u, 2u) to Rational(5129057792891, 97977600), - listOf(7u, 2u) to Rational(-106334191, 5103), - listOf(8u, 2u) to Rational(-1024113911, 435456), - listOf(0u, 3u) to Rational(76223843, 6000), - listOf(1u, 3u) to Rational(57425857357, 2592000), - listOf(2u, 3u) to Rational(-2044736497573, 46656000), - listOf(3u, 3u) to Rational(-26155810120031, 293932800), - listOf(4u, 3u) to Rational(-1064419459813, 6998400), - listOf(5u, 3u) to Rational(-753782018389, 4082400), - listOf(6u, 3u) to Rational(-291973360873, 2799360), - listOf(7u, 3u) to Rational(-46372122599, 816480), - listOf(8u, 3u) to Rational(3579859657, 653184), - listOf(0u, 4u) to Rational(-13374241901, 4320000), - listOf(1u, 4u) to Rational(306606499811, 54432000), - listOf(2u, 4u) to Rational(964267124745437, 13716864000), - listOf(3u, 4u) to Rational(21603809415373, 182891520), - listOf(4u, 4u) to Rational(1097860214654027, 6858432000), - listOf(5u, 4u) to Rational(161615254570669, 914457600), - listOf(6u, 4u) to Rational(758415239461, 22861440), - listOf(7u, 4u) to Rational(2585568355471, 274337280), - listOf(8u, 4u) to Rational(-70433747863, 9144576), - listOf(0u, 5u) to Rational(-9582586217, 2520000), - listOf(1u, 5u) to Rational(-19093471394171, 635040000), - listOf(2u, 5u) to Rational(-13010261944411, 381024000), - listOf(3u, 5u) to Rational(-259039825301861, 4572288000), - listOf(4u, 5u) to Rational(-305081119071079, 2286144000), - listOf(5u, 5u) to Rational(-1923114383311, 19595520), - listOf(6u, 5u) to Rational(-14181787253231, 228614400), - listOf(7u, 5u) to Rational(-3959584789, 4354560), - listOf(8u, 5u) to Rational(4691742523, 762048), - listOf(0u, 6u) to Rational(-588323437, 180000), - listOf(1u, 6u) to Rational(5952234691, 52920000), - listOf(2u, 6u) to Rational(21001851056959, 1088640000), - listOf(3u, 6u) to Rational(84668034357563, 2133734400), - listOf(4u, 6u) to Rational(2029754605811557, 25604812800), - listOf(5u, 6u) to Rational(11721216739823, 426746880), - listOf(6u, 6u) to Rational(-8275903187003, 2133734400), - listOf(7u, 6u) to Rational(-4730447299, 2540160), - listOf(8u, 6u) to Rational(-46069985, 21168), - listOf(0u, 7u) to Rational(-75711301, 117600), - listOf(1u, 7u) to Rational(32430417413, 7056000), - listOf(2u, 7u) to Rational(677988533153, 98784000), - listOf(3u, 7u) to Rational(-948417645827, 71124480), - listOf(4u, 7u) to Rational(-11320265215207, 711244800), - listOf(5u, 7u) to Rational(-676438627783, 50803200), - listOf(6u, 7u) to Rational(-7382274253, 1975680), - listOf(7u, 7u) to Rational(6505733, 2205), - listOf(8u, 7u) to Rational(450137, 882), - listOf(0u, 8u) to Rational(-8368253, 78400), - listOf(1u, 8u) to Rational(6833783, 117600), - listOf(2u, 8u) to Rational(4528971133, 5927040), - listOf(3u, 8u) to Rational(146252636617, 29635200), - listOf(4u, 8u) to Rational(8321882556889, 1659571200), - listOf(5u, 8u) to Rational(-4686033011, 1975680), - listOf(6u, 8u) to Rational(-1074445963, 987840), - listOf(7u, 8u) to Rational(-142313, 588), - listOf(8u, 8u) to Rational(-4281, 49) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(14, 4), - listOf(1u) to Rational(7, 6), - listOf(2u) to Rational(7, 2), - listOf(0u, 1u) to Rational(-15, 2), - listOf(1u, 1u) to Rational(-13, 8), - listOf(2u, 1u) to Rational(-14, 3), - listOf(0u, 2u) to Rational(-7, 6), - listOf(1u, 2u) to Rational(7, 4), - listOf(2u, 2u) to Rational(9, 7), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-7, 4), - listOf(1u) to Rational(-6, 3), - listOf(2u) to Rational(-16, 2), - listOf(0u, 1u) to Rational(-15, 5), - listOf(1u, 1u) to Rational(4, 6), - listOf(2u, 1u) to Rational(5, 4), - listOf(0u, 2u) to Rational(-12, 5), - listOf(1u, 2u) to Rational(-18, 2), - listOf(2u, 2u) to Rational(6, 7), - ) - ), - )), - "test 4" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-506213, 2800), - listOf(1u) to Rational(9859, 315), - listOf(2u) to Rational(17384377, 11340), - listOf(3u) to Rational(-9662, 63), - listOf(4u) to Rational(-12563, 4), - listOf(0u, 1u) to Rational(-486293, 22400), - listOf(1u, 1u) to Rational(-6530947, 25200), - listOf(2u, 1u) to Rational(866125, 18144), - listOf(3u, 1u) to Rational(2948747, 2520), - listOf(4u, 1u) to Rational(1196611, 2016), - listOf(0u, 2u) to Rational(-20266021, 117600), - listOf(1u, 2u) to Rational(26656339, 44100), - listOf(2u, 2u) to Rational(19499183, 18144), - listOf(3u, 2u) to Rational(-19801849, 7560), - listOf(4u, 2u) to Rational(-2639635, 1296), - listOf(0u, 3u) to Rational(-5017697, 29400), - listOf(1u, 3u) to Rational(-606007, 1575), - listOf(2u, 3u) to Rational(127494487, 132300), - listOf(3u, 3u) to Rational(166567, 105), - listOf(4u, 3u) to Rational(486403, 18144), - listOf(0u, 4u) to Rational(-32182, 735), - listOf(1u, 4u) to Rational(2420671, 8820), - listOf(2u, 4u) to Rational(-12619193, 26460), - listOf(3u, 4u) to Rational(-6823067, 5670), - listOf(4u, 4u) to Rational(-2311693, 13608), - listOf(0u, 5u) to Rational(-13324, 245), - listOf(1u, 5u) to Rational(1966, 35), - listOf(2u, 5u) to Rational(1052719, 2520), - listOf(3u, 5u) to Rational(19153, 270), - listOf(4u, 5u) to Rational(701, 54), - listOf(0u, 6u) to Rational(4647, 196), - listOf(1u, 6u) to Rational(2197, 28), - listOf(2u, 6u) to Rational(-43853, 336), - listOf(3u, 6u) to Rational(-301, 3), - listOf(4u, 6u) to Rational(34, 3) - ), - NumberedPolynomialAsIs( - listOf() to Rational(-2843, 1600), - listOf(1u) to Rational(-1483, 240), - listOf(2u) to Rational(110623, 1296), - listOf(3u) to Rational(1265, 72), - listOf(4u) to Rational(-5011, 16), - listOf(0u, 1u) to Rational(47743, 1800), - listOf(1u, 1u) to Rational(619229, 32400), - listOf(2u, 1u) to Rational(-5978369, 58320), - listOf(3u, 1u) to Rational(-86081, 1620), - listOf(4u, 1u) to Rational(6325, 72), - listOf(0u, 2u) to Rational(110951, 3360), - listOf(1u, 2u) to Rational(-9550649, 302400), - listOf(2u, 2u) to Rational(6542933, 85050), - listOf(3u, 2u) to Rational(4708291, 38880), - listOf(4u, 2u) to Rational(-433327, 1296), - listOf(0u, 3u) to Rational(56143, 600), - listOf(1u, 3u) to Rational(94243, 720), - listOf(2u, 3u) to Rational(-46779139, 226800), - listOf(3u, 3u) to Rational(-6948253, 12960), - listOf(4u, 3u) to Rational(-260261, 486), - listOf(0u, 4u) to Rational(-3205317, 19600), - listOf(1u, 4u) to Rational(-201253, 1050), - listOf(2u, 4u) to Rational(332192677, 302400), - listOf(3u, 4u) to Rational(351511, 360), - listOf(4u, 4u) to Rational(-40547, 81), - listOf(0u, 5u) to Rational(-65421, 1960), - listOf(1u, 5u) to Rational(-10118, 35), - listOf(2u, 5u) to Rational(-4341709, 10080), - listOf(3u, 5u) to Rational(-91703, 360), - listOf(4u, 5u) to Rational(-85, 9), - listOf(0u, 6u) to Rational(-25965, 784), - listOf(1u, 6u) to Rational(3351, 16), - listOf(2u, 6u) to Rational(595159, 1344), - listOf(3u, 6u) to Rational(-1381, 12), - listOf(4u, 6u) to Rational(-155, 3) - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, bufferOf( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-17, 5), - listOf(1u) to Rational(2, 6), - listOf(2u) to Rational(14, 1), - listOf(0u, 1u) to Rational(-6, 6), - listOf(1u, 1u) to Rational(-7, 3), - listOf(2u, 1u) to Rational(-2, 9), - listOf(0u, 2u) to Rational(-9, 6), - listOf(1u, 2u) to Rational(17, 4), - listOf(2u, 2u) to Rational(2, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(5, 4), - listOf(1u) to Rational(-5, 9), - listOf(2u) to Rational(-3, 6), - listOf(0u, 1u) to Rational(6, 5), - listOf(1u, 1u) to Rational(14, 5), - listOf(2u, 1u) to Rational(5, 2), - listOf(0u, 2u) to Rational(-18, 7), - listOf(1u, 2u) to Rational(-8, 2), - listOf(2u, 2u) to Rational(18, 9), - ) - ), - )), - "test 5" - ) - assertEquals( - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(10, 2), - listOf(1u) to Rational(6, 7), - listOf(2u) to Rational(-16, 1), - listOf(0u, 1u) to Rational(13, 8), - listOf(1u, 1u) to Rational(-12, 1), - listOf(2u, 1u) to Rational(16, 8), - listOf(0u, 2u) to Rational(10, 4), - listOf(1u, 2u) to Rational(4, 1), - listOf(2u, 2u) to Rational(-11, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1, 4), - listOf(1u) to Rational(-17, 4), - listOf(2u) to Rational(-14, 8), - listOf(0u, 1u) to Rational(17, 9), - listOf(1u, 1u) to Rational(1, 3), - listOf(2u, 1u) to Rational(7, 6), - listOf(0u, 2u) to Rational(16, 3), - listOf(1u, 2u) to Rational(-17, 1), - listOf(2u, 2u) to Rational(-10, 8), - ) - ).substitute(RationalField, bufferOf>()), - "test 6" - ) - } - @Test - fun test_Polynomial_substituteFully_Double_Buffer() { - assertEquals( - 0.0, - NumberedPolynomialAsIs( - listOf() to 1.0, - listOf(1u) to -2.0, - listOf(2u) to 1.0, - ).substituteFully(bufferOf( - 1.0 - )), - 0.001, - "test 1" - ) - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 2" - ) { - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substituteFully(bufferOf()) - } - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 3" - ) { - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substituteFully(bufferOf( - 0.0, - )) - } - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 4" - ) { - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substituteFully(bufferOf( - 0.4846192734143442, - )) - } - assertEquals( - 1.934530767358133, - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substituteFully(bufferOf( - 0.4846192734143442, - 0.8400458576651112, - )), - 0.001, - "test 5" - ) - assertEquals( - 1.934530767358133, - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substituteFully(bufferOf( - 0.4846192734143442, - 0.8400458576651112, - 0.9211194782050933 - )), - 0.001, - "test 6" - ) - assertEquals( - 1.934530767358133, - NumberedPolynomialAsIs( - listOf() to 0.8597048543814783, - listOf(1u) to 0.22997637465889875, - listOf(2u) to 0.32675302591924016, - listOf(0u, 1u) to 0.4561746111587508, - listOf(1u, 1u) to 0.5304946210170756, - listOf(2u, 1u) to 0.6244313712888998, - listOf(0u, 2u) to 0.2700930201481795, - listOf(1u, 2u) to -0.06962351375204712, - listOf(2u, 2u) to -0.015206988092131501, - ).substituteFully(bufferOf( - 0.4846192734143442, - 0.8400458576651112, - 0.9211194782050933, - 0.4752854632152105 - )), - 0.001, - "test 7" - ) - } - @Test - fun test_Polynomial_substituteFully_Constant_Buffer() { - assertEquals( - Rational(0), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ).substituteFully(RationalField, bufferOf( - Rational(1) - )), - "test 1" - ) - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 2" - ) { - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substituteFully(RationalField, bufferOf()) - } - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 3" - ) { - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substituteFully( - RationalField, bufferOf( - Rational(-2, 5), - ) - ) - } - // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9 - assertEquals( - Rational(143, 150), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substituteFully(RationalField, bufferOf( - Rational(-2, 5), - Rational(12, 9), - )), - "test 4" - ) - assertEquals( - Rational(143, 150), - NumberedPolynomialAsIs( - listOf() to Rational(-3, 2), - listOf(1u) to Rational(8, 6), - listOf(2u) to Rational(14, 6), - listOf(0u, 1u) to Rational(-3, 1), - listOf(1u, 1u) to Rational(-19, 2), - listOf(2u, 1u) to Rational(9, 4), - listOf(0u, 2u) to Rational(5, 5), - listOf(1u, 2u) to Rational(18, 9), - listOf(2u, 2u) to Rational(5, 2), - ).substituteFully(RationalField, bufferOf( - Rational(-2, 5), - Rational(12, 9), - Rational(57, 179), - )), - "test 5" - ) - // https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9 - assertEquals( - Rational(47639065216, 2562890625), - NumberedPolynomialAsIs( - listOf(8u) to Rational(-3, 2), - listOf(7u, 1u) to Rational(8, 6), - listOf(6u, 2u) to Rational(14, 6), - listOf(5u, 3u) to Rational(-3, 1), - listOf(4u, 4u) to Rational(-19, 2), - listOf(3u, 5u) to Rational(9, 4), - listOf(2u, 6u) to Rational(5, 5), - listOf(1u, 7u) to Rational(18, 9), - listOf(0u, 8u) to Rational(5, 2), - ).substituteFully(RationalField, bufferOf( - Rational(-2, 5), - Rational(12, 9), - )), - "test 6" - ) - } - @Test - fun test_RationalFunction_substituteFully_Double_Buffer() { - assertEquals( - 0.0, - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 1.0, - listOf(1u) to -2.0, - listOf(2u) to 1.0, - ), - NumberedPolynomialAsIs( - listOf() to 1.0, - ) - ).substituteFully(bufferOf( - 1.0 - )), - 0.001, - "test 1" - ) - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 2" - ) { - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substituteFully(bufferOf()) - } - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 3" - ) { - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substituteFully( - bufferOf( - -8.11707689492641, - ) - ) - } - assertEquals( - -0.012718636022899672, - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substituteFully(bufferOf( - -8.11707689492641, - 0.795265651276015, - )), - 0.001, - "test 4" - ) - assertEquals( - -0.012718636022899672, - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to 6.593754860231304, - listOf(1u) to -7.853302571550634, - listOf(2u) to 1.2265042281530025, - listOf(0u, 1u) to 3.762648877294904, - listOf(1u, 1u) to -8.945144619305292, - listOf(2u, 1u) to -5.141384718042281, - listOf(0u, 2u) to 7.359794483988782, - listOf(1u, 2u) to -4.3526172680518815, - listOf(2u, 2u) to 0.907910924854372, - ), - NumberedPolynomialAsIs( - listOf() to 9.533292132172562, - listOf(1u) to -1.982814534018857, - listOf(2u) to -5.974248303415283, - listOf(0u, 1u) to 1.5876716499288879, - listOf(1u, 1u) to -7.535152566659664, - listOf(2u, 1u) to 0.7549300500153517, - listOf(0u, 2u) to -5.242030058021028, - listOf(1u, 2u) to -0.7265704289690582, - listOf(2u, 2u) to -7.139677818189821, - ) - ).substituteFully(bufferOf( - -8.11707689492641, - 0.795265651276015, - 0.9211194782050933 - )), - 0.001, - "test 5" - ) - } - @Test - fun test_RationalFunction_substituteFully_Constant_Buffer() { - assertEquals( - Rational(0), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1) - ), - NumberedPolynomialAsIs( - listOf() to Rational(1) - ) - ).substituteFully(RationalField, bufferOf( - Rational(1) - )), - "test 1" - ) - assertEquals( - Rational(-1322820, 2204953), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substituteFully(RationalField, bufferOf( - Rational(7, 5), - Rational(-13, 7), - Rational(-16, 4), - )), - "test 2" - ) - assertEquals( - Rational(-1322820, 2204953), - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substituteFully(RationalField, bufferOf( - Rational(7, 5), - Rational(-13, 7), - )), - "test 3" - ) - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 4" - ) { - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substituteFully( - RationalField, bufferOf( - Rational(7, 5), - ) - ) - } - assertFailsWithTypeAndMessage( - fullSubstitutionExceptionMessage, - "test 5" - ) { - NumberedRationalFunction( - NumberedPolynomialAsIs( - listOf() to Rational(-3, 5), - listOf(1u) to Rational(-18, 4), - listOf(2u) to Rational(9, 8), - listOf(0u, 1u) to Rational(-11, 6), - listOf(1u, 1u) to Rational(-16, 3), - listOf(2u, 1u) to Rational(12, 2), - listOf(0u, 2u) to Rational(5, 3), - listOf(1u, 2u) to Rational(17, 8), - listOf(2u, 2u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(11, 1), - listOf(1u) to Rational(4, 1), - listOf(2u) to Rational(-18, 3), - listOf(0u, 1u) to Rational(12, 9), - listOf(1u, 1u) to Rational(14, 7), - listOf(2u, 1u) to Rational(-17, 5), - listOf(0u, 2u) to Rational(-4, 1), - listOf(1u, 2u) to Rational(-5, 5), - listOf(2u, 2u) to Rational(-7, 8), - ) - ).substituteFully(RationalField, bufferOf()) - } - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_derivativeWithRespectTo_variable() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-2), - listOf(1u) to Rational(2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).derivativeWithRespectTo(RationalField, 0), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 3), - listOf(1u) to Rational(1, 1), - listOf(2u) to Rational(-33, 8), - listOf(3u) to Rational(72, 1), - listOf(0u, 1u) to Rational(2, 3), - listOf(1u, 1u) to Rational(-22, 1), - listOf(2u, 1u) to Rational(-1, 1), - listOf(3u, 1u) to Rational(-36, 1), - listOf(0u, 2u) to Rational(-8, 5), - listOf(1u, 2u) to Rational(-1, 4), - listOf(2u, 2u) to Rational(12, 7), - listOf(3u, 2u) to Rational(-2, 1), - listOf(0u, 3u) to Rational(16, 8), - listOf(1u, 3u) to Rational(-4, 1), - listOf(2u, 3u) to Rational(9, 2), - listOf(3u, 3u) to Rational(20, 9), - listOf(0u, 4u) to Rational(-10, 1), - listOf(1u, 4u) to Rational(-14, 1), - listOf(2u, 4u) to Rational(3, 7), - listOf(3u, 4u) to Rational(20, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, 0), - "test 2a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-18, 3), - listOf(1u) to Rational(2, 3), - listOf(2u) to Rational(-11, 1), - listOf(3u) to Rational(-1, 3), - listOf(4u) to Rational(-18, 2), - listOf(0u, 1u) to Rational(-20, 3), - listOf(1u, 1u) to Rational(-16, 5), - listOf(2u, 1u) to Rational(-1, 4), - listOf(3u, 1u) to Rational(8, 7), - listOf(4u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(9, 7), - listOf(1u, 2u) to Rational(6, 1), - listOf(2u, 2u) to Rational(-6, 1), - listOf(3u, 2u) to Rational(9, 2), - listOf(4u, 2u) to Rational(5, 3), - listOf(0u, 3u) to Rational(-9, 1), - listOf(1u, 3u) to Rational(-40, 1), - listOf(2u, 3u) to Rational(-28, 1), - listOf(3u, 3u) to Rational(4, 7), - listOf(4u, 3u) to Rational(20, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, 1), - "test 2b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(-1, 4), - listOf(2u, 2u) to Rational(12, 7), - listOf(3u, 2u) to Rational(-2, 1), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(-4, 1), - listOf(2u, 3u) to Rational(9, 2), - listOf(3u, 3u) to Rational(20, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(-14, 1), - listOf(2u, 4u) to Rational(3, 7), - listOf(3u, 4u) to Rational(20, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, 0), - "test 3a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(-1, 4), - listOf(3u, 1u) to Rational(8, 7), - listOf(4u, 1u) to Rational(-1, 1), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-6, 1), - listOf(3u, 2u) to Rational(9, 2), - listOf(4u, 2u) to Rational(5, 3), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-28, 1), - listOf(3u, 3u) to Rational(4, 7), - listOf(4u, 3u) to Rational(20, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, 1), - "test 3b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-2, 3), - listOf(1u) to Rational(1, 1), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 1u) to Rational(2, 3), - listOf(1u, 1u) to Rational(-22, 1), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-8, 5), - listOf(1u, 2u) to Rational(-1, 4), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).derivativeWithRespectTo(RationalField, 0), - "test 4a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-18, 3), - listOf(1u) to Rational(2, 3), - listOf(2u) to Rational(-11, 1), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-20, 3), - listOf(1u, 1u) to Rational(-16, 5), - listOf(2u, 1u) to Rational(-1, 4), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).derivativeWithRespectTo(RationalField, 1), - "test 4b" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).derivativeWithRespectTo(RationalField, 5), - "test 5" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthDerivativeWithRespectTo_variable_order() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-2), - listOf(1u) to Rational(2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 0, 1u), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 0, 0u), - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 0, 2u), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 0, 3u), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 0, 4u), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 1, 0u), - "test 6" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 1, 1u), - "test 7" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, 1, 2u), - "test 8" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1, 1), - listOf(1u) to Rational(-33, 4), - listOf(2u) to Rational(216, 1), - listOf(0u, 1u) to Rational(-22, 1), - listOf(1u, 1u) to Rational(-2, 1), - listOf(2u, 1u) to Rational(-108, 1), - listOf(0u, 2u) to Rational(-1, 4), - listOf(1u, 2u) to Rational(24, 7), - listOf(2u, 2u) to Rational(-6, 1), - listOf(0u, 3u) to Rational(-4, 1), - listOf(1u, 3u) to Rational(9, 1), - listOf(2u, 3u) to Rational(20, 3), - listOf(0u, 4u) to Rational(-14, 1), - listOf(1u, 4u) to Rational(6, 7), - listOf(2u, 4u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, 0, 2u), - "test 9a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-20, 3), - listOf(1u) to Rational(-16, 5), - listOf(2u) to Rational(-1, 4), - listOf(3u) to Rational(8, 7), - listOf(4u) to Rational(-1, 1), - listOf(0u, 1u) to Rational(18, 7), - listOf(1u, 1u) to Rational(12, 1), - listOf(2u, 1u) to Rational(-12, 1), - listOf(3u, 1u) to Rational(9, 1), - listOf(4u, 1u) to Rational(10, 3), - listOf(0u, 2u) to Rational(-27, 1), - listOf(1u, 2u) to Rational(-120, 1), - listOf(2u, 2u) to Rational(-84, 1), - listOf(3u, 2u) to Rational(12, 7), - listOf(4u, 2u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, 1, 2u), - "test 9b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-1, 4), - listOf(1u, 2u) to Rational(24, 7), - listOf(2u, 2u) to Rational(-6, 1), - listOf(0u, 3u) to Rational(-4, 1), - listOf(1u, 3u) to Rational(9, 1), - listOf(2u, 3u) to Rational(20, 3), - listOf(0u, 4u) to Rational(-14, 1), - listOf(1u, 4u) to Rational(6, 7), - listOf(2u, 4u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, 0, 2u), - "test 10a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(-1, 4), - listOf(3u) to Rational(8, 7), - listOf(4u) to Rational(-1, 1), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(-12, 1), - listOf(3u, 1u) to Rational(9, 1), - listOf(4u, 1u) to Rational(10, 3), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-84, 1), - listOf(3u, 2u) to Rational(12, 7), - listOf(4u, 2u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, 1, 2u), - "test 10b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1, 1), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(0u, 1u) to Rational(-22, 1), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-1, 4), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, 0, 2u), - "test 11a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-20, 3), - listOf(1u) to Rational(-16, 5), - listOf(2u) to Rational(-1, 4), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, 1, 2u), - "test 11b" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthDerivativeWithRespectTo_variablesAndOrders() { - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-2), - listOf(1u) to Rational(2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 1u)), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 0u)), - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 3u)), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 4u)), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 0u)), - "test 6" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 1u)), - "test 7" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 8" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf()), - "test 9" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-2), - listOf(1u) to Rational(2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf( - 0 to 1u, - 1 to 0u - )), - "test 10" - ) - assertEquals( - NumberedPolynomialAsIs(), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthDerivativeWithRespectTo(RationalField, mapOf( - 0 to 0u, - 1 to 1u - )), - "test 11" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1, 1), - listOf(1u) to Rational(-33, 4), - listOf(2u) to Rational(216, 1), - listOf(0u, 1u) to Rational(-22, 1), - listOf(1u, 1u) to Rational(-2, 1), - listOf(2u, 1u) to Rational(-108, 1), - listOf(0u, 2u) to Rational(-1, 4), - listOf(1u, 2u) to Rational(24, 7), - listOf(2u, 2u) to Rational(-6, 1), - listOf(0u, 3u) to Rational(-4, 1), - listOf(1u, 3u) to Rational(9, 1), - listOf(2u, 3u) to Rational(20, 3), - listOf(0u, 4u) to Rational(-14, 1), - listOf(1u, 4u) to Rational(6, 7), - listOf(2u, 4u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 12a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(2, 3), - listOf(1u) to Rational(-22, 1), - listOf(2u) to Rational(-1, 1), - listOf(3u) to Rational(-36, 1), - listOf(0u, 1u) to Rational(-16, 5), - listOf(1u, 1u) to Rational(-1, 2), - listOf(2u, 1u) to Rational(24, 7), - listOf(3u, 1u) to Rational(-4, 1), - listOf(0u, 2u) to Rational(6, 1), - listOf(1u, 2u) to Rational(-12, 1), - listOf(2u, 2u) to Rational(27, 2), - listOf(3u, 2u) to Rational(20, 3), - listOf(0u, 3u) to Rational(-40, 1), - listOf(1u, 3u) to Rational(-56, 1), - listOf(2u, 3u) to Rational(12, 7), - listOf(3u, 3u) to Rational(80, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 1u, 1 to 1u)), - "test 12b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-20, 3), - listOf(1u) to Rational(-16, 5), - listOf(2u) to Rational(-1, 4), - listOf(3u) to Rational(8, 7), - listOf(4u) to Rational(-1, 1), - listOf(0u, 1u) to Rational(18, 7), - listOf(1u, 1u) to Rational(12, 1), - listOf(2u, 1u) to Rational(-12, 1), - listOf(3u, 1u) to Rational(9, 1), - listOf(4u, 1u) to Rational(10, 3), - listOf(0u, 2u) to Rational(-27, 1), - listOf(1u, 2u) to Rational(-120, 1), - listOf(2u, 2u) to Rational(-84, 1), - listOf(3u, 2u) to Rational(12, 7), - listOf(4u, 2u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 12c" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-1, 4), - listOf(1u, 2u) to Rational(24, 7), - listOf(2u, 2u) to Rational(-6, 1), - listOf(0u, 3u) to Rational(-4, 1), - listOf(1u, 3u) to Rational(9, 1), - listOf(2u, 3u) to Rational(20, 3), - listOf(0u, 4u) to Rational(-14, 1), - listOf(1u, 4u) to Rational(6, 7), - listOf(2u, 4u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 13a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(-1, 2), - listOf(2u, 1u) to Rational(24, 7), - listOf(3u, 1u) to Rational(-4, 1), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(-12, 1), - listOf(2u, 2u) to Rational(27, 2), - listOf(3u, 2u) to Rational(20, 3), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(-56, 1), - listOf(2u, 3u) to Rational(12, 7), - listOf(3u, 3u) to Rational(80, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 1u, 1 to 1u)), - "test 13b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(-1, 4), - listOf(3u) to Rational(8, 7), - listOf(4u) to Rational(-1, 1), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(-12, 1), - listOf(3u, 1u) to Rational(9, 1), - listOf(4u, 1u) to Rational(10, 3), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-84, 1), - listOf(3u, 2u) to Rational(12, 7), - listOf(4u, 2u) to Rational(60, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 13c" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1, 1), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(0u, 1u) to Rational(-22, 1), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-1, 4), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 14a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(2, 3), - listOf(1u) to Rational(-22, 1), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(0u, 1u) to Rational(-16, 5), - listOf(1u, 1u) to Rational(-1, 2), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 1u, 1 to 1u)), - "test 14b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(-20, 3), - listOf(1u) to Rational(-16, 5), - listOf(2u) to Rational(-1, 4), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 14c" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_antiderivativeWithRespectTo_variable() { - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(1), - listOf(2u) to Rational(-1), - listOf(3u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).antiderivativeWithRespectTo(RationalField, 0), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(-6, 8), - listOf(2u) to Rational(-1, 3), - listOf(3u) to Rational(1, 6), - listOf(4u) to Rational(-11, 32), - listOf(5u) to Rational(18, 5), - listOf(1u, 1u) to Rational(-18, 3), - listOf(2u, 1u) to Rational(1, 3), - listOf(3u, 1u) to Rational(-11, 3), - listOf(4u, 1u) to Rational(-1, 12), - listOf(5u, 1u) to Rational(-18, 10), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(-4, 5), - listOf(3u, 2u) to Rational(-1, 24), - listOf(4u, 2u) to Rational(1, 7), - listOf(5u, 2u) to Rational(-1, 10), - listOf(1u, 3u) to Rational(3, 7), - listOf(2u, 3u) to Rational(1, 1), - listOf(3u, 3u) to Rational(-2, 3), - listOf(4u, 3u) to Rational(3, 8), - listOf(5u, 3u) to Rational(1, 9), - listOf(1u, 4u) to Rational(-18, 8), - listOf(2u, 4u) to Rational(-5, 1), - listOf(3u, 4u) to Rational(-7, 3), - listOf(4u, 4u) to Rational(1, 28), - listOf(5u, 4u) to Rational(1, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, 0), - "test 2a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 1u) to Rational(-6, 8), - listOf(1u, 1u) to Rational(-2, 3), - listOf(2u, 1u) to Rational(1, 2), - listOf(3u, 1u) to Rational(-11, 8), - listOf(4u, 1u) to Rational(18, 1), - listOf(0u, 2u) to Rational(-9, 3), - listOf(1u, 2u) to Rational(1, 3), - listOf(2u, 2u) to Rational(-11, 2), - listOf(3u, 2u) to Rational(-1, 6), - listOf(4u, 2u) to Rational(-9, 2), - listOf(0u, 3u) to Rational(-10, 9), - listOf(1u, 3u) to Rational(-8, 15), - listOf(2u, 3u) to Rational(-1, 24), - listOf(3u, 3u) to Rational(4, 21), - listOf(4u, 3u) to Rational(-1, 6), - listOf(0u, 4u) to Rational(3, 28), - listOf(1u, 4u) to Rational(1, 2), - listOf(2u, 4u) to Rational(-1, 2), - listOf(3u, 4u) to Rational(3, 8), - listOf(4u, 4u) to Rational(5, 36), - listOf(0u, 5u) to Rational(-9, 20), - listOf(1u, 5u) to Rational(-2, 1), - listOf(2u, 5u) to Rational(-7, 5), - listOf(3u, 5u) to Rational(1, 35), - listOf(4u, 5u) to Rational(1, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, 1), - "test 2b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(5u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(5u, 1u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(-1, 24), - listOf(4u, 2u) to Rational(1, 7), - listOf(5u, 2u) to Rational(-1, 10), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(-2, 3), - listOf(4u, 3u) to Rational(3, 8), - listOf(5u, 3u) to Rational(1, 9), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(-7, 3), - listOf(4u, 4u) to Rational(1, 28), - listOf(5u, 4u) to Rational(1, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, 0), - "test 3a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-1, 24), - listOf(3u, 3u) to Rational(4, 21), - listOf(4u, 3u) to Rational(-1, 6), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-1, 2), - listOf(3u, 4u) to Rational(3, 8), - listOf(4u, 4u) to Rational(5, 36), - listOf(0u, 5u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(-7, 5), - listOf(3u, 5u) to Rational(1, 35), - listOf(4u, 5u) to Rational(1, 1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, 1), - "test 3b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(-6, 8), - listOf(2u) to Rational(-1, 3), - listOf(3u) to Rational(1, 6), - listOf(4u) to Rational(0), - listOf(5u) to Rational(0), - listOf(1u, 1u) to Rational(-18, 3), - listOf(2u, 1u) to Rational(1, 3), - listOf(3u, 1u) to Rational(-11, 3), - listOf(4u, 1u) to Rational(0), - listOf(5u, 1u) to Rational(0), - listOf(1u, 2u) to Rational(-10, 3), - listOf(2u, 2u) to Rational(-4, 5), - listOf(3u, 2u) to Rational(-1, 24), - listOf(4u, 2u) to Rational(0), - listOf(5u, 2u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(5u, 3u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(5u, 4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).antiderivativeWithRespectTo(RationalField, 0), - "test 4a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 1u) to Rational(-6, 8), - listOf(1u, 1u) to Rational(-2, 3), - listOf(2u, 1u) to Rational(1, 2), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-9, 3), - listOf(1u, 2u) to Rational(1, 3), - listOf(2u, 2u) to Rational(-11, 2), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(-10, 9), - listOf(1u, 3u) to Rational(-8, 15), - listOf(2u, 3u) to Rational(-1, 24), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(0u, 5u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(0), - listOf(3u, 5u) to Rational(0), - listOf(4u, 5u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).antiderivativeWithRespectTo(RationalField, 1), - "test 4b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 0u, 0u, 0u, 0u, 1u) to Rational(-6, 8), - listOf(1u, 0u, 0u, 0u, 0u, 1u) to Rational(-2, 3), - listOf(2u, 0u, 0u, 0u, 0u, 1u) to Rational(1, 2), - listOf(3u, 0u, 0u, 0u, 0u, 1u) to Rational(-11, 8), - listOf(4u, 0u, 0u, 0u, 0u, 1u) to Rational(18, 1), - listOf(0u, 1u, 0u, 0u, 0u, 1u) to Rational(-18, 3), - listOf(1u, 1u, 0u, 0u, 0u, 1u) to Rational(2, 3), - listOf(2u, 1u, 0u, 0u, 0u, 1u) to Rational(-11, 1), - listOf(3u, 1u, 0u, 0u, 0u, 1u) to Rational(-1, 3), - listOf(4u, 1u, 0u, 0u, 0u, 1u) to Rational(-18, 2), - listOf(0u, 2u, 0u, 0u, 0u, 1u) to Rational(-10, 3), - listOf(1u, 2u, 0u, 0u, 0u, 1u) to Rational(-8, 5), - listOf(2u, 2u, 0u, 0u, 0u, 1u) to Rational(-1, 8), - listOf(3u, 2u, 0u, 0u, 0u, 1u) to Rational(4, 7), - listOf(4u, 2u, 0u, 0u, 0u, 1u) to Rational(-4, 8), - listOf(0u, 3u, 0u, 0u, 0u, 1u) to Rational(3, 7), - listOf(1u, 3u, 0u, 0u, 0u, 1u) to Rational(16, 8), - listOf(2u, 3u, 0u, 0u, 0u, 1u) to Rational(-16, 8), - listOf(3u, 3u, 0u, 0u, 0u, 1u) to Rational(12, 8), - listOf(4u, 3u, 0u, 0u, 0u, 1u) to Rational(5, 9), - listOf(0u, 4u, 0u, 0u, 0u, 1u) to Rational(-18, 8), - listOf(1u, 4u, 0u, 0u, 0u, 1u) to Rational(-10, 1), - listOf(2u, 4u, 0u, 0u, 0u, 1u) to Rational(-14, 2), - listOf(3u, 4u, 0u, 0u, 0u, 1u) to Rational(1, 7), - listOf(4u, 4u, 0u, 0u, 0u, 1u) to Rational(15, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).antiderivativeWithRespectTo(RationalField, 5), - "test 5" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthAntiderivativeWithRespectTo_variable_order() { - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(1), - listOf(2u) to Rational(-1), - listOf(3u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 1u), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 0u), - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-1, 3), - listOf(4u) to Rational(1, 12), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 2u), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(3u) to Rational(1, 6), - listOf(4u) to Rational(-1, 12), - listOf(5u) to Rational(1, 60), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 3u), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(4u) to Rational(1, 24), - listOf(5u) to Rational(-1, 60), - listOf(6u) to Rational(1, 360), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 4u), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 0u), - "test 6" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 1u) to Rational(1), - listOf(1u, 1u) to Rational(-2), - listOf(2u, 1u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 1u), - "test 7" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(1, 2), - listOf(1u, 2u) to Rational(-1), - listOf(2u, 2u) to Rational(1, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 2u), - "test 8" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(-3, 8), - listOf(3u) to Rational(-1, 9), - listOf(4u) to Rational(1, 24), - listOf(5u) to Rational(-11, 160), - listOf(6u) to Rational(3, 5), - listOf(2u, 1u) to Rational(-9, 3), - listOf(3u, 1u) to Rational(1, 9), - listOf(4u, 1u) to Rational(-11, 12), - listOf(5u, 1u) to Rational(-1, 60), - listOf(6u, 1u) to Rational(-3, 10), - listOf(2u, 2u) to Rational(-5, 3), - listOf(3u, 2u) to Rational(-4, 15), - listOf(4u, 2u) to Rational(-1, 96), - listOf(5u, 2u) to Rational(1, 35), - listOf(6u, 2u) to Rational(-1, 60), - listOf(2u, 3u) to Rational(3, 14), - listOf(3u, 3u) to Rational(1, 3), - listOf(4u, 3u) to Rational(-1, 6), - listOf(5u, 3u) to Rational(3, 40), - listOf(6u, 3u) to Rational(1, 54), - listOf(2u, 4u) to Rational(-9, 8), - listOf(3u, 4u) to Rational(-5, 3), - listOf(4u, 4u) to Rational(-7, 12), - listOf(5u, 4u) to Rational(1, 140), - listOf(6u, 4u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 2u), - "test 9a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(-3, 8), - listOf(1u, 2u) to Rational(-1, 3), - listOf(2u, 2u) to Rational(1, 4), - listOf(3u, 2u) to Rational(-11, 16), - listOf(4u, 2u) to Rational(9, 1), - listOf(0u, 3u) to Rational(-1, 1), - listOf(1u, 3u) to Rational(1, 9), - listOf(2u, 3u) to Rational(-11, 6), - listOf(3u, 3u) to Rational(-1, 18), - listOf(4u, 3u) to Rational(-9, 6), - listOf(0u, 4u) to Rational(-5, 18), - listOf(1u, 4u) to Rational(-2, 15), - listOf(2u, 4u) to Rational(-1, 96), - listOf(3u, 4u) to Rational(1, 21), - listOf(4u, 4u) to Rational(-1, 24), - listOf(0u, 5u) to Rational(3, 140), - listOf(1u, 5u) to Rational(1, 10), - listOf(2u, 5u) to Rational(-1, 10), - listOf(3u, 5u) to Rational(3, 40), - listOf(4u, 5u) to Rational(1, 36), - listOf(0u, 6u) to Rational(-3, 40), - listOf(1u, 6u) to Rational(-1, 3), - listOf(2u, 6u) to Rational(-7, 30), - listOf(3u, 6u) to Rational(1, 210), - listOf(4u, 6u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 2u), - "test 9b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(5u) to Rational(0), - listOf(6u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(5u, 1u) to Rational(0), - listOf(6u, 1u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(-1, 96), - listOf(5u, 2u) to Rational(1, 35), - listOf(6u, 2u) to Rational(-1, 60), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(-1, 6), - listOf(5u, 3u) to Rational(3, 40), - listOf(6u, 3u) to Rational(1, 54), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(-7, 12), - listOf(5u, 4u) to Rational(1, 140), - listOf(6u, 4u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 2u), - "test 10a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-1, 96), - listOf(3u, 4u) to Rational(1, 21), - listOf(4u, 4u) to Rational(-1, 24), - listOf(0u, 5u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(-1, 10), - listOf(3u, 5u) to Rational(3, 40), - listOf(4u, 5u) to Rational(1, 36), - listOf(0u, 6u) to Rational(0), - listOf(1u, 6u) to Rational(0), - listOf(2u, 6u) to Rational(-7, 30), - listOf(3u, 6u) to Rational(1, 210), - listOf(4u, 6u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 2u), - "test 10b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(-3, 8), - listOf(3u) to Rational(-1, 9), - listOf(4u) to Rational(1, 24), - listOf(5u) to Rational(0), - listOf(6u) to Rational(0), - listOf(2u, 1u) to Rational(-9, 3), - listOf(3u, 1u) to Rational(1, 9), - listOf(4u, 1u) to Rational(-11, 12), - listOf(5u, 1u) to Rational(0), - listOf(6u, 1u) to Rational(0), - listOf(2u, 2u) to Rational(-5, 3), - listOf(3u, 2u) to Rational(-4, 15), - listOf(4u, 2u) to Rational(-1, 96), - listOf(5u, 2u) to Rational(0), - listOf(6u, 2u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(5u, 3u) to Rational(0), - listOf(6u, 3u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(5u, 4u) to Rational(0), - listOf(6u, 4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 2u), - "test 11a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(-3, 8), - listOf(1u, 2u) to Rational(-1, 3), - listOf(2u, 2u) to Rational(1, 4), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(-1, 1), - listOf(1u, 3u) to Rational(1, 9), - listOf(2u, 3u) to Rational(-11, 6), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(-5, 18), - listOf(1u, 4u) to Rational(-2, 15), - listOf(2u, 4u) to Rational(-1, 96), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(0u, 5u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(0), - listOf(3u, 5u) to Rational(0), - listOf(4u, 5u) to Rational(0), - listOf(0u, 6u) to Rational(0), - listOf(1u, 6u) to Rational(0), - listOf(2u, 6u) to Rational(0), - listOf(3u, 6u) to Rational(0), - listOf(4u, 6u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 2u), - "test 11b" - ) - } - @Test - @OptIn(UnstableKMathAPI::class) - fun test_Polynomial_nthAntiderivativeWithRespectTo_variablesAndOrders() { - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(1), - listOf(2u) to Rational(-1), - listOf(3u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 1u)), - "test 1" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 0u), - "test 2" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-1, 3), - listOf(4u) to Rational(1, 12), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 2u), - "test 3" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(3u) to Rational(1, 6), - listOf(4u) to Rational(-1, 12), - listOf(5u) to Rational(1, 60), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 3u), - "test 4" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(4u) to Rational(1, 24), - listOf(5u) to Rational(-1, 60), - listOf(6u) to Rational(1, 360), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 0, 4u), - "test 5" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 0u), - "test 6" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 1u) to Rational(1), - listOf(1u, 1u) to Rational(-2), - listOf(2u, 1u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 1u), - "test 7" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(1, 2), - listOf(1u, 2u) to Rational(-1), - listOf(2u, 2u) to Rational(1, 2), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, 1, 2u), - "test 8" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf()), - "test 9" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u) to Rational(1), - listOf(2u) to Rational(-1), - listOf(3u) to Rational(1, 3), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf( - 0 to 1u, - 1 to 0u - )), - "test 10" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 1u) to Rational(1), - listOf(1u, 1u) to Rational(-2), - listOf(2u, 1u) to Rational(1), - ), - NumberedPolynomialAsIs( - listOf() to Rational(1), - listOf(1u) to Rational(-2), - listOf(2u) to Rational(1), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf( - 0 to 0u, - 1 to 1u - )), - "test 11" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(-3, 8), - listOf(3u) to Rational(-1, 9), - listOf(4u) to Rational(1, 24), - listOf(5u) to Rational(-11, 160), - listOf(6u) to Rational(3, 5), - listOf(2u, 1u) to Rational(-9, 3), - listOf(3u, 1u) to Rational(1, 9), - listOf(4u, 1u) to Rational(-11, 12), - listOf(5u, 1u) to Rational(-1, 60), - listOf(6u, 1u) to Rational(-3, 10), - listOf(2u, 2u) to Rational(-5, 3), - listOf(3u, 2u) to Rational(-4, 15), - listOf(4u, 2u) to Rational(-1, 96), - listOf(5u, 2u) to Rational(1, 35), - listOf(6u, 2u) to Rational(-1, 60), - listOf(2u, 3u) to Rational(3, 14), - listOf(3u, 3u) to Rational(1, 3), - listOf(4u, 3u) to Rational(-1, 6), - listOf(5u, 3u) to Rational(3, 40), - listOf(6u, 3u) to Rational(1, 54), - listOf(2u, 4u) to Rational(-9, 8), - listOf(3u, 4u) to Rational(-5, 3), - listOf(4u, 4u) to Rational(-7, 12), - listOf(5u, 4u) to Rational(1, 140), - listOf(6u, 4u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 12a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u, 1u) to Rational(-6, 8), - listOf(2u, 1u) to Rational(-1, 3), - listOf(3u, 1u) to Rational(1, 6), - listOf(4u, 1u) to Rational(-11, 32), - listOf(5u, 1u) to Rational(18, 5), - listOf(1u, 2u) to Rational(-9, 3), - listOf(2u, 2u) to Rational(1, 6), - listOf(3u, 2u) to Rational(-11, 6), - listOf(4u, 2u) to Rational(-1, 24), - listOf(5u, 2u) to Rational(-9, 10), - listOf(1u, 3u) to Rational(-10, 9), - listOf(2u, 3u) to Rational(-4, 15), - listOf(3u, 3u) to Rational(-1, 72), - listOf(4u, 3u) to Rational(1, 21), - listOf(5u, 3u) to Rational(-1, 30), - listOf(1u, 4u) to Rational(3, 28), - listOf(2u, 4u) to Rational(1, 4), - listOf(3u, 4u) to Rational(-1, 6), - listOf(4u, 4u) to Rational(3, 32), - listOf(5u, 4u) to Rational(1, 36), - listOf(1u, 5u) to Rational(-9, 20), - listOf(2u, 5u) to Rational(-1, 1), - listOf(3u, 5u) to Rational(-7, 15), - listOf(4u, 5u) to Rational(1, 140), - listOf(5u, 5u) to Rational(1, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 1u, 1 to 1u)), - "test 12b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(-3, 8), - listOf(1u, 2u) to Rational(-1, 3), - listOf(2u, 2u) to Rational(1, 4), - listOf(3u, 2u) to Rational(-11, 16), - listOf(4u, 2u) to Rational(9, 1), - listOf(0u, 3u) to Rational(-1, 1), - listOf(1u, 3u) to Rational(1, 9), - listOf(2u, 3u) to Rational(-11, 6), - listOf(3u, 3u) to Rational(-1, 18), - listOf(4u, 3u) to Rational(-9, 6), - listOf(0u, 4u) to Rational(-5, 18), - listOf(1u, 4u) to Rational(-2, 15), - listOf(2u, 4u) to Rational(-1, 96), - listOf(3u, 4u) to Rational(1, 21), - listOf(4u, 4u) to Rational(-1, 24), - listOf(0u, 5u) to Rational(3, 140), - listOf(1u, 5u) to Rational(1, 10), - listOf(2u, 5u) to Rational(-1, 10), - listOf(3u, 5u) to Rational(3, 40), - listOf(4u, 5u) to Rational(1, 36), - listOf(0u, 6u) to Rational(-3, 40), - listOf(1u, 6u) to Rational(-1, 3), - listOf(2u, 6u) to Rational(-7, 30), - listOf(3u, 6u) to Rational(1, 210), - listOf(4u, 6u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(-11, 8), - listOf(4u) to Rational(18, 1), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(-1, 3), - listOf(4u, 1u) to Rational(-18, 2), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(3, 7), - listOf(1u, 3u) to Rational(16, 8), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(-18, 8), - listOf(1u, 4u) to Rational(-10, 1), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 12c" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(5u) to Rational(0), - listOf(6u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(5u, 1u) to Rational(0), - listOf(6u, 1u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(-1, 96), - listOf(5u, 2u) to Rational(1, 35), - listOf(6u, 2u) to Rational(-1, 60), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(-1, 6), - listOf(5u, 3u) to Rational(3, 40), - listOf(6u, 3u) to Rational(1, 54), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(-7, 12), - listOf(5u, 4u) to Rational(1, 140), - listOf(6u, 4u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 13a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(5u, 1u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(5u, 2u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(-1, 72), - listOf(4u, 3u) to Rational(1, 21), - listOf(5u, 3u) to Rational(-1, 30), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(-1, 6), - listOf(4u, 4u) to Rational(3, 32), - listOf(5u, 4u) to Rational(1, 36), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(0), - listOf(3u, 5u) to Rational(-7, 15), - listOf(4u, 5u) to Rational(1, 140), - listOf(5u, 5u) to Rational(1, 5), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 1u, 1 to 1u)), - "test 13b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(0), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-1, 96), - listOf(3u, 4u) to Rational(1, 21), - listOf(4u, 4u) to Rational(-1, 24), - listOf(0u, 5u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(-1, 10), - listOf(3u, 5u) to Rational(3, 40), - listOf(4u, 5u) to Rational(1, 36), - listOf(0u, 6u) to Rational(0), - listOf(1u, 6u) to Rational(0), - listOf(2u, 6u) to Rational(-7, 30), - listOf(3u, 6u) to Rational(1, 210), - listOf(4u, 6u) to Rational(1, 6), - ), - NumberedPolynomialAsIs( - listOf() to Rational(0), - listOf(1u) to Rational(0), - listOf(2u) to Rational(0), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(0), - listOf(1u, 1u) to Rational(0), - listOf(2u, 1u) to Rational(0), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(0), - listOf(1u, 2u) to Rational(0), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(4, 7), - listOf(4u, 2u) to Rational(-4, 8), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(-16, 8), - listOf(3u, 3u) to Rational(12, 8), - listOf(4u, 3u) to Rational(5, 9), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(-14, 2), - listOf(3u, 4u) to Rational(1, 7), - listOf(4u, 4u) to Rational(15, 3), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 13c" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(2u) to Rational(-3, 8), - listOf(3u) to Rational(-1, 9), - listOf(4u) to Rational(1, 24), - listOf(5u) to Rational(0), - listOf(6u) to Rational(0), - listOf(2u, 1u) to Rational(-9, 3), - listOf(3u, 1u) to Rational(1, 9), - listOf(4u, 1u) to Rational(-11, 12), - listOf(5u, 1u) to Rational(0), - listOf(6u, 1u) to Rational(0), - listOf(2u, 2u) to Rational(-5, 3), - listOf(3u, 2u) to Rational(-4, 15), - listOf(4u, 2u) to Rational(-1, 96), - listOf(5u, 2u) to Rational(0), - listOf(6u, 2u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(5u, 3u) to Rational(0), - listOf(6u, 3u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(5u, 4u) to Rational(0), - listOf(6u, 4u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 2u)), - "test 14a" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(1u, 1u) to Rational(-6, 8), - listOf(2u, 1u) to Rational(-1, 3), - listOf(3u, 1u) to Rational(1, 6), - listOf(4u, 1u) to Rational(0), - listOf(5u, 1u) to Rational(0), - listOf(1u, 2u) to Rational(-9, 3), - listOf(2u, 2u) to Rational(1, 6), - listOf(3u, 2u) to Rational(-11, 6), - listOf(4u, 2u) to Rational(0), - listOf(5u, 2u) to Rational(0), - listOf(1u, 3u) to Rational(-10, 9), - listOf(2u, 3u) to Rational(-4, 15), - listOf(3u, 3u) to Rational(-1, 72), - listOf(4u, 3u) to Rational(0), - listOf(5u, 3u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(5u, 4u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(0), - listOf(3u, 5u) to Rational(0), - listOf(4u, 5u) to Rational(0), - listOf(5u, 5u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 1u, 1 to 1u)), - "test 14b" - ) - assertEquals( - NumberedPolynomialAsIs( - listOf(0u, 2u) to Rational(-3, 8), - listOf(1u, 2u) to Rational(-1, 3), - listOf(2u, 2u) to Rational(1, 4), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(-1, 1), - listOf(1u, 3u) to Rational(1, 9), - listOf(2u, 3u) to Rational(-11, 6), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(-5, 18), - listOf(1u, 4u) to Rational(-2, 15), - listOf(2u, 4u) to Rational(-1, 96), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - listOf(0u, 5u) to Rational(0), - listOf(1u, 5u) to Rational(0), - listOf(2u, 5u) to Rational(0), - listOf(3u, 5u) to Rational(0), - listOf(4u, 5u) to Rational(0), - listOf(0u, 6u) to Rational(0), - listOf(1u, 6u) to Rational(0), - listOf(2u, 6u) to Rational(0), - listOf(3u, 6u) to Rational(0), - listOf(4u, 6u) to Rational(0), - ), - NumberedPolynomialAsIs( - listOf() to Rational(-6, 8), - listOf(1u) to Rational(-2, 3), - listOf(2u) to Rational(1, 2), - listOf(3u) to Rational(0), - listOf(4u) to Rational(0), - listOf(0u, 1u) to Rational(-18, 3), - listOf(1u, 1u) to Rational(2, 3), - listOf(2u, 1u) to Rational(-11, 1), - listOf(3u, 1u) to Rational(0), - listOf(4u, 1u) to Rational(0), - listOf(0u, 2u) to Rational(-10, 3), - listOf(1u, 2u) to Rational(-8, 5), - listOf(2u, 2u) to Rational(-1, 8), - listOf(3u, 2u) to Rational(0), - listOf(4u, 2u) to Rational(0), - listOf(0u, 3u) to Rational(0), - listOf(1u, 3u) to Rational(0), - listOf(2u, 3u) to Rational(0), - listOf(3u, 3u) to Rational(0), - listOf(4u, 3u) to Rational(0), - listOf(0u, 4u) to Rational(0), - listOf(1u, 4u) to Rational(0), - listOf(2u, 4u) to Rational(0), - listOf(3u, 4u) to Rational(0), - listOf(4u, 4u) to Rational(0), - ).nthAntiderivativeWithRespectTo(RationalField, mapOf(1 to 2u)), - "test 14c" - ) - } -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt deleted file mode 100644 index ab912a464..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt +++ /dev/null @@ -1,12 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions.testUtils - -import space.kscience.kmath.structures.Buffer -import space.kscience.kmath.structures.asBuffer - - -fun bufferOf(vararg elements: T): Buffer = elements.asBuffer() \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/IntModulo.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/IntModulo.kt deleted file mode 100644 index a037dcd18..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/IntModulo.kt +++ /dev/null @@ -1,133 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions.testUtils - -import space.kscience.kmath.operations.Ring - - -class IntModulo { - val residue: Int - val modulus: Int - - @PublishedApi - internal constructor(residue: Int, modulus: Int, toCheckInput: Boolean = true) { - if (toCheckInput) { - require(modulus != 0) { "modulus can not be zero" } - this.modulus = if (modulus < 0) -modulus else modulus - this.residue = residue.mod(this.modulus) - } else { - this.residue = residue - this.modulus = modulus - } - } - - constructor(residue: Int, modulus: Int) : this(residue, modulus, true) - - operator fun unaryPlus(): IntModulo = this - operator fun unaryMinus(): IntModulo = - IntModulo( - if (residue == 0) 0 else modulus - residue, - modulus, - toCheckInput = false - ) - operator fun plus(other: IntModulo): IntModulo { - require(modulus == other.modulus) { "can not add two residue different modulo" } - return IntModulo( - (residue + other.residue) % modulus, - modulus, - toCheckInput = false - ) - } - operator fun plus(other: Int): IntModulo = - IntModulo( - (residue + other) % modulus, - modulus, - toCheckInput = false - ) - operator fun minus(other: IntModulo): IntModulo { - require(modulus == other.modulus) { "can not subtract two residue different modulo" } - return IntModulo( - (residue - other.residue) % modulus, - modulus, - toCheckInput = false - ) - } - operator fun minus(other: Int): IntModulo = - IntModulo( - (residue - other) % modulus, - modulus, - toCheckInput = false - ) - operator fun times(other: IntModulo): IntModulo { - require(modulus == other.modulus) { "can not multiply two residue different modulo" } - return IntModulo( - (residue * other.residue) % modulus, - modulus, - toCheckInput = false - ) - } - operator fun times(other: Int): IntModulo = - IntModulo( - (residue * other) % modulus, - modulus, - toCheckInput = false - ) - operator fun div(other: IntModulo): IntModulo { - require(modulus == other.modulus) { "can not divide two residue different modulo" } - val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other.residue, modulus) - require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" } - return IntModulo( - (residue * reciprocalCandidate) % modulus, - modulus, - toCheckInput = false - ) - } - operator fun div(other: Int): IntModulo { - val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other, modulus) - require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" } - return IntModulo( - (residue * reciprocalCandidate) % modulus, - modulus, - toCheckInput = false - ) - } - override fun equals(other: Any?): Boolean = - when (other) { - is IntModulo -> residue == other.residue && modulus == other.modulus - else -> false - } - - override fun hashCode(): Int = residue.hashCode() - - override fun toString(): String = "$residue mod $modulus" -} - -@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE") -class IntModuloRing : Ring { - - val modulus: Int - - constructor(modulus: Int) { - require(modulus != 0) { "modulus can not be zero" } - this.modulus = if (modulus < 0) -modulus else modulus - } - - override inline val zero: IntModulo get() = IntModulo(0, modulus, toCheckInput = false) - override inline val one: IntModulo get() = IntModulo(1, modulus, toCheckInput = false) - - fun number(arg: Int): IntModulo = IntModulo(arg, modulus, toCheckInput = false) - - override inline fun add(left: IntModulo, right: IntModulo): IntModulo = left + right - override inline fun multiply(left: IntModulo, right: IntModulo): IntModulo = left * right - - override inline fun IntModulo.unaryMinus(): IntModulo = -this - override inline fun IntModulo.plus(arg: IntModulo): IntModulo = this + arg - override inline fun IntModulo.minus(arg: IntModulo): IntModulo = this - arg - override inline fun IntModulo.times(arg: IntModulo): IntModulo = this * arg - inline fun IntModulo.div(arg: IntModulo): IntModulo = this / arg -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/IntModuloUtils.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/IntModuloUtils.kt deleted file mode 100644 index 615523873..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/IntModuloUtils.kt +++ /dev/null @@ -1,19 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions.testUtils - -import space.kscience.kmath.functions.ListPolynomial -import space.kscience.kmath.functions.ListPolynomialSpace -import space.kscience.kmath.functions.PolynomialSpaceOverRing - - -fun ListPolynomialSpace.ListPolynomial(vararg coefs: Int): ListPolynomial = - ListPolynomial(coefs.map { IntModulo(it, ring.modulus) }) -fun IntModuloRing.ListPolynomial(vararg coefs: Int): ListPolynomial = - ListPolynomial(coefs.map { IntModulo(it, modulus) }) - -fun IntModuloRing.m(arg: Int): IntModulo = IntModulo(arg, modulus) -fun PolynomialSpaceOverRing.m(arg: Int): IntModulo = IntModulo(arg, ring.modulus) \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/NTMisc.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/NTMisc.kt deleted file mode 100644 index 61b50f128..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/NTMisc.kt +++ /dev/null @@ -1,29 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions.testUtils - -import kotlin.math.abs - - -internal data class BezoutIdentityWithGCD(val first: T, val second: T, val gcd: T) - -internal tailrec fun gcd(a: Long, b: Long): Long = if (a == 0L) abs(b) else gcd(b % a, a) - -internal fun bezoutIdentityWithGCD(a: Int, b: Int): BezoutIdentityWithGCD = - when { - a < 0 && b < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, -second, gcd) } - a < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, second, gcd) } - b < 0 -> with(bezoutIdentityWithGCDInternalLogic(a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(first, -second, gcd) } - else -> bezoutIdentityWithGCDInternalLogic(a, b, 1, 0, 0, 1) - } - -internal tailrec fun bezoutIdentityWithGCDInternalLogic(a: Int, b: Int, m1: Int, m2: Int, m3: Int, m4: Int): BezoutIdentityWithGCD = - if (b == 0) BezoutIdentityWithGCD(m1, m3, a) - else { - val quotient = a / b - val reminder = a % b - bezoutIdentityWithGCDInternalLogic(b, reminder, m2, m1 - quotient * m2, m4, m3 - quotient * m4) - } \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/Rational.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/Rational.kt deleted file mode 100644 index 0a3d00e96..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/Rational.kt +++ /dev/null @@ -1,177 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress") - -package space.kscience.kmath.functions.testUtils - -import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.operations.Field -import space.kscience.kmath.operations.NumbersAddOps - -@Suppress("NAME_SHADOWING") -class Rational { - companion object { - val ZERO: Rational = Rational(0L) - val ONE: Rational = Rational(1L) - } - - val numerator: Long - val denominator: Long - - internal constructor(numerator: Long, denominator: Long, toCheckInput: Boolean = true) { - if (toCheckInput) { - if (denominator == 0L) throw ArithmeticException("/ by zero") - - val greatestCommonDivider = gcd(numerator, denominator).let { if (denominator < 0L) -it else it } - - this.numerator = numerator / greatestCommonDivider - this.denominator = denominator / greatestCommonDivider - } else { - this.numerator = numerator - this.denominator = denominator - } - } - - constructor(numerator: Int, denominator: Int) : this(numerator.toLong(), denominator.toLong(), true) - constructor(numerator: Int, denominator: Long) : this(numerator.toLong(), denominator, true) - constructor(numerator: Long, denominator: Int) : this(numerator, denominator.toLong(), true) - constructor(numerator: Long, denominator: Long) : this(numerator, denominator, true) - constructor(numerator: Int) : this(numerator.toLong(), 1L, false) - constructor(numerator: Long) : this(numerator, 1L, false) - - operator fun unaryPlus(): Rational = this - operator fun unaryMinus(): Rational = Rational(-this.numerator, this.denominator) - operator fun plus(other: Rational): Rational { - val denominatorsGcd = gcd(denominator, other.denominator) - val dividedThisDenominator = denominator / denominatorsGcd - val dividedOtherDenominator = other.denominator / denominatorsGcd - val numeratorCandidate = numerator * dividedOtherDenominator + dividedThisDenominator * other.numerator - val secondGcd = gcd(numeratorCandidate, denominatorsGcd) - return Rational( - numeratorCandidate / secondGcd, - dividedThisDenominator * (other.denominator / secondGcd), - toCheckInput = false - ) - } - operator fun plus(other: Int): Rational = - Rational( - numerator + denominator * other.toLong(), - denominator, - toCheckInput = false - ) - operator fun plus(other: Long): Rational = - Rational( - numerator + denominator * other, - denominator, - toCheckInput = false - ) - operator fun minus(other: Rational): Rational { - val denominatorsGcd = gcd(denominator, other.denominator) - val dividedThisDenominator = denominator / denominatorsGcd - val dividedOtherDenominator = other.denominator / denominatorsGcd - val numeratorCandidate = numerator * dividedOtherDenominator - dividedThisDenominator * other.numerator - val secondGcd = gcd(numeratorCandidate, denominatorsGcd) - return Rational( - numeratorCandidate / secondGcd, - dividedThisDenominator * (other.denominator / secondGcd), - toCheckInput = false - ) - } - operator fun minus(other: Int): Rational = - Rational( - numerator - denominator * other.toLong(), - denominator, - toCheckInput = false - ) - operator fun minus(other: Long): Rational = - Rational( - numerator - denominator * other, - denominator, - toCheckInput = false - ) - operator fun times(other: Rational): Rational { - val thisDenominatorAndOtherNumeratorGcd = gcd(denominator, other.numerator) - val otherDenominatorAndThisNumeratorGcd = gcd(other.denominator, numerator) - return Rational( - (numerator / otherDenominatorAndThisNumeratorGcd) * (other.numerator / thisDenominatorAndOtherNumeratorGcd), - (denominator / thisDenominatorAndOtherNumeratorGcd) * (other.denominator / otherDenominatorAndThisNumeratorGcd), - toCheckInput = false - ) - } - operator fun times(other: Int): Rational { - val other = other.toLong() - val denominatorAndOtherGcd = gcd(denominator, other) - return Rational( - numerator * (other / denominatorAndOtherGcd), - denominator / denominatorAndOtherGcd, - toCheckInput = false - ) - } - operator fun times(other: Long): Rational { - val denominatorAndOtherGcd = gcd(denominator, other) - return Rational( - numerator * (other / denominatorAndOtherGcd), - denominator / denominatorAndOtherGcd, - toCheckInput = false - ) - } - operator fun div(other: Rational): Rational { - val denominatorsGcd = gcd(denominator, other.denominator) - val numeratorsGcd = gcd(numerator, other.numerator) - return Rational( - (numerator / numeratorsGcd) * (other.denominator / denominatorsGcd), - (denominator / denominatorsGcd) * (other.numerator / numeratorsGcd) - ) - } - operator fun div(other: Int): Rational { - val other = other.toLong() - val numeratorAndOtherGcd = gcd(numerator, other) - return Rational( - numerator / numeratorAndOtherGcd, - denominator * (other / numeratorAndOtherGcd), - toCheckInput = false - ) - } - operator fun div(other: Long): Rational { - val numeratorAndOtherGcd = gcd(numerator, other) - return Rational( - numerator / numeratorAndOtherGcd, - denominator * (other / numeratorAndOtherGcd), - toCheckInput = false - ) - } - override fun equals(other: Any?): Boolean = - when (other) { - is Rational -> numerator == other.numerator && denominator == other.denominator - is Int -> numerator == other && denominator == 1L - is Long -> numerator == other && denominator == 1L - else -> false - } - - override fun hashCode(): Int = 31 * numerator.hashCode() + denominator.hashCode() - - override fun toString(): String = if (denominator == 1L) "$numerator" else "$numerator/$denominator" -} - -@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE") -@OptIn(UnstableKMathAPI::class) -object RationalField : Field, NumbersAddOps { - override inline val zero: Rational get() = Rational.ZERO - override inline val one: Rational get() = Rational.ONE - - override inline fun number(value: Number): Rational = Rational(value.toLong()) - - override inline fun add(left: Rational, right: Rational): Rational = left + right - override inline fun multiply(left: Rational, right: Rational): Rational = left * right - override inline fun divide(left: Rational, right: Rational): Rational = left / right - override inline fun scale(a: Rational, value: Double): Rational = a * number(value) - - override inline fun Rational.unaryMinus(): Rational = -this - override inline fun Rational.plus(arg: Rational): Rational = this + arg - override inline fun Rational.minus(arg: Rational): Rational = this - arg - override inline fun Rational.times(arg: Rational): Rational = this * arg - override inline fun Rational.div(arg: Rational): Rational = this / arg -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt deleted file mode 100644 index c70c229ca..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt +++ /dev/null @@ -1,104 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions.testUtils - -import space.kscience.kmath.functions.LabeledPolynomial -import space.kscience.kmath.functions.LabeledRationalFunction -import space.kscience.kmath.functions.NumberedPolynomial -import space.kscience.kmath.functions.NumberedRationalFunction -import kotlin.test.assertEquals -import kotlin.test.assertFailsWith - - -fun assertContentEquals( - expected: Map, - actual: Map, - absoluteTolerance: Double, - message: String? = null -) { - assertEquals(expected.keys, actual.keys, message) - for ((key, expectedValue) in expected) assertEquals(expectedValue, actual[key]!!, absoluteTolerance, message) -} - -fun assertEquals( - expected: NumberedPolynomial, - actual: NumberedPolynomial, - absoluteTolerance: Double, - message: String? = null -) { - assertContentEquals( - expected.coefficients, - actual.coefficients, - absoluteTolerance, - message - ) -} - -fun assertEquals( - expected: LabeledPolynomial, - actual: LabeledPolynomial, - absoluteTolerance: Double, - message: String? = null -) { - assertContentEquals( - expected.coefficients, - actual.coefficients, - absoluteTolerance, - message - ) -} - -fun assertEquals( - expected: NumberedRationalFunction, - actual: NumberedRationalFunction, - absoluteTolerance: Double, - message: String? = null -) { - assertEquals( - expected.numerator, - actual.numerator, - absoluteTolerance, - message - ) - assertEquals( - expected.denominator, - actual.denominator, - absoluteTolerance, - message - ) -} - -fun assertEquals( - expected: LabeledRationalFunction, - actual: LabeledRationalFunction, - absoluteTolerance: Double, - message: String? = null -) { - assertEquals( - expected.numerator, - actual.numerator, - absoluteTolerance, - message - ) - assertEquals( - expected.denominator, - actual.denominator, - absoluteTolerance, - message - ) -} - -inline fun assertFailsWithTypeAndMessage( - expectedMessage: String? = null, - assertionMessage: String? = null, - block: () -> Unit -) { - assertEquals( - expectedMessage, - assertFailsWith(T::class, assertionMessage, block).message, - assertionMessage - ) -} \ No newline at end of file diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/misc.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/misc.kt deleted file mode 100644 index 66e46c902..000000000 --- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/testUtils/misc.kt +++ /dev/null @@ -1,19 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.functions.testUtils - -import space.kscience.kmath.expressions.Symbol -import space.kscience.kmath.expressions.symbol - - -val o: Rational = Rational(0) - -val x: Symbol by symbol -val y: Symbol by symbol -val z: Symbol by symbol -val t: Symbol by symbol -val s: Symbol by symbol -val iota: Symbol by symbol \ No newline at end of file diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/Distribution.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/Distribution.kt index cf2fd5b08..806da5560 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/Distribution.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/Distribution.kt @@ -6,7 +6,7 @@ package space.kscience.kmath.distributions import space.kscience.kmath.chains.Chain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.stat.Sampler /** diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/FactorizedDistribution.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/FactorizedDistribution.kt index 14f49a35f..999fbffbc 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/FactorizedDistribution.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/FactorizedDistribution.kt @@ -7,7 +7,7 @@ package space.kscience.kmath.distributions import space.kscience.kmath.chains.Chain import space.kscience.kmath.chains.SimpleChain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator /** * A multivariate distribution that takes a map of parameters. diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/NormalDistribution.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/NormalDistribution.kt index 8a249c340..ca3537005 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/NormalDistribution.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/NormalDistribution.kt @@ -6,11 +6,11 @@ package space.kscience.kmath.distributions import space.kscience.kmath.chains.Chain -import space.kscience.kmath.internal.InternalErf +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.samplers.GaussianSampler +import space.kscience.kmath.samplers.InternalErf import space.kscience.kmath.samplers.NormalizedGaussianSampler import space.kscience.kmath.samplers.ZigguratNormalizedGaussianSampler -import space.kscience.kmath.stat.RandomGenerator import kotlin.math.* /** diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/UniformDistribution.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/UniformDistribution.kt similarity index 87% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/UniformDistribution.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/UniformDistribution.kt index fa51bb521..953be06fd 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/UniformDistribution.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/UniformDistribution.kt @@ -3,12 +3,11 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.stat +package space.kscience.kmath.distributions import space.kscience.kmath.chains.Chain import space.kscience.kmath.chains.SimpleChain -import space.kscience.kmath.distributions.Distribution -import space.kscience.kmath.distributions.Distribution1D +import space.kscience.kmath.random.RandomGenerator public class UniformDistribution(public val range: ClosedFloatingPointRange) : Distribution1D { private val length: Double = range.endInclusive - range.start diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/MCScope.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/MCScope.kt similarity index 91% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/MCScope.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/MCScope.kt index 37e6ea13b..2049a84fc 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/MCScope.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/MCScope.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.stat +package space.kscience.kmath.random import kotlinx.coroutines.* import kotlin.contracts.InvocationKind @@ -22,6 +22,10 @@ public class MCScope( public val random: RandomGenerator, ) +public fun MCScope.asCoroutineScope(): CoroutineScope = object : CoroutineScope { + override val coroutineContext: CoroutineContext get() = this@asCoroutineScope.coroutineContext +} + /** * Launches a supervised Monte-Carlo scope */ diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/RandomChain.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/RandomChain.kt similarity index 97% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/RandomChain.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/RandomChain.kt index ac7977659..7e0ee3cd4 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/RandomChain.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/RandomChain.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.stat +package space.kscience.kmath.random import space.kscience.kmath.chains.BlockingDoubleChain import space.kscience.kmath.chains.Chain diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/RandomGenerator.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/RandomGenerator.kt similarity index 99% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/RandomGenerator.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/RandomGenerator.kt index 94b2bfbea..f7388006e 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/RandomGenerator.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/random/RandomGenerator.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.stat +package space.kscience.kmath.random import space.kscience.kmath.structures.DoubleBuffer import kotlin.random.Random diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterExponentialSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterExponentialSampler.kt index d861fddae..e5a48d4d8 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterExponentialSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterExponentialSampler.kt @@ -6,7 +6,7 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingDoubleChain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.stat.Sampler import space.kscience.kmath.structures.DoubleBuffer import kotlin.math.ln @@ -67,7 +67,7 @@ public class AhrensDieterExponentialSampler(public val mean: Double) : Sampler - qi += ln2.pow(i + 1.0) / space.kscience.kmath.internal.InternalUtils.factorial(i + 1) + qi += ln2.pow(i + 1.0) / InternalUtils.factorial(i + 1) qi } } diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterMarsagliaTsangGammaSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterMarsagliaTsangGammaSampler.kt index 912bb0fa3..d301ff637 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterMarsagliaTsangGammaSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterMarsagliaTsangGammaSampler.kt @@ -6,9 +6,9 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.Chain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator +import space.kscience.kmath.random.chain import space.kscience.kmath.stat.Sampler -import space.kscience.kmath.stat.chain import space.kscience.kmath.stat.next import kotlin.math.* @@ -25,14 +25,14 @@ import kotlin.math.* */ public class AhrensDieterMarsagliaTsangGammaSampler private constructor( alpha: Double, - theta: Double + theta: Double, ) : Sampler { private val delegate: BaseGammaSampler = if (alpha < 1) AhrensDieterGammaSampler(alpha, theta) else MarsagliaTsangGammaSampler(alpha, theta) private abstract class BaseGammaSampler internal constructor( protected val alpha: Double, - protected val theta: Double + protected val theta: Double, ) : Sampler { init { require(alpha > 0) { "alpha is not strictly positive: $alpha" } @@ -119,7 +119,7 @@ public class AhrensDieterMarsagliaTsangGammaSampler private constructor( public companion object { public fun of( alpha: Double, - theta: Double + theta: Double, ): Sampler = AhrensDieterMarsagliaTsangGammaSampler(alpha, theta) } } \ No newline at end of file diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AliasMethodDiscreteSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AliasMethodDiscreteSampler.kt index 34d1131b4..2ec40c347 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AliasMethodDiscreteSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AliasMethodDiscreteSampler.kt @@ -6,10 +6,9 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.Chain -import space.kscience.kmath.internal.InternalUtils -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator +import space.kscience.kmath.random.chain import space.kscience.kmath.stat.Sampler -import space.kscience.kmath.stat.chain import kotlin.math.ceil import kotlin.math.max import kotlin.math.min diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/BoxMullerSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/BoxMullerSampler.kt index 60a8491f2..7795ff297 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/BoxMullerSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/BoxMullerSampler.kt @@ -6,7 +6,7 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingDoubleChain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.structures.DoubleBuffer import kotlin.math.* diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/GaussianSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/GaussianSampler.kt index 4a4bfdfeb..28d588165 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/GaussianSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/GaussianSampler.kt @@ -7,7 +7,7 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingDoubleChain import space.kscience.kmath.chains.map -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator /** * Sampling from a Gaussian distribution with given mean and standard deviation. @@ -21,7 +21,7 @@ import space.kscience.kmath.stat.RandomGenerator public class GaussianSampler( public val mean: Double, public val standardDeviation: Double, - private val normalized: NormalizedGaussianSampler = BoxMullerSampler + private val normalized: NormalizedGaussianSampler = BoxMullerSampler, ) : BlockingDoubleSampler { init { diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalErf.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalErf.kt similarity index 93% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalErf.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalErf.kt index bb2bfdd09..0c1a5b36f 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalErf.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalErf.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.internal +package space.kscience.kmath.samplers import kotlin.math.abs diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalGamma.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalGamma.kt similarity index 99% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalGamma.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalGamma.kt index 1ef2ec02c..43c5a0d3c 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalGamma.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalGamma.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.internal +package space.kscience.kmath.samplers import kotlin.math.* diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalUtils.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalUtils.kt similarity index 98% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalUtils.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalUtils.kt index a80407773..9f633e3db 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/internal/InternalUtils.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalUtils.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.internal +package space.kscience.kmath.samplers import kotlin.math.ln import kotlin.math.min diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/KempSmallMeanPoissonSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/KempSmallMeanPoissonSampler.kt index 145946b14..6d2899314 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/KempSmallMeanPoissonSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/KempSmallMeanPoissonSampler.kt @@ -6,7 +6,7 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingIntChain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.stat.Sampler import space.kscience.kmath.structures.IntBuffer import kotlin.math.exp diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/MarsagliaNormalizedGaussianSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/MarsagliaNormalizedGaussianSampler.kt index a8d289d47..3c3fe10fd 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/MarsagliaNormalizedGaussianSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/MarsagliaNormalizedGaussianSampler.kt @@ -6,7 +6,7 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingDoubleChain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.structures.DoubleBuffer import kotlin.math.ln import kotlin.math.sqrt diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/NormalizedGaussianSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/NormalizedGaussianSampler.kt index 3f6797881..291d0bffe 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/NormalizedGaussianSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/NormalizedGaussianSampler.kt @@ -6,10 +6,10 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingDoubleChain -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.stat.Sampler -public interface BlockingDoubleSampler: Sampler{ +public interface BlockingDoubleSampler : Sampler { override fun sample(generator: RandomGenerator): BlockingDoubleChain } @@ -18,6 +18,6 @@ public interface BlockingDoubleSampler: Sampler{ * Marker interface for a sampler that generates values from an N(0,1) * [Gaussian distribution](https://en.wikipedia.org/wiki/Normal_distribution). */ -public fun interface NormalizedGaussianSampler : BlockingDoubleSampler{ +public fun interface NormalizedGaussianSampler : BlockingDoubleSampler { public companion object } diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/PoissonSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/PoissonSampler.kt index 83480b4ba..454691e05 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/PoissonSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/PoissonSampler.kt @@ -6,9 +6,8 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingIntChain -import space.kscience.kmath.internal.InternalUtils import space.kscience.kmath.misc.toIntExact -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.stat.Sampler import space.kscience.kmath.structures.IntBuffer import kotlin.math.* diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Sampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/Sampler.kt similarity index 95% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Sampler.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/Sampler.kt index 66ade8119..52e400bf1 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Sampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/Sampler.kt @@ -9,6 +9,7 @@ import kotlinx.coroutines.flow.first import space.kscience.kmath.chains.Chain import space.kscience.kmath.chains.combine import space.kscience.kmath.misc.UnstableKMathAPI +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.structures.Buffer import space.kscience.kmath.structures.BufferFactory import space.kscience.kmath.structures.DoubleBuffer diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/SamplerAlgebra.kt similarity index 93% rename from kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt rename to kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/SamplerAlgebra.kt index 1e34fa434..44b87a431 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/SamplerAlgebra.kt @@ -3,7 +3,7 @@ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. */ -package space.kscience.kmath.stat +package space.kscience.kmath.samplers import space.kscience.kmath.chains.Chain import space.kscience.kmath.chains.ConstantChain @@ -12,6 +12,8 @@ import space.kscience.kmath.chains.zip import space.kscience.kmath.operations.Group import space.kscience.kmath.operations.ScaleOperations import space.kscience.kmath.operations.invoke +import space.kscience.kmath.random.RandomGenerator +import space.kscience.kmath.stat.Sampler /** * Implements [Sampler] by sampling only certain [value]. diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/ZigguratNormalizedGaussianSampler.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/ZigguratNormalizedGaussianSampler.kt index 2cd561468..40ce37d15 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/ZigguratNormalizedGaussianSampler.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/ZigguratNormalizedGaussianSampler.kt @@ -6,8 +6,7 @@ package space.kscience.kmath.samplers import space.kscience.kmath.chains.BlockingDoubleChain -import space.kscience.kmath.misc.toIntExact -import space.kscience.kmath.stat.RandomGenerator +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.structures.DoubleBuffer import kotlin.math.* diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/SeriesAlgebra.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/SeriesAlgebra.kt new file mode 100644 index 000000000..3cd2212f6 --- /dev/null +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/SeriesAlgebra.kt @@ -0,0 +1,193 @@ +package space.kscience.kmath.series + +import space.kscience.kmath.operations.BufferAlgebra +import space.kscience.kmath.operations.Ring +import space.kscience.kmath.operations.RingOps +import space.kscience.kmath.stat.StatisticalAlgebra +import space.kscience.kmath.structures.Buffer +import space.kscience.kmath.structures.BufferView +import kotlin.math.max +import kotlin.math.min + +@PublishedApi +internal fun IntRange.intersect(other: IntRange): IntRange = + max(first, other.first)..min(last, other.last) + +@PublishedApi +internal val IntRange.size: Int + get() = last - first + 1 + +@PublishedApi +internal operator fun IntRange.contains(other: IntRange): Boolean = (other.first in this) && (other.last in this) + +//TODO add permutation sort +//TODO check rank statistics + + +public interface Series : Buffer { + public val origin: Buffer + + /** + * Absolute position of start of this [Series] in [SeriesAlgebra] + */ + public val position: Int +} + +public val Series.absoluteIndices: IntRange get() = position until position + size + +/** + * A [BufferView] with index offset (both positive and negative) and possible size change + */ +private class SeriesImpl( + override val origin: Buffer, + override val position: Int, + override val size: Int = origin.size, +) : Series, Buffer by origin { + + init { + require(size > 0) { "Size must be positive" } + require(size <= origin.size) { "Slice size is larger than the original buffer" } + } + + override fun toString(): String = "$origin-->${position}" +} + +/** + * A scope to operation on series + */ +public class SeriesAlgebra, out BA : BufferAlgebra, L>( + override val bufferAlgebra: BA, + private val labelResolver: (Int) -> L, +) : RingOps>, StatisticalAlgebra { + + public val Buffer.indices: IntRange + get() = if (this is Series) { + absoluteIndices + } else { + 0 until size + } + + /** + * Get the value by absolute index in the series algebra or return null if index is out of range + */ + public fun Buffer.getAbsoluteOrNull(index: Int): T? = when { + index !in indices -> null + this is Series -> origin[index - position] + else -> get(index) + } + + /** + * Get the value by absolute index in the series algebra or throw [IndexOutOfBoundsException] if index is out of range + */ + public fun Buffer.getAbsolute(index: Int): T = + getAbsoluteOrNull(index) ?: throw IndexOutOfBoundsException("Index $index is not in $indices") + + /** + * Create an offset series with index starting point at [index] + */ + public fun Buffer.moveTo(index: Int): Series = if (this is Series) { + SeriesImpl(origin, index, size) + } else { + SeriesImpl(this, index, size) + } + + public val Buffer.offset: Int get() = if (this is Series) position else 0 + + /** + * Build a new series + */ + public fun series(size: Int, fromIndex: Int = 0, block: A.(label: L) -> T): Series { + return elementAlgebra.bufferFactory(size) { + val index = it + fromIndex + elementAlgebra.block(labelResolver(index)) + }.moveTo(fromIndex) + } + + /** + * Get a label buffer for given buffer. + */ + public val Buffer.labels: List get() = indices.map(labelResolver) + + + /** + * Try to resolve element by label and return null if element with a given label is not found + */ + public operator fun Buffer.get(label: L): T? { + val index = labels.indexOf(label) + if (index == -1) return null + return getAbsolute(index + offset) + } + + /** + * Map a series to another series of the same size + */ + public inline fun Buffer.map(crossinline transform: A.(T) -> T): Series { + val buf = elementAlgebra.bufferFactory(size) { + elementAlgebra.transform(getAbsolute(it)) + } + return buf.moveTo(indices.first) + } + + /** + * Map series to another series of the same size with label + */ + public inline fun Buffer.mapWithLabel(crossinline transform: A.(arg: T, label: L) -> T): Series { + val labels = labels + val buf = elementAlgebra.bufferFactory(size) { + elementAlgebra.transform(getAbsolute(it), labels[it]) + } + return buf.moveTo(indices.first) + } + + public inline fun Buffer.fold(initial: R, operation: A.(acc: R, T) -> R): R { + var accumulator = initial + for (index in this.indices) accumulator = elementAlgebra.operation(accumulator, getAbsolute(index)) + return accumulator + } + + public inline fun Buffer.foldWithLabel(initial: R, operation: A.(acc: R, arg: T, label: L) -> R): R { + val labels = labels + var accumulator = initial + for (index in this.indices) accumulator = + elementAlgebra.operation(accumulator, getAbsolute(index), labels[index]) + return accumulator + } + + /** + * Zip two buffers in the range whe they overlap + */ + public inline fun Buffer.zip( + other: Buffer, + crossinline operation: A.(left: T, right: T) -> T, + ): Series { + val newRange = indices.intersect(other.indices) + return elementAlgebra.bufferFactory(newRange.size) { + elementAlgebra.operation( + getAbsolute(it), + other.getAbsolute(it) + ) + }.moveTo(newRange.first) + } + + override fun Buffer.unaryMinus(): Buffer = map { -it } + + override fun add(left: Buffer, right: Buffer): Series = left.zip(right) { l, r -> l + r } + + override fun multiply(left: Buffer, right: Buffer): Buffer = left.zip(right) { l, r -> l * r } +} + +public fun , BA : BufferAlgebra, L> BA.seriesAlgebra(labels: Iterable): SeriesAlgebra { + val l = labels.toList() + return SeriesAlgebra(this) { + if (it in l.indices) l[it] else error("Index $it is outside of labels range ${l.indices}") + } +} + +public fun , BA : BufferAlgebra, L> BA.seriesAlgebra(labelGenerator: (Int) -> L): SeriesAlgebra = + SeriesAlgebra(this, labelGenerator) + +/** + * Create a series algebra using offset as a label + */ +public fun , BA : BufferAlgebra> BA.seriesAlgebra(): SeriesAlgebra = + SeriesAlgebra(this) { it } \ No newline at end of file diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/seriesExtensions.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/seriesExtensions.kt new file mode 100644 index 000000000..882fa2c46 --- /dev/null +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/seriesExtensions.kt @@ -0,0 +1,97 @@ +package space.kscience.kmath.series + +import space.kscience.kmath.operations.BufferAlgebra +import space.kscience.kmath.operations.ExponentialOperations +import space.kscience.kmath.operations.PowerOperations +import space.kscience.kmath.operations.TrigonometricOperations +import space.kscience.kmath.structures.Buffer + + +//trigonometric + +public fun SeriesAlgebra.sin( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : TrigonometricOperations> = + bufferAlgebra.sin(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.cos( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : TrigonometricOperations> = + bufferAlgebra.cos(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.tan( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : TrigonometricOperations> = + bufferAlgebra.tan(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.asin( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : TrigonometricOperations> = + bufferAlgebra.asin(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.acos( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : TrigonometricOperations> = + bufferAlgebra.acos(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.atan( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : TrigonometricOperations> = + bufferAlgebra.atan(arg).moveTo(arg.offset) + + +//exponential + +public fun SeriesAlgebra.exp( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.exp(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.ln( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.ln(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.sinh( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.sinh(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.cosh( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.cosh(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.tanh( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.tanh(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.asinh( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.asinh(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.acosh( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.acosh(arg).moveTo(arg.offset) + +public fun SeriesAlgebra.atanh( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : ExponentialOperations> = + bufferAlgebra.atanh(arg).moveTo(arg.offset) + + +//power + +public fun SeriesAlgebra.power( + arg: Buffer, + pow: Number, +): Series where BA : BufferAlgebra, BA : PowerOperations> = + bufferAlgebra.power(arg, pow).moveTo(arg.offset) + +public fun SeriesAlgebra.sqrt( + arg: Buffer, +): Series where BA : BufferAlgebra, BA : PowerOperations> = + bufferAlgebra.sqrt(arg).moveTo(arg.offset) \ No newline at end of file diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Mean.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Mean.kt index fb14a95be..3bf8b33e8 100644 --- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Mean.kt +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Mean.kt @@ -45,21 +45,23 @@ public class Mean( public companion object { @Deprecated("Use Double.mean instead") public val double: Mean = Mean(DoubleField) { sum, count -> sum / count } + @Deprecated("Use Int.mean instead") public val int: Mean = Mean(IntRing) { sum, count -> sum / count } + @Deprecated("Use Long.mean instead") public val long: Mean = Mean(LongRing) { sum, count -> sum / count } - public fun evaluate(buffer: Buffer): Double = Double.mean.evaluateBlocking(buffer) - public fun evaluate(buffer: Buffer): Int = Int.mean.evaluateBlocking(buffer) - public fun evaluate(buffer: Buffer): Long = Long.mean.evaluateBlocking(buffer) + public fun evaluate(buffer: Buffer): Double = DoubleField.mean.evaluateBlocking(buffer) + public fun evaluate(buffer: Buffer): Int = IntRing.mean.evaluateBlocking(buffer) + public fun evaluate(buffer: Buffer): Long = LongRing.mean.evaluateBlocking(buffer) } } //TODO replace with optimized version which respects overflow -public val Double.Companion.mean: Mean get() = Mean(DoubleField) { sum, count -> sum / count } -public val Int.Companion.mean: Mean get() = Mean(IntRing) { sum, count -> sum / count } -public val Long.Companion.mean: Mean get() = Mean(LongRing) { sum, count -> sum / count } +public val DoubleField.mean: Mean get() = Mean(DoubleField) { sum, count -> sum / count } +public val IntRing.mean: Mean get() = Mean(IntRing) { sum, count -> sum / count } +public val LongRing.mean: Mean get() = Mean(LongRing) { sum, count -> sum / count } diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Rank.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Rank.kt new file mode 100644 index 000000000..5a873b466 --- /dev/null +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Rank.kt @@ -0,0 +1,35 @@ +package space.kscience.kmath.stat + +import space.kscience.kmath.operations.asIterable +import space.kscience.kmath.structures.Buffer + +/** + * Rank statistics + */ +public class Rank> : BlockingStatistic { + override fun evaluateBlocking(data: Buffer): IntArray = Companion.evaluate(data) + + public companion object { + public fun > evaluate(data: Buffer): IntArray { + // https://www.geeksforgeeks.org/rank-elements-array/ + val permutations = ArrayList>(data.size) + data.asIterable().mapIndexedTo(permutations) { i, v -> v to i } + permutations.sortBy { it.first } + var rank = 1 + var i = 0 + val r = IntArray(data.size) + while (i < data.size) { + var j = i + while (j < data.size - 1 && permutations[j].first == permutations[j + 1]) ++j + val n = j - i + 1 + (0 until n).map { k -> + val idx = permutations[i + k].second + r[idx] = rank + ((n - 1) * 0.5f).toInt() + } + rank += n + i += n + } + return r + } + } +} \ No newline at end of file diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/StatisticalAlgebra.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/StatisticalAlgebra.kt new file mode 100644 index 000000000..f36826c28 --- /dev/null +++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/StatisticalAlgebra.kt @@ -0,0 +1,67 @@ +package space.kscience.kmath.stat + +import space.kscience.kmath.misc.UnstableKMathAPI +import space.kscience.kmath.misc.sorted +import space.kscience.kmath.operations.* +import space.kscience.kmath.structures.Buffer +import space.kscience.kmath.structures.MutableBufferFactory + +public interface StatisticalAlgebra, out BA : BufferAlgebra> : Algebra> { + public val bufferAlgebra: BA + public val elementAlgebra: A get() = bufferAlgebra.elementAlgebra + override val bufferFactory: MutableBufferFactory> get() = bufferAlgebra.bufferFactory +} + +/** + * Compute [empirical CDF function](https://en.wikipedia.org/wiki/Empirical_distribution_function) + */ +public fun > StatisticalAlgebra.ecdf(buffer: Buffer): (T) -> Double = { arg -> + buffer.asIterable().count { it < arg }.toDouble() / buffer.size +} + +/** + * Resulting value of kolmogorov-smirnov two-sample statistic + */ +@UnstableKMathAPI +public data class KMComparisonResult>(val n: Int, val m: Int, val value: T) + +/** + * Kolmogorov-Smirnov sample comparison test + * Implementation copied from https://commons.apache.org/proper/commons-math/javadocs/api-3.6.1/index.html?org/apache/commons/math3/stat/inference/KolmogorovSmirnovTest.html + */ +@UnstableKMathAPI +public fun , A, BA : BufferAlgebra> StatisticalAlgebra.ksComparisonStatistic( + x: Buffer, + y: Buffer, +): KMComparisonResult where A : Group, A : NumericAlgebra = elementAlgebra.invoke { + // Copy and sort the sample arrays + val sx = x.sorted() + val sy = y.sorted() + val n = sx.size + val m = sy.size + + var rankX: Int = 0 + var rankY: Int = 0 + var curD: T = zero + + // Find the max difference between cdf_x and cdf_y + var supD: T = zero + do { + val z = if (sx[rankX] <= sy[rankY]) sx[rankX] else sy[rankY] + while (rankX < n && sx[rankX].compareTo(z) == 0) { + rankX += 1 + curD += number(m) + } + + while (rankY < m && sy[rankY].compareTo(z) == 0) { + rankY += 1 + curD -= number(n) + } + + when { + curD > supD -> supD = curD + -curD > supD -> supD = -curD + } + } while (rankX < n && rankY < m) + return KMComparisonResult(n, m, supD) +} \ No newline at end of file diff --git a/kmath-stat/src/jvmMain/kotlin/space/kscience/kmath/stat/RandomSourceGenerator.kt b/kmath-stat/src/jvmMain/kotlin/space/kscience/kmath/stat/RandomSourceGenerator.kt index 2da9a9e21..2c6391612 100644 --- a/kmath-stat/src/jvmMain/kotlin/space/kscience/kmath/stat/RandomSourceGenerator.kt +++ b/kmath-stat/src/jvmMain/kotlin/space/kscience/kmath/stat/RandomSourceGenerator.kt @@ -7,13 +7,17 @@ package space.kscience.kmath.stat import org.apache.commons.rng.UniformRandomProvider import org.apache.commons.rng.simple.RandomSource +import space.kscience.kmath.random.RandomGenerator /** * Implements [RandomGenerator] by delegating all operations to [RandomSource]. * * @property source the underlying [RandomSource] object. */ -public class RandomSourceGenerator internal constructor(public val source: RandomSource, seed: Long?) : RandomGenerator { +public class RandomSourceGenerator internal constructor( + public val source: RandomSource, + seed: Long?, +) : RandomGenerator { internal val random: UniformRandomProvider = seed?.let { RandomSource.create(source, seed) } ?: RandomSource.create(source) diff --git a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/CommonsDistributionsTest.kt b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/CommonsDistributionsTest.kt index 802f3ac24..b9b9dadba 100644 --- a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/CommonsDistributionsTest.kt +++ b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/CommonsDistributionsTest.kt @@ -8,6 +8,7 @@ package space.kscience.kmath.stat import kotlinx.coroutines.runBlocking import org.junit.jupiter.api.Assertions import org.junit.jupiter.api.Test +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.samplers.GaussianSampler internal class CommonsDistributionsTest { diff --git a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/MCScopeTest.kt b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/MCScopeTest.kt index 889274c86..dbcf32e27 100644 --- a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/MCScopeTest.kt +++ b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/MCScopeTest.kt @@ -6,20 +6,22 @@ package space.kscience.kmath.stat import kotlinx.coroutines.* +import space.kscience.kmath.random.launch +import space.kscience.kmath.random.mcScope import java.util.* import kotlin.test.Test import kotlin.test.assertEquals data class RandomResult(val branch: String, val order: Int, val value: Int) -typealias ATest = suspend CoroutineScope.() -> Set +internal typealias ATest = suspend () -> Set -class MCScopeTest { +internal class MCScopeTest { val simpleTest: ATest = { mcScope(1111) { val res = Collections.synchronizedSet(HashSet()) - launch { + launch{ //println(random) repeat(10) { delay(10) diff --git a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/SamplerTest.kt b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/SamplerTest.kt index 7b76fb4b6..0076006e6 100644 --- a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/SamplerTest.kt +++ b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/SamplerTest.kt @@ -6,6 +6,8 @@ package space.kscience.kmath.stat import kotlinx.coroutines.runBlocking +import space.kscience.kmath.random.RandomGenerator +import space.kscience.kmath.random.chain import kotlin.test.Test class SamplerTest { diff --git a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/StatisticTest.kt b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/StatisticTest.kt index 0db22fef4..3be7fa314 100644 --- a/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/StatisticTest.kt +++ b/kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/StatisticTest.kt @@ -9,6 +9,9 @@ import kotlinx.coroutines.flow.first import kotlinx.coroutines.flow.last import kotlinx.coroutines.flow.take import kotlinx.coroutines.runBlocking +import space.kscience.kmath.operations.DoubleField +import space.kscience.kmath.random.RandomGenerator +import space.kscience.kmath.random.chain import space.kscience.kmath.streaming.chunked import kotlin.test.Test import kotlin.test.assertEquals @@ -25,26 +28,26 @@ internal class StatisticTest { @Test fun singleBlockingMean() { - val first = runBlocking { chunked.first()} - val res = Double.mean(first) - assertEquals(0.5,res, 1e-1) + val first = runBlocking { chunked.first() } + val res = DoubleField.mean(first) + assertEquals(0.5, res, 1e-1) } @Test fun singleSuspendMean() = runBlocking { - val first = runBlocking { chunked.first()} - val res = Double.mean(first) - assertEquals(0.5,res, 1e-1) + val first = runBlocking { chunked.first() } + val res = DoubleField.mean(first) + assertEquals(0.5, res, 1e-1) } @Test fun parallelMean() = runBlocking { - val average = Double.mean + val average = DoubleField.mean .flow(chunked) //create a flow from evaluated results .take(100) // Take 100 data chunks from the source and accumulate them .last() //get 1e5 data samples average - assertEquals(0.5,average, 1e-2) + assertEquals(0.5, average, 1e-2) } } diff --git a/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowAlgebra.kt b/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowAlgebra.kt index c4d192792..27a20aafe 100644 --- a/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowAlgebra.kt +++ b/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowAlgebra.kt @@ -13,8 +13,8 @@ import org.tensorflow.types.TFloat64 import space.kscience.kmath.expressions.Symbol import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.nd.DefaultStrides -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ColumnStrides +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.operations.PowerOperations @@ -28,6 +28,8 @@ public class DoubleTensorFlowOutput( } +internal fun ShapeND.toLongArray(): LongArray = LongArray(size) { get(it).toLong() } + public class DoubleTensorFlowAlgebra internal constructor( graph: Graph, ) : TensorFlowAlgebra(graph), PowerOperations> { @@ -35,11 +37,11 @@ public class DoubleTensorFlowAlgebra internal constructor( override val elementAlgebra: DoubleField get() = DoubleField override fun structureND( - shape: Shape, + shape: ShapeND, initializer: DoubleField.(IntArray) -> Double, ): StructureND { val res = TFloat64.tensorOf(org.tensorflow.ndarray.Shape.of(*shape.toLongArray())) { array -> - DefaultStrides(shape).forEach { index -> + ColumnStrides(shape).forEach { index -> array.setDouble(elementAlgebra.initializer(index), *index.toLongArray()) } } diff --git a/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/TensorFlowAlgebra.kt b/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/TensorFlowAlgebra.kt index 74fcf2d7d..bc5fb9616 100644 --- a/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/TensorFlowAlgebra.kt +++ b/kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/TensorFlowAlgebra.kt @@ -18,9 +18,12 @@ import org.tensorflow.types.TInt32 import org.tensorflow.types.family.TNumber import org.tensorflow.types.family.TType import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.misc.UnsafeKMathAPI import space.kscience.kmath.misc.UnstableKMathAPI -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND +import space.kscience.kmath.nd.asArray +import space.kscience.kmath.nd.contentEquals import space.kscience.kmath.operations.Ring import space.kscience.kmath.tensors.api.Tensor import space.kscience.kmath.tensors.api.TensorAlgebra @@ -38,12 +41,14 @@ public sealed interface TensorFlowTensor : Tensor */ @JvmInline public value class TensorFlowArray(public val tensor: NdArray) : Tensor { - override val shape: Shape get() = tensor.shape().asArray().toIntArray() + override val shape: ShapeND get() = ShapeND(tensor.shape().asArray().toIntArray()) + @PerformancePitfall override fun get(index: IntArray): T = tensor.getObject(*index.toLongArray()) //TODO implement native element sequence + @PerformancePitfall override fun set(index: IntArray, value: T) { tensor.setObject(value, *index.toLongArray()) } @@ -62,7 +67,7 @@ public abstract class TensorFlowOutput( public var output: Output = output internal set - override val shape: Shape get() = output.shape().asArray().toIntArray() + override val shape: ShapeND get() = ShapeND(output.shape().asArray().toIntArray()) protected abstract fun org.tensorflow.Tensor.actualizeTensor(): NdArray @@ -72,11 +77,13 @@ public abstract class TensorFlowOutput( } } + @PerformancePitfall override fun get(index: IntArray): T = actualTensor[index] @PerformancePitfall override fun elements(): Sequence> = actualTensor.elements() + @PerformancePitfall override fun set(index: IntArray, value: T) { actualTensor[index] = value } @@ -96,8 +103,9 @@ public abstract class TensorFlowAlgebra> internal c protected abstract fun const(value: T): Constant - override fun StructureND.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) - get(Shape(0)) else null + @OptIn(PerformancePitfall::class) + override fun StructureND.valueOrNull(): T? = if (shape contentEquals ShapeND(1)) + get(intArrayOf(0)) else null /** * Perform binary lazy operation on tensor. Both arguments are implicitly converted @@ -188,12 +196,13 @@ public abstract class TensorFlowAlgebra> internal c StridedSliceHelper.stridedSlice(ops.scope(), it, Indices.at(i.toLong())) } - override fun Tensor.transposed(i: Int, j: Int): Tensor = operate { + override fun StructureND.transposed(i: Int, j: Int): Tensor = operate { ops.linalg.transpose(it, ops.constant(intArrayOf(i, j))) } - override fun Tensor.view(shape: IntArray): Tensor = operate { - ops.reshape(it, ops.constant(shape)) + override fun Tensor.view(shape: ShapeND): Tensor = operate { + @OptIn(UnsafeKMathAPI::class) + ops.reshape(it, ops.constant(shape.asArray())) } override fun Tensor.viewAs(other: StructureND): Tensor = operate(other) { l, r -> @@ -208,7 +217,7 @@ public abstract class TensorFlowAlgebra> internal c } override fun diagonalEmbedding( - diagonalEntries: Tensor, + diagonalEntries: StructureND, offset: Int, dim1: Int, dim2: Int, diff --git a/kmath-tensorflow/src/test/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowOps.kt b/kmath-tensorflow/src/test/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowOps.kt index a35556be1..af754f841 100644 --- a/kmath-tensorflow/src/test/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowOps.kt +++ b/kmath-tensorflow/src/test/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowOps.kt @@ -7,11 +7,13 @@ package space.kscience.kmath.tensorflow import org.junit.jupiter.api.Test import space.kscience.kmath.misc.UnstableKMathAPI +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.get import space.kscience.kmath.nd.structureND import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.tensors.core.DoubleTensorAlgebra import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.sum +import space.kscience.kmath.tensors.core.randomNormal import kotlin.test.assertEquals @OptIn(UnstableKMathAPI::class) @@ -31,8 +33,8 @@ class DoubleTensorFlowOps { fun dot(){ val dim = 1000 - val tensor1 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12224) - val tensor2 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12225) + val tensor1 = DoubleTensorAlgebra.randomNormal(shape = ShapeND(dim, dim), 12224) + val tensor2 = DoubleTensorAlgebra.randomNormal(shape = ShapeND(dim, dim), 12225) DoubleField.produceWithTF { tensor1 dot tensor2 diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/AnalyticTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/AnalyticTensorAlgebra.kt index 587096500..1a324b200 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/AnalyticTensorAlgebra.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/AnalyticTensorAlgebra.kt @@ -21,7 +21,7 @@ public interface AnalyticTensorAlgebra> : /** * @return the mean of all elements in the input tensor. */ - public fun StructureND.mean(): T + public fun mean(structureND: StructureND): T /** * Returns the mean of each row of the input tensor in the given dimension [dim]. @@ -34,12 +34,12 @@ public interface AnalyticTensorAlgebra> : * @param keepDim whether the output tensor has [dim] retained or not. * @return the mean of each row of the input tensor in the given dimension [dim]. */ - public fun StructureND.mean(dim: Int, keepDim: Boolean): Tensor + public fun mean(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor /** * @return the standard deviation of all elements in the input tensor. */ - public fun StructureND.std(): T + public fun std(structureND: StructureND): T /** * Returns the standard deviation of each row of the input tensor in the given dimension [dim]. @@ -52,12 +52,12 @@ public interface AnalyticTensorAlgebra> : * @param keepDim whether the output tensor has [dim] retained or not. * @return the standard deviation of each row of the input tensor in the given dimension [dim]. */ - public fun StructureND.std(dim: Int, keepDim: Boolean): Tensor + public fun std(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor /** * @return the variance of all elements in the input tensor. */ - public fun StructureND.variance(): T + public fun variance(structureND: StructureND): T /** * Returns the variance of each row of the input tensor in the given dimension [dim]. @@ -70,80 +70,45 @@ public interface AnalyticTensorAlgebra> : * @param keepDim whether the output tensor has [dim] retained or not. * @return the variance of each row of the input tensor in the given dimension [dim]. */ - public fun StructureND.variance(dim: Int, keepDim: Boolean): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.exp.html - public fun StructureND.exp(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.log.html - public fun StructureND.ln(): Tensor + public fun variance(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor //For information: https://pytorch.org/docs/stable/generated/torch.sqrt.html - public fun StructureND.sqrt(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.cos - public fun StructureND.cos(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.acos - public fun StructureND.acos(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.cosh - public fun StructureND.cosh(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.acosh - public fun StructureND.acosh(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sin - public fun StructureND.sin(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asin - public fun StructureND.asin(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sinh - public fun StructureND.sinh(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asinh - public fun StructureND.asinh(): Tensor + override fun sqrt(arg: StructureND): Tensor //For information: https://pytorch.org/docs/stable/generated/torch.atan.html#torch.tan - public fun StructureND.tan(): Tensor + override fun tan(arg: StructureND): Tensor //https://pytorch.org/docs/stable/generated/torch.atan.html#torch.atan - public fun StructureND.atan(): Tensor + override fun atan(arg: StructureND): Tensor //For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.tanh - public fun StructureND.tanh(): Tensor - - //For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.atanh - public fun StructureND.atanh(): Tensor + override fun tanh(arg: StructureND): Tensor //For information: https://pytorch.org/docs/stable/generated/torch.ceil.html#torch.ceil - public fun StructureND.ceil(): Tensor + public fun ceil(arg: StructureND): Tensor //For information: https://pytorch.org/docs/stable/generated/torch.floor.html#torch.floor - public fun StructureND.floor(): Tensor + public fun floor(structureND: StructureND): Tensor - override fun sin(arg: StructureND): StructureND = arg.sin() + override fun sin(arg: StructureND): StructureND - override fun cos(arg: StructureND): StructureND = arg.cos() + override fun cos(arg: StructureND): StructureND - override fun asin(arg: StructureND): StructureND = arg.asin() + override fun asin(arg: StructureND): StructureND - override fun acos(arg: StructureND): StructureND = arg.acos() + override fun acos(arg: StructureND): StructureND - override fun atan(arg: StructureND): StructureND = arg.atan() + override fun exp(arg: StructureND): StructureND - override fun exp(arg: StructureND): StructureND = arg.exp() + override fun ln(arg: StructureND): StructureND - override fun ln(arg: StructureND): StructureND = arg.ln() + override fun sinh(arg: StructureND): StructureND - override fun sinh(arg: StructureND): StructureND = arg.sinh() + override fun cosh(arg: StructureND): StructureND - override fun cosh(arg: StructureND): StructureND = arg.cosh() + override fun asinh(arg: StructureND): StructureND - override fun asinh(arg: StructureND): StructureND = arg.asinh() + override fun acosh(arg: StructureND): StructureND - override fun acosh(arg: StructureND): StructureND = arg.acosh() - - override fun atanh(arg: StructureND): StructureND = arg.atanh() + override fun atanh(arg: StructureND): StructureND } \ No newline at end of file diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt index 07dfd1597..faff2eb80 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt @@ -21,7 +21,7 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * * @return the determinant. */ - public fun StructureND.det(): Tensor + public fun StructureND.det(): StructureND /** * Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input. @@ -31,7 +31,7 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * * @return the multiplicative inverse of a matrix. */ - public fun StructureND.inv(): Tensor + public fun StructureND.inv(): StructureND /** * Cholesky decomposition. @@ -47,7 +47,7 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * @receiver the `input`. * @return the batch of `L` matrices. */ - public fun StructureND.cholesky(): Tensor + public fun cholesky(structureND: StructureND): StructureND /** * QR decomposition. @@ -61,7 +61,7 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * @receiver the `input`. * @return pair of `Q` and `R` tensors. */ - public fun StructureND.qr(): Pair, Tensor> + public fun qr(structureND: StructureND): Pair, StructureND> /** * LUP decomposition @@ -75,7 +75,7 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * @receiver the `input`. * @return triple of P, L and U tensors */ - public fun StructureND.lu(): Triple, Tensor, Tensor> + public fun lu(structureND: StructureND): Triple, StructureND, StructureND> /** * Singular Value Decomposition. @@ -91,7 +91,7 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * @receiver the `input`. * @return triple `Triple(U, S, V)`. */ - public fun StructureND.svd(): Triple, Tensor, Tensor> + public fun svd(structureND: StructureND): Triple, StructureND, StructureND> /** * Returns eigenvalues and eigenvectors of a real symmetric matrix `input` or a batch of real symmetric matrices, @@ -101,6 +101,6 @@ public interface LinearOpsTensorAlgebra> : TensorPartialDivision * @receiver the `input`. * @return a pair `eigenvalues to eigenvectors` */ - public fun StructureND.symEig(): Pair, Tensor> + public fun symEig(structureND: StructureND): Pair, StructureND> } diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt index 70b985a54..f923400c5 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt @@ -6,6 +6,7 @@ package space.kscience.kmath.tensors.api import space.kscience.kmath.nd.RingOpsND +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.StructureND import space.kscience.kmath.operations.Ring @@ -176,11 +177,13 @@ public interface TensorAlgebra> : RingOpsND { * Returns a tensor that is a transposed version of this tensor. The given dimensions [i] and [j] are swapped. * For more information: https://pytorch.org/docs/stable/generated/torch.transpose.html * + * If axis indices are negative, they are counted from shape end. + * * @param i the first dimension to be transposed * @param j the second dimension to be transposed * @return transposed tensor */ - public fun Tensor.transposed(i: Int = -2, j: Int = -1): Tensor + public fun StructureND.transposed(i: Int = shape.size - 2, j: Int = shape.size - 1): Tensor /** * Returns a new tensor with the same data as the self tensor but of a different shape. @@ -190,7 +193,7 @@ public interface TensorAlgebra> : RingOpsND { * @param shape the desired size * @return tensor with new shape */ - public fun Tensor.view(shape: IntArray): Tensor + public fun Tensor.view(shape: ShapeND): Tensor /** * View this tensor as the same size as [other]. @@ -248,7 +251,7 @@ public interface TensorAlgebra> : RingOpsND { * are filled by [diagonalEntries] */ public fun diagonalEmbedding( - diagonalEntries: Tensor, + diagonalEntries: StructureND, offset: Int = 0, dim1: Int = -2, dim2: Int = -1, diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BufferedTensor.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BufferedTensor.kt index 0b043db56..a7283e4c8 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BufferedTensor.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BufferedTensor.kt @@ -6,6 +6,8 @@ package space.kscience.kmath.tensors.core import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.RowStrides +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.nd.Strides import space.kscience.kmath.structures.MutableBuffer import space.kscience.kmath.tensors.api.Tensor @@ -14,15 +16,15 @@ import space.kscience.kmath.tensors.api.Tensor * Represents [Tensor] over a [MutableBuffer] intended to be used through [DoubleTensor] and [IntTensor] */ public abstract class BufferedTensor( - override val shape: IntArray, + override val shape: ShapeND, ) : Tensor { public abstract val source: MutableBuffer /** - * Buffer strides based on [TensorLinearStructure] implementation + * Buffer strides based on [RowStrides] implementation */ - override val indices: Strides get() = TensorLinearStructure(shape) + override val indices: Strides get() = RowStrides(shape) /** * Number of elements in tensor diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor.kt index e9589eb0a..4eed7a2a8 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor.kt @@ -5,32 +5,35 @@ package space.kscience.kmath.tensors.core +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.misc.UnstableKMathAPI +import space.kscience.kmath.nd.* import space.kscience.kmath.structures.* import space.kscience.kmath.tensors.core.internal.toPrettyString public class OffsetDoubleBuffer( - private val source: DoubleBuffer, + override val origin: DoubleBuffer, private val offset: Int, override val size: Int, -) : MutableBuffer { +) : MutableBuffer, BufferView { init { require(offset >= 0) { "Offset must be non-negative" } require(size >= 0) { "Size must be non-negative" } - require(offset + size <= source.size) { "Maximum index must be inside source dimension" } + require(offset + size <= origin.size) { "Maximum index must be inside source dimension" } } override fun set(index: Int, value: Double) { require(index in 0 until size) { "Index must be in [0, size)" } - source[index + offset] = value + origin[index + offset] = value } - override fun get(index: Int): Double = source[index + offset] + override fun get(index: Int): Double = origin[index + offset] /** - * Copy only a part of buffer that belongs to this tensor + * Copy only a part of buffer that belongs to this [OffsetDoubleBuffer] */ - override fun copy(): DoubleBuffer = source.array.copyOfRange(offset, offset + size).asBuffer() + override fun copy(): DoubleBuffer = origin.array.copyOfRange(offset, offset + size).asBuffer() override fun iterator(): Iterator = iterator { for (i in indices) { @@ -41,7 +44,14 @@ public class OffsetDoubleBuffer( override fun toString(): String = Buffer.toString(this) public fun view(addOffset: Int, newSize: Int = size - addOffset): OffsetDoubleBuffer = - OffsetDoubleBuffer(source, offset + addOffset, newSize) + OffsetDoubleBuffer(origin, offset + addOffset, newSize) + + @UnstableKMathAPI + override fun originIndex(index: Int): Int = if (index in 0 until size) { + index + offset + } else { + -1 + } } public fun OffsetDoubleBuffer.slice(range: IntRange): OffsetDoubleBuffer = view(range.first, range.last - range.first) @@ -68,25 +78,41 @@ public inline fun OffsetDoubleBuffer.mapInPlace(operation: (Double) -> Double) { } /** - * Default [BufferedTensor] implementation for [Double] values + * Default [BufferedTensor] implementation for [Double] values. + * + * [DoubleTensor] always uses row-based strides */ -public class DoubleTensor( - shape: IntArray, - override val source: OffsetDoubleBuffer, -) : BufferedTensor(shape) { +public open class DoubleTensor( + shape: ShapeND, + final override val source: OffsetDoubleBuffer, +) : BufferedTensor(shape), MutableStructureNDOfDouble { init { require(linearSize == source.size) { "Source buffer size must be equal tensor size" } } - public constructor(shape: IntArray, buffer: DoubleBuffer) : this(shape, OffsetDoubleBuffer(buffer, 0, buffer.size)) + public constructor(shape: ShapeND, buffer: DoubleBuffer) : this(shape, OffsetDoubleBuffer(buffer, 0, buffer.size)) - override fun get(index: IntArray): Double = this.source[indices.offset(index)] + @OptIn(PerformancePitfall::class) + override fun get(index: IntArray): Double = source[indices.offset(index)] + + @OptIn(PerformancePitfall::class) override fun set(index: IntArray, value: Double) { source[indices.offset(index)] = value } + override fun getDouble(index: IntArray): Double = source[indices.offset(index)] + + override fun setDouble(index: IntArray, value: Double) { + set(index, value) + } override fun toString(): String = toPrettyString() } + +public fun DoubleTensor.asDoubleBuffer(): OffsetDoubleBuffer = if (shape.size == 1) { + source +} else { + error("Only 1D tensors could be cast to 1D") +} diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor1D.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor1D.kt new file mode 100644 index 000000000..e74f73800 --- /dev/null +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor1D.kt @@ -0,0 +1,45 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.tensors.core + +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.MutableStructure1D +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.structures.MutableBuffer + +public class DoubleTensor1D( + source: OffsetDoubleBuffer, +) : DoubleTensor(ShapeND(source.size), source), MutableStructure1D { + + @PerformancePitfall + override fun get(index: IntArray): Double = super.get(index) + + @PerformancePitfall + override fun set(index: IntArray, value: Double) { + super.set(index, value) + } + + override val size: Int get() = source.size + + override fun get(index: Int): Double = source[index] + + override fun set(index: Int, value: Double) { + source[index] = value + } + + override fun copy(): MutableBuffer = source.copy() + + @PerformancePitfall + override fun elements(): Sequence> = super.elements() +} + +/** + * A zero-copy cast to 1D structure. Changes in resulting structure are reflected on original tensor. + */ +public fun DoubleTensor.asDoubleTensor1D(): DoubleTensor1D { + require(shape.size == 1) { "Only 1D tensors could be cast to 1D" } + return DoubleTensor1D(source) +} \ No newline at end of file diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor2D.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor2D.kt new file mode 100644 index 000000000..7c84b91e1 --- /dev/null +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor2D.kt @@ -0,0 +1,71 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.tensors.core + +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.MutableStructure2D +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.linearSize +import space.kscience.kmath.structures.PermutedMutableBuffer +import space.kscience.kmath.structures.permute + +public class DoubleTensor2D( + override val rowNum: Int, + override val colNum: Int, + source: OffsetDoubleBuffer, +) : DoubleTensor(ShapeND(rowNum, colNum), source), MutableStructure2D { + + override fun get(i: Int, j: Int): Double = source[i * colNum + j] + + @OptIn(PerformancePitfall::class) + override fun get(index: IntArray): Double = getDouble(index) + + override fun set(i: Int, j: Int, value: Double) { + source[i * colNum + j] = value + } + + @OptIn(PerformancePitfall::class) + override val rows: List + get() = List(rowNum) { i -> + source.view(i * colNum, colNum) + } + + + @OptIn(PerformancePitfall::class) + override val columns: List> + get() = List(colNum) { j -> + val indices = IntArray(rowNum) { i -> j + i * colNum } + source.permute(indices) + } + + override val shape: ShapeND get() = super.shape + + @PerformancePitfall + override fun elements(): Sequence> = super.elements() +} + +/** + * A zero-copy cast to 2D structure. Changes in resulting structure are reflected on original tensor. + */ +public fun DoubleTensor.asDoubleTensor2D(): DoubleTensor2D { + require(shape.size == 2) { "Only 2D tensors could be cast to 2D" } + return DoubleTensor2D(shape[0], shape[1], source) +} + + +public inline fun DoubleTensor.forEachMatrix(block: (index: IntArray, matrix: DoubleTensor2D) -> Unit) { + val n = shape.size + check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" } + val matrixOffset = shape[n - 1] * shape[n - 2] + val matrixShape = ShapeND(shape[n - 2], shape[n - 1]) + + val size = matrixShape.linearSize + for (i in 0 until linearSize / matrixOffset) { + val offset = i * matrixOffset + val index = indices.index(offset).sliceArray(0 until (shape.size - 2)) + block(index, DoubleTensor(matrixShape, source.view(offset, size)).asDoubleTensor2D()) + } +} diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt index f563d00ae..997c0a316 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt @@ -11,12 +11,12 @@ package space.kscience.kmath.tensors.core import space.kscience.kmath.misc.PerformancePitfall import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.nd.* +import space.kscience.kmath.operations.DoubleBufferOps import space.kscience.kmath.operations.DoubleField import space.kscience.kmath.structures.* import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra import space.kscience.kmath.tensors.api.Tensor -import space.kscience.kmath.tensors.api.TensorPartialDivisionAlgebra import space.kscience.kmath.tensors.core.internal.* import kotlin.math.* @@ -25,7 +25,6 @@ import kotlin.math.* */ @OptIn(PerformancePitfall::class) public open class DoubleTensorAlgebra : - TensorPartialDivisionAlgebra, AnalyticTensorAlgebra, LinearOpsTensorAlgebra { @@ -33,6 +32,8 @@ public open class DoubleTensorAlgebra : override val elementAlgebra: DoubleField get() = DoubleField + public val bufferAlgebra: DoubleBufferOps get() = DoubleBufferOps + /** * Applies the [transform] function to each element of the tensor and returns the resulting modified tensor. @@ -59,20 +60,16 @@ public open class DoubleTensorAlgebra : } } - public inline fun Tensor.mapIndexedInPlace(operation: (IntArray, Double) -> Double) { - indices.forEach { set(it, operation(it, get(it))) } + public inline fun Tensor.mapIndexedInPlace(operation: DoubleField.(IntArray, Double) -> Double) { + indices.forEach { set(it, DoubleField.operation(it, get(it))) } } @Suppress("OVERRIDE_BY_INLINE") final override inline fun StructureND.mapIndexed(transform: DoubleField.(index: IntArray, Double) -> Double): DoubleTensor { - val tensor = this.asDoubleTensor() - //TODO remove additional copy - val buffer = DoubleBuffer(tensor.source.size) { - DoubleField.transform(tensor.indices.index(it), tensor.source[it]) - } - return DoubleTensor(tensor.shape, buffer) + return copyToTensor().apply { mapIndexedInPlace(transform) } } + @Suppress("OVERRIDE_BY_INLINE") final override inline fun zip( left: StructureND, @@ -92,16 +89,26 @@ public open class DoubleTensorAlgebra : public inline fun StructureND.reduceElements(transform: (DoubleBuffer) -> Double): Double = transform(asDoubleTensor().source.copy()) - //TODO do we need protective copy? + //TODO Add read-only DoubleBuffer wrapper. To avoid protective copy override fun StructureND.valueOrNull(): Double? { val dt = asDoubleTensor() - return if (dt.shape contentEquals intArrayOf(1)) dt.source[0] else null + return if (dt.shape contentEquals ShapeND(1)) dt.source[0] else null } override fun StructureND.value(): Double = valueOrNull() ?: throw IllegalArgumentException("The tensor shape is $shape, but value method is allowed only for shape [1]") + public fun fromBuffer(shape: ShapeND, buffer: Buffer): DoubleTensor { + checkNotEmptyShape(shape) + check(buffer.size > 0) { "Illegal empty buffer provided" } + check(buffer.size == shape.linearSize) { + "Inconsistent shape $shape for buffer of size ${buffer.size} provided" + } + return DoubleTensor(shape, buffer.toDoubleBuffer()) + } + + /** * Constructs a tensor with the specified shape and data. * @@ -109,12 +116,7 @@ public open class DoubleTensorAlgebra : * @param array one-dimensional data array. * @return tensor with the [shape] shape and [array] data. */ - public fun fromArray(shape: IntArray, array: DoubleArray): DoubleTensor { - checkNotEmptyShape(shape) - checkEmptyDoubleBuffer(array) - checkBufferShapeConsistency(shape, array) - return DoubleTensor(shape, array.asBuffer()) - } + public fun fromArray(shape: ShapeND, array: DoubleArray): DoubleTensor = fromBuffer(shape, array.asBuffer()) /** * Constructs a tensor with the specified shape and initializer. @@ -123,18 +125,18 @@ public open class DoubleTensorAlgebra : * @param initializer mapping tensor indices to values. * @return tensor with the [shape] shape and data generated by the [initializer]. */ - override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): DoubleTensor = fromArray( + override fun structureND(shape: ShapeND, initializer: DoubleField.(IntArray) -> Double): DoubleTensor = fromArray( shape, - TensorLinearStructure(shape).asSequence().map { DoubleField.initializer(it) }.toMutableList().toDoubleArray() + RowStrides(shape).asSequence().map { DoubleField.initializer(it) }.toMutableList().toDoubleArray() ) override fun Tensor.getTensor(i: Int): DoubleTensor { val dt = asDoubleTensor() - val lastShape = shape.drop(1).toIntArray() - val newShape = if (lastShape.isNotEmpty()) lastShape else intArrayOf(1) + val lastShape = shape.last(shape.size - 1) + val newShape: ShapeND = if (lastShape.isNotEmpty()) lastShape else ShapeND(1) return DoubleTensor( newShape, - dt.source.view(newShape.reduce(Int::times) * i, TensorLinearStructure.linearSizeOf(newShape)) + dt.source.view(newShape.linearSize * i, newShape.linearSize) ) } @@ -145,9 +147,9 @@ public open class DoubleTensorAlgebra : * @param shape array of integers defining the shape of the output tensor. * @return tensor with the [shape] shape and filled with [value]. */ - public fun full(value: Double, shape: IntArray): DoubleTensor { + public fun full(value: Double, shape: ShapeND): DoubleTensor { checkNotEmptyShape(shape) - val buffer = DoubleBuffer(shape.reduce(Int::times)) { value } + val buffer = DoubleBuffer(shape.linearSize) { value } return DoubleTensor(shape, buffer) } @@ -169,7 +171,7 @@ public open class DoubleTensorAlgebra : * @param shape array of integers defining the shape of the output tensor. * @return tensor filled with the scalar value `0.0`, with the [shape] shape. */ - public fun zeros(shape: IntArray): DoubleTensor = full(0.0, shape) + public fun zeros(shape: ShapeND): DoubleTensor = full(0.0, shape) /** * Returns a tensor filled with the scalar value `0.0`, with the same shape as a given array. @@ -184,7 +186,7 @@ public open class DoubleTensorAlgebra : * @param shape array of integers defining the shape of the output tensor. * @return tensor filled with the scalar value `1.0`, with the [shape] shape. */ - public fun ones(shape: IntArray): DoubleTensor = full(1.0, shape) + public fun ones(shape: ShapeND): DoubleTensor = full(1.0, shape) /** * Returns a tensor filled with the scalar value `1.0`, with the same shape as a given array. @@ -200,7 +202,7 @@ public open class DoubleTensorAlgebra : * @return a 2-D tensor with ones on the diagonal and zeros elsewhere. */ public fun eye(n: Int): DoubleTensor { - val shape = intArrayOf(n, n) + val shape = ShapeND(n, n) val buffer = DoubleBuffer(n * n) { 0.0 } val res = DoubleTensor(shape, buffer) for (i in 0 until n) { @@ -238,7 +240,7 @@ public open class DoubleTensorAlgebra : override fun Tensor.minusAssign(arg: StructureND) { checkShapesCompatible(this, arg) - mapIndexedInPlace { index, value -> value - arg[index] } + mapIndexedInPlace { index, value -> value - arg.getDouble(index) } } override fun Double.times(arg: StructureND): DoubleTensor = arg.map { this@times * it } @@ -273,32 +275,44 @@ public open class DoubleTensorAlgebra : override fun StructureND.unaryMinus(): DoubleTensor = map { -it } - override fun Tensor.transposed(i: Int, j: Int): DoubleTensor { - // TODO change strides instead of changing content - val dt = asDoubleTensor() - val ii = dt.minusIndex(i) - val jj = dt.minusIndex(j) - checkTranspose(dt.dimension, ii, jj) - val n = dt.linearSize - val resBuffer = DoubleArray(n) - - val resShape = dt.shape.copyOf() - resShape[ii] = resShape[jj].also { resShape[jj] = resShape[ii] } - - val resTensor = DoubleTensor(resShape, resBuffer.asBuffer()) - - for (offset in 0 until n) { - val oldMultiIndex = dt.indices.index(offset) - val newMultiIndex = oldMultiIndex.copyOf() - newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] } - - val linearIndex = resTensor.indices.offset(newMultiIndex) - resTensor.source[linearIndex] = dt.source[offset] + override fun StructureND.transposed(i: Int, j: Int): Tensor { + val actualI = if (i >= 0) i else shape.size + i + val actualJ = if (j >= 0) j else shape.size + j + return asDoubleTensor().permute( + shape.transposed(actualI, actualJ) + ) { originIndex -> + originIndex.copyOf().apply { + val ith = get(actualI) + val jth = get(actualJ) + set(actualI, jth) + set(actualJ, ith) + } } - return resTensor +// // TODO change strides instead of changing content +// val dt = asDoubleTensor() +// val ii = dt.minusIndex(i) +// val jj = dt.minusIndex(j) +// checkTranspose(dt.dimension, ii, jj) +// val n = dt.linearSize +// val resBuffer = DoubleArray(n) +// +// val resShape = dt.shape.copyOf() +// resShape[ii] = resShape[jj].also { resShape[jj] = resShape[ii] } +// +// val resTensor = DoubleTensor(resShape, resBuffer.asBuffer()) +// +// for (offset in 0 until n) { +// val oldMultiIndex = dt.indices.index(offset) +// val newMultiIndex = oldMultiIndex.copyOf() +// newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] } +// +// val linearIndex = resTensor.indices.offset(newMultiIndex) +// resTensor.source[linearIndex] = dt.source[offset] +// } +// return resTensor } - override fun Tensor.view(shape: IntArray): DoubleTensor { + override fun Tensor.view(shape: ShapeND): DoubleTensor { checkView(asDoubleTensor(), shape) return DoubleTensor(shape, asDoubleTensor().source) } @@ -338,7 +352,7 @@ public open class DoubleTensorAlgebra : @UnstableKMathAPI public infix fun StructureND.matmul(other: StructureND): DoubleTensor { if (shape.size == 1 && other.shape.size == 1) { - return DoubleTensor(intArrayOf(1), DoubleBuffer(times(other).sum())) + return DoubleTensor(ShapeND(1), DoubleBuffer(times(other).sum())) } var penultimateDim = false @@ -350,7 +364,7 @@ public open class DoubleTensorAlgebra : if (shape.size == 1) { penultimateDim = true - newThis = newThis.view(intArrayOf(1) + shape) + newThis = newThis.view(ShapeND(1) + shape) } if (other.shape.size == 1) { @@ -370,8 +384,8 @@ public open class DoubleTensorAlgebra : "Tensors dot operation dimension mismatch: ($l, $m1) x ($m2, $n)" } - val resShape = newThis.shape.sliceArray(0..(newThis.shape.size - 2)) + intArrayOf(newOther.shape.last()) - val resSize = resShape.reduce { acc, i -> acc * i } + val resShape = newThis.shape.slice(0..(newThis.shape.size - 2)) + intArrayOf(newOther.shape.last()) + val resSize = resShape.linearSize val resTensor = DoubleTensor(resShape, DoubleArray(resSize).asBuffer()) val resMatrices = resTensor.matrices @@ -388,9 +402,9 @@ public open class DoubleTensorAlgebra : // } return if (penultimateDim) { - resTensor.view(resTensor.shape.dropLast(2).toIntArray() + intArrayOf(resTensor.shape.last())) + resTensor.view(resTensor.shape.first(resTensor.shape.size - 2) + ShapeND(resTensor.shape.last())) } else if (lastDim) { - resTensor.view(resTensor.shape.dropLast(1).toIntArray()) + resTensor.view(resTensor.shape.first(resTensor.shape.size - 1)) } else { resTensor } @@ -402,7 +416,7 @@ public open class DoubleTensorAlgebra : } override fun diagonalEmbedding( - diagonalEntries: Tensor, + diagonalEntries: StructureND, offset: Int, dim1: Int, dim2: Int, @@ -426,11 +440,11 @@ public open class DoubleTensorAlgebra : lessDim = greaterDim.also { greaterDim = lessDim } } - val resShape = diagonalEntries.shape.slice(0 until lessDim).toIntArray() + + val resShape = diagonalEntries.shape.slice(0 until lessDim) + intArrayOf(diagonalEntries.shape[n - 1] + abs(realOffset)) + - diagonalEntries.shape.slice(lessDim until greaterDim - 1).toIntArray() + + diagonalEntries.shape.slice(lessDim until greaterDim - 1) + intArrayOf(diagonalEntries.shape[n - 1] + abs(realOffset)) + - diagonalEntries.shape.slice(greaterDim - 1 until n - 1).toIntArray() + diagonalEntries.shape.slice(greaterDim - 1 until n - 1) val resTensor: DoubleTensor = zeros(resShape) for (i in 0 until diagonalEntries.indices.linearSize) { @@ -490,48 +504,6 @@ public open class DoubleTensorAlgebra : return true } - /** - * Returns a tensor of random numbers drawn from normal distributions with `0.0` mean and `1.0` standard deviation. - * - * @param shape the desired shape for the output tensor. - * @param seed the random seed of the pseudo-random number generator. - * @return tensor of a given shape filled with numbers from the normal distribution - * with `0.0` mean and `1.0` standard deviation. - */ - public fun randomNormal(shape: IntArray, seed: Long = 0): DoubleTensor = - DoubleTensor(shape, getRandomNormals(shape.reduce(Int::times), seed)) - - /** - * Returns a tensor with the same shape as `input` of random numbers drawn from normal distributions - * with `0.0` mean and `1.0` standard deviation. - * - * @receiver the `input`. - * @param seed the random seed of the pseudo-random number generator. - * @return a tensor with the same shape as `input` filled with numbers from the normal distribution - * with `0.0` mean and `1.0` standard deviation. - */ - public fun Tensor.randomNormalLike(seed: Long = 0): DoubleTensor = - DoubleTensor(shape, getRandomNormals(shape.reduce(Int::times), seed)) - - /** - * Concatenates a sequence of tensors with equal shapes along the first dimension. - * - * @param tensors the [List] of tensors with same shapes to concatenate - * @return tensor with concatenation result - */ - public fun stack(tensors: List>): DoubleTensor { - check(tensors.isNotEmpty()) { "List must have at least 1 element" } - val shape = tensors[0].shape - check(tensors.all { it.shape contentEquals shape }) { "Tensors must have same shapes" } - val resShape = intArrayOf(tensors.size) + shape -// val resBuffer: List = tensors.flatMap { -// it.asDoubleTensor().source.array.drop(it.asDoubleTensor().bufferStart) -// .take(it.asDoubleTensor().linearSize) -// } - val resBuffer = tensors.map { it.asDoubleTensor().source }.concat() - return DoubleTensor(resShape, resBuffer) - } - /** * Builds tensor from rows of the input tensor. * @@ -548,11 +520,11 @@ public open class DoubleTensorAlgebra : ): DoubleTensor { check(dim < dimension) { "Dimension $dim out of range $dimension" } val resShape = if (keepDim) { - shape.take(dim).toIntArray() + intArrayOf(1) + shape.takeLast(dimension - dim - 1).toIntArray() + shape.first(dim) + intArrayOf(1) + shape.last(dimension - dim - 1) } else { - shape.take(dim).toIntArray() + shape.takeLast(dimension - dim - 1).toIntArray() + shape.first(dim) + shape.last(dimension - dim - 1) } - val resNumElements = resShape.reduce(Int::times) + val resNumElements = resShape.linearSize val init = foldFunction(DoubleArray(1) { 0.0 }) val resTensor = DoubleTensor( resShape, @@ -576,11 +548,11 @@ public open class DoubleTensorAlgebra : ): IntTensor { check(dim < dimension) { "Dimension $dim out of range $dimension" } val resShape = if (keepDim) { - shape.take(dim).toIntArray() + intArrayOf(1) + shape.takeLast(dimension - dim - 1).toIntArray() + shape.first(dim) + intArrayOf(1) + shape.last(dimension - dim - 1) } else { - shape.take(dim).toIntArray() + shape.takeLast(dimension - dim - 1).toIntArray() + shape.first(dim) + shape.last(dimension - dim - 1) } - val resNumElements = resShape.reduce(Int::times) + val resNumElements = resShape.linearSize val init = foldFunction(DoubleArray(1) { 0.0 }) val resTensor = IntTensor( resShape, @@ -623,102 +595,75 @@ public open class DoubleTensorAlgebra : } - override fun StructureND.mean(): Double = sum() / indices.linearSize + override fun mean(structureND: StructureND): Double = structureND.sum() / structureND.indices.linearSize - override fun StructureND.mean(dim: Int, keepDim: Boolean): DoubleTensor = - foldDimToDouble(dim, keepDim) { arr -> - check(dim < dimension) { "Dimension $dim out of range $dimension" } - arr.sum() / shape[dim] + override fun mean(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor = + structureND.foldDimToDouble(dim, keepDim) { arr -> + check(dim < structureND.dimension) { "Dimension $dim out of range ${structureND.dimension}" } + arr.sum() / structureND.shape[dim] } - override fun StructureND.std(): Double = reduceElements { arr -> - val mean = arr.array.sum() / indices.linearSize - sqrt(arr.array.sumOf { (it - mean) * (it - mean) } / (indices.linearSize - 1)) + override fun std(structureND: StructureND): Double = structureND.reduceElements { arr -> + val mean = arr.array.sum() / structureND.indices.linearSize + sqrt(arr.array.sumOf { (it - mean) * (it - mean) } / (structureND.indices.linearSize - 1)) } - override fun StructureND.std(dim: Int, keepDim: Boolean): DoubleTensor = foldDimToDouble( - dim, - keepDim - ) { arr -> - check(dim < dimension) { "Dimension $dim out of range $dimension" } - val mean = arr.sum() / shape[dim] - sqrt(arr.sumOf { (it - mean) * (it - mean) } / (shape[dim] - 1)) - } + override fun std(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor = + structureND.foldDimToDouble( + dim, + keepDim + ) { arr -> + check(dim < structureND.dimension) { "Dimension $dim out of range ${structureND.dimension}" } + val mean = arr.sum() / structureND.shape[dim] + sqrt(arr.sumOf { (it - mean) * (it - mean) } / (structureND.shape[dim] - 1)) + } - override fun StructureND.variance(): Double = reduceElements { arr -> - val linearSize = indices.linearSize + override fun variance(structureND: StructureND): Double = structureND.reduceElements { arr -> + val linearSize = structureND.indices.linearSize val mean = arr.array.sum() / linearSize arr.array.sumOf { (it - mean) * (it - mean) } / (linearSize - 1) } - override fun StructureND.variance(dim: Int, keepDim: Boolean): DoubleTensor = foldDimToDouble( - dim, - keepDim - ) { arr -> - check(dim < dimension) { "Dimension $dim out of range $dimension" } - val mean = arr.sum() / shape[dim] - arr.sumOf { (it - mean) * (it - mean) } / (shape[dim] - 1) - } - - private fun cov(x: StructureND, y: StructureND): Double { - val n = x.shape[0] - return ((x - x.mean()) * (y - y.mean())).mean() * n / (n - 1) - } - - /** - * Returns the covariance matrix `M` of given vectors. - * - * `M[i, j]` contains covariance of `i`-th and `j`-th given vectors - * - * @param tensors the [List] of 1-dimensional tensors with same shape - * @return `M`. - */ - public fun cov(tensors: List>): DoubleTensor { - check(tensors.isNotEmpty()) { "List must have at least 1 element" } - val n = tensors.size - val m = tensors[0].shape[0] - check(tensors.all { it.shape contentEquals intArrayOf(m) }) { "Tensors must have same shapes" } - val resTensor = DoubleTensor( - intArrayOf(n, n), - DoubleBuffer(n * n) { 0.0 } - ) - for (i in 0 until n) { - for (j in 0 until n) { - resTensor[intArrayOf(i, j)] = cov(tensors[i], tensors[j]) - } + override fun variance(structureND: StructureND, dim: Int, keepDim: Boolean): Tensor = + structureND.foldDimToDouble( + dim, + keepDim + ) { arr -> + check(dim < structureND.dimension) { "Dimension $dim out of range ${structureND.dimension}" } + val mean = arr.sum() / structureND.shape[dim] + arr.sumOf { (it - mean) * (it - mean) } / (structureND.shape[dim] - 1) } - return resTensor - } - override fun StructureND.exp(): DoubleTensor = map { exp(it) } - override fun StructureND.ln(): DoubleTensor = map { ln(it) } + override fun exp(arg: StructureND): DoubleTensor = arg.map { this.exp(it) } - override fun StructureND.sqrt(): DoubleTensor = map { sqrt(it) } + override fun ln(arg: StructureND): DoubleTensor = arg.map { this.ln(it) } - override fun StructureND.cos(): DoubleTensor = map { cos(it) } + override fun sqrt(arg: StructureND): DoubleTensor = arg.map { this.sqrt(it) } - override fun StructureND.acos(): DoubleTensor = map { acos(it) } + override fun cos(arg: StructureND): DoubleTensor = arg.map { this.cos(it) } - override fun StructureND.cosh(): DoubleTensor = map { cosh(it) } + override fun acos(arg: StructureND): DoubleTensor = arg.map { this.acos(it) } - override fun StructureND.acosh(): DoubleTensor = map { acosh(it) } + override fun cosh(arg: StructureND): DoubleTensor = arg.map { this.cosh(it) } - override fun StructureND.sin(): DoubleTensor = map { sin(it) } + override fun acosh(arg: StructureND): DoubleTensor = arg.map { this.acosh(it) } - override fun StructureND.asin(): DoubleTensor = map { asin(it) } + override fun sin(arg: StructureND): DoubleTensor = arg.map { this.sin(it) } - override fun StructureND.sinh(): DoubleTensor = map { sinh(it) } + override fun asin(arg: StructureND): DoubleTensor = arg.map { this.asin(it) } - override fun StructureND.asinh(): DoubleTensor = map { asinh(it) } + override fun sinh(arg: StructureND): DoubleTensor = arg.map { this.sinh(it) } - override fun StructureND.tan(): DoubleTensor = map { tan(it) } + override fun asinh(arg: StructureND): DoubleTensor = arg.map { this.asinh(it) } - override fun StructureND.atan(): DoubleTensor = map { atan(it) } + override fun tan(arg: StructureND): DoubleTensor = arg.map { this.tan(it) } - override fun StructureND.tanh(): DoubleTensor = map { tanh(it) } + override fun atan(arg: StructureND): DoubleTensor = arg.map { this.atan(it) } - override fun StructureND.atanh(): DoubleTensor = map { atanh(it) } + override fun tanh(arg: StructureND): DoubleTensor = arg.map { this.tanh(it) } + + override fun atanh(arg: StructureND): DoubleTensor = arg.map { this.atanh(it) } override fun power(arg: StructureND, pow: Number): StructureND = if (pow is Int) { arg.map { it.pow(pow) } @@ -726,317 +671,45 @@ public open class DoubleTensorAlgebra : arg.map { it.pow(pow.toDouble()) } } - override fun StructureND.ceil(): DoubleTensor = map { ceil(it) } + override fun ceil(arg: StructureND): DoubleTensor = arg.map { ceil(it) } - override fun StructureND.floor(): DoubleTensor = map { floor(it) } + override fun floor(structureND: StructureND): DoubleTensor = structureND.map { floor(it) } - override fun StructureND.inv(): DoubleTensor = invLU(1e-9) + override fun StructureND.inv(): DoubleTensor = invLU(this, 1e-9) - override fun StructureND.det(): DoubleTensor = detLU(1e-9) + override fun StructureND.det(): DoubleTensor = detLU(this, 1e-9) - /** - * Computes the LU factorization of a matrix or batches of matrices `input`. - * Returns a tuple containing the LU factorization and pivots of `input`. - * - * @param epsilon permissible error when comparing the determinant of a matrix with zero - * @return pair of `factorization` and `pivots`. - * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor. - * The `pivots` has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows. - */ - public fun StructureND.luFactor(epsilon: Double): Pair = - computeLU(this, epsilon) - ?: throw IllegalArgumentException("Tensor contains matrices which are singular at precision $epsilon") + override fun lu(structureND: StructureND): Triple = + lu(structureND, 1e-9) - /** - * Computes the LU factorization of a matrix or batches of matrices `input`. - * Returns a tuple containing the LU factorization and pivots of `input`. - * Uses an error of ``1e-9`` when calculating whether a matrix is degenerate. - * - * @return pair of `factorization` and `pivots`. - * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor. - * The `pivots` has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows. - */ - public fun StructureND.luFactor(): Pair = luFactor(1e-9) + override fun cholesky(structureND: StructureND): DoubleTensor = cholesky(structureND, 1e-6) - /** - * Unpacks the data and pivots from a LU factorization of a tensor. - * Given a tensor [luTensor], return tensors `Triple(P, L, U)` satisfying `P dot luTensor = L dot U`, - * with `P` being a permutation matrix or batch of matrices, - * `L` being a lower triangular matrix or batch of matrices, - * `U` being an upper triangular matrix or batch of matrices. - * - * @param luTensor the packed LU factorization data - * @param pivotsTensor the packed LU factorization pivots - * @return triple of `P`, `L` and `U` tensors - */ - public fun luPivot( - luTensor: StructureND, - pivotsTensor: Tensor, - ): Triple { - checkSquareMatrix(luTensor.shape) - check( - luTensor.shape.dropLast(2).toIntArray() contentEquals pivotsTensor.shape.dropLast(1).toIntArray() || - luTensor.shape.last() == pivotsTensor.shape.last() - 1 - ) { "Inappropriate shapes of input tensors" } - - val n = luTensor.shape.last() - val pTensor = zeroesLike(luTensor) - pTensor - .matrixSequence() - .zip(pivotsTensor.asIntTensor().vectorSequence()) - .forEach { (p, pivot) -> pivInit(p.as2D(), pivot.as1D(), n) } - - val lTensor = zeroesLike(luTensor) - val uTensor = zeroesLike(luTensor) - - lTensor.matrixSequence() - .zip(uTensor.matrixSequence()) - .zip(luTensor.asDoubleTensor().matrixSequence()) - .forEach { (pairLU, lu) -> - val (l, u) = pairLU - luPivotHelper(l.as2D(), u.as2D(), lu.as2D(), n) - } - - return Triple(pTensor, lTensor, uTensor) - } - - /** - * QR decomposition. - * - * Computes the QR decomposition of a matrix or a batch of matrices, and returns a pair `Q to R` of tensors. - * Given a tensor `input`, return tensors `Q to R` satisfying `input == Q dot R`, - * with `Q` being an orthogonal matrix or batch of orthogonal matrices - * and `R` being an upper triangular matrix or batch of upper triangular matrices. - * - * @receiver the `input`. - * @param epsilon the permissible error when comparing tensors for equality. - * Used when checking the positive definiteness of the input matrix or matrices. - * @return a pair of `Q` and `R` tensors. - */ - public fun StructureND.cholesky(epsilon: Double): DoubleTensor { - checkSquareMatrix(shape) - checkPositiveDefinite(asDoubleTensor(), epsilon) - - val n = shape.last() - val lTensor = zeroesLike(this) - - for ((a, l) in asDoubleTensor().matrixSequence().zip(lTensor.matrixSequence())) - for (i in 0 until n) choleskyHelper(a.as2D(), l.as2D(), n) - - return lTensor - } - - override fun StructureND.cholesky(): DoubleTensor = cholesky(1e-6) - - override fun StructureND.qr(): Pair { - checkSquareMatrix(shape) - val qTensor = zeroesLike(this) - val rTensor = zeroesLike(this) + override fun qr(structureND: StructureND): Pair { + checkSquareMatrix(structureND.shape) + val qTensor = zeroesLike(structureND) + val rTensor = zeroesLike(structureND) //TODO replace with cycle - asDoubleTensor().matrixSequence() + structureND.asDoubleTensor().matrixSequence() .zip( (qTensor.matrixSequence() .zip(rTensor.matrixSequence())) ).forEach { (matrix, qr) -> val (q, r) = qr - qrHelper(matrix, q, r.as2D()) + qrHelper(matrix, q, r.asDoubleTensor2D()) } return qTensor to rTensor } - override fun StructureND.svd(): Triple = - svd(epsilon = 1e-10) + override fun svd( + structureND: StructureND, + ): Triple, StructureND, StructureND> = + svd(structureND = structureND, epsilon = 1e-10) - /** - * Singular Value Decomposition. - * - * Computes the singular value decomposition of either a matrix or batch of matrices `input`. - * The singular value decomposition is represented as a triple `Triple(U, S, V)`, - * such that `input == U dot diagonalEmbedding(S) dot V.transpose()`. - * If `input` is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as `input. - * - * @receiver the `input`. - * @param epsilon permissible error when calculating the dot product of vectors - * i.e., the precision with which the cosine approaches 1 in an iterative algorithm. - * @return a triple `Triple(U, S, V)`. - */ - public fun StructureND.svd(epsilon: Double): Triple { - val size = dimension - val commonShape = shape.sliceArray(0 until size - 2) - val (n, m) = shape.sliceArray(size - 2 until size) - val uTensor = zeros(commonShape + intArrayOf(min(n, m), n)) - val sTensor = zeros(commonShape + intArrayOf(min(n, m))) - val vTensor = zeros(commonShape + intArrayOf(min(n, m), m)) + override fun symEig(structureND: StructureND): Pair = + symEigJacobi(structureND = structureND, maxIteration = 50, epsilon = 1e-15) - val matrices: VirtualBuffer = asDoubleTensor().matrices - val uTensors = uTensor.matrices - val sTensorVectors = sTensor.vectors - val vTensors = vTensor.matrices - - for (index in matrices.indices) { - val matrix = matrices[index] - val usv = Triple( - uTensors[index], - sTensorVectors[index], - vTensors[index] - ) - val matrixSize = matrix.shape.reduce { acc, i -> acc * i } - val curMatrix = DoubleTensor( - matrix.shape, - matrix.source.view(0, matrixSize) - ) - svdHelper(curMatrix, usv, m, n, epsilon) - } - - return Triple(uTensor.transposed(), sTensor, vTensor.transposed()) - } - - override fun StructureND.symEig(): Pair = - symEigJacobi(maxIteration = 50, epsilon = 1e-15) - - /** - * Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices, - * represented by a pair `eigenvalues to eigenvectors`. - * - * @param epsilon the permissible error when comparing tensors for equality - * and when the cosine approaches 1 in the SVD algorithm. - * @return a pair `eigenvalues to eigenvectors`. - */ - public fun StructureND.symEigSvd(epsilon: Double): Pair { - //TODO optimize conversion - checkSymmetric(asDoubleTensor(), epsilon) - - fun MutableStructure2D.cleanSym(n: Int) { - for (i in 0 until n) { - for (j in 0 until n) { - if (i == j) { - this[i, j] = sign(this[i, j]) - } else { - this[i, j] = 0.0 - } - } - } - } - - val (u, s, v) = svd(epsilon) - val shp = s.shape + intArrayOf(1) - val utv = u.transposed() matmul v - val n = s.shape.last() - for (matrix in utv.matrixSequence()) { - matrix.as2D().cleanSym(n) - } - - val eig = (utv dot s.view(shp)).view(s.shape) - return eig to v - } - - public fun StructureND.symEigJacobi(maxIteration: Int, epsilon: Double): Pair { - //TODO optimize conversion - checkSymmetric(asDoubleTensor(), epsilon) - - val size = this.dimension - val eigenvectors = zeros(this.shape) - val eigenvalues = zeros(this.shape.sliceArray(0 until size - 1)) - - var eigenvalueStart = 0 - var eigenvectorStart = 0 - for (matrix in asDoubleTensor().matrixSequence()) { - val matrix2D = matrix.as2D() - val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon) - - for (i in 0 until matrix2D.rowNum) { - for (j in 0 until matrix2D.colNum) { - eigenvectors.source[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j] - } - } - - for (i in 0 until matrix2D.rowNum) { - eigenvalues.source[eigenvalueStart + i] = d[i] - } - - eigenvalueStart += this.shape.last() - eigenvectorStart += this.shape.last() * this.shape.last() - } - - return eigenvalues to eigenvectors - } - - /** - * Computes the determinant of a square matrix input, or of each square matrix in a batched input - * using LU factorization algorithm. - * - * @param epsilon the error in the LU algorithm—permissible error when comparing the determinant of a matrix - * with zero. - * @return the determinant. - */ - public fun StructureND.detLU(epsilon: Double = 1e-9): DoubleTensor { - checkSquareMatrix(shape) - //TODO check for unnecessary copies - val luTensor = copyToTensor() - val pivotsTensor = setUpPivots() - - val n = shape.size - - val detTensorShape = IntArray(n - 1) { i -> shape[i] } - detTensorShape[n - 2] = 1 - val resBuffer = DoubleBuffer(detTensorShape.reduce(Int::times)) { 0.0 } - - val detTensor = DoubleTensor( - detTensorShape, - resBuffer - ) - - luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).forEachIndexed { index, (lu, pivots) -> - resBuffer[index] = if (luHelper(lu.as2D(), pivots.as1D(), epsilon)) - 0.0 else luMatrixDet(lu.as2D(), pivots.as1D()) - } - - return detTensor - } - - /** - * Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input - * using LU factorization algorithm. - * Given a square matrix `a`, return the matrix `aInv` satisfying - * `a dot aInv == aInv dot a == eye(a.shape[0])`. - * - * @param epsilon error in the LU algorithm—permissible error when comparing the determinant of a matrix with zero - * @return the multiplicative inverse of a matrix. - */ - public fun StructureND.invLU(epsilon: Double = 1e-9): DoubleTensor { - val (luTensor, pivotsTensor) = luFactor(epsilon) - val invTensor = zeroesLike(luTensor) - - //TODO replace sequence with a cycle - val seq = luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence()) - for ((luP, invMatrix) in seq) { - val (lu, pivots) = luP - luMatrixInv(lu.as2D(), pivots.as1D(), invMatrix.as2D()) - } - - return invTensor - } - - /** - * LUP decomposition. - * - * Computes the LUP decomposition of a matrix or a batch of matrices. - * Given a tensor `input`, return tensors `Triple(P, L, U)` satisfying `P dot input == L dot U`, - * with `P` being a permutation matrix or batch of matrices, - * `L` being a lower triangular matrix or batch of matrices, - * `U` being an upper triangular matrix or batch of matrices. - * - * @param epsilon permissible error when comparing the determinant of a matrix with zero. - * @return triple of `P`, `L` and `U` tensors. - */ - public fun StructureND.lu(epsilon: Double = 1e-9): Triple { - val (lu, pivots) = luFactor(epsilon) - return luPivot(lu, pivots) - } - - override fun StructureND.lu(): Triple = lu(1e-9) } public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra get() = DoubleTensorAlgebra diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensor.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensor.kt index ed96b6c8f..a77c4de4c 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensor.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensor.kt @@ -5,6 +5,8 @@ package space.kscience.kmath.tensors.core +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.structures.* /** @@ -73,7 +75,7 @@ public inline fun OffsetIntBuffer.mapInPlace(operation: (Int) -> Int) { * Default [BufferedTensor] implementation for [Int] values */ public class IntTensor( - shape: IntArray, + shape: ShapeND, override val source: OffsetIntBuffer, ) : BufferedTensor(shape) { @@ -81,10 +83,12 @@ public class IntTensor( require(linearSize == source.size) { "Source buffer size must be equal tensor size" } } - public constructor(shape: IntArray, buffer: IntBuffer) : this(shape, OffsetIntBuffer(buffer, 0, buffer.size)) + public constructor(shape: ShapeND, buffer: IntBuffer) : this(shape, OffsetIntBuffer(buffer, 0, buffer.size)) + @OptIn(PerformancePitfall::class) override fun get(index: IntArray): Int = this.source[indices.offset(index)] + @OptIn(PerformancePitfall::class) override fun set(index: IntArray, value: Int) { source[indices.offset(index)] = value } diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensorAlgebra.kt index 124ccc668..429b3ffa9 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensorAlgebra.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/IntTensorAlgebra.kt @@ -23,6 +23,7 @@ public open class IntTensorAlgebra : TensorAlgebra { public companion object : IntTensorAlgebra() + override val elementAlgebra: IntRing get() = IntRing @@ -88,7 +89,7 @@ public open class IntTensorAlgebra : TensorAlgebra { override fun StructureND.valueOrNull(): Int? { val dt = asIntTensor() - return if (dt.shape contentEquals intArrayOf(1)) dt.source[0] else null + return if (dt.shape contentEquals ShapeND(1)) dt.source[0] else null } override fun StructureND.value(): Int = valueOrNull() @@ -101,11 +102,11 @@ public open class IntTensorAlgebra : TensorAlgebra { * @param array one-dimensional data array. * @return tensor with the [shape] shape and [array] data. */ - public fun fromArray(shape: IntArray, array: IntArray): IntTensor { + public fun fromArray(shape: ShapeND, array: IntArray): IntTensor { checkNotEmptyShape(shape) check(array.isNotEmpty()) { "Illegal empty buffer provided" } - check(array.size == shape.reduce(Int::times)) { - "Inconsistent shape ${shape.toList()} for buffer of size ${array.size} provided" + check(array.size == shape.linearSize) { + "Inconsistent shape ${shape} for buffer of size ${array.size} provided" } return IntTensor(shape, array.asBuffer()) } @@ -117,16 +118,16 @@ public open class IntTensorAlgebra : TensorAlgebra { * @param initializer mapping tensor indices to values. * @return tensor with the [shape] shape and data generated by the [initializer]. */ - override fun structureND(shape: IntArray, initializer: IntRing.(IntArray) -> Int): IntTensor = fromArray( + override fun structureND(shape: ShapeND, initializer: IntRing.(IntArray) -> Int): IntTensor = fromArray( shape, - TensorLinearStructure(shape).asSequence().map { IntRing.initializer(it) }.toMutableList().toIntArray() + RowStrides(shape).asSequence().map { IntRing.initializer(it) }.toMutableList().toIntArray() ) override fun Tensor.getTensor(i: Int): IntTensor { val dt = asIntTensor() - val lastShape = shape.drop(1).toIntArray() - val newShape = if (lastShape.isNotEmpty()) lastShape else intArrayOf(1) - return IntTensor(newShape, dt.source.view(newShape.reduce(Int::times) * i)) + val lastShape = shape.last(shape.size - 1) + val newShape = if (lastShape.isNotEmpty()) lastShape else ShapeND(1) + return IntTensor(newShape, dt.source.view(newShape.linearSize * i)) } /** @@ -136,9 +137,9 @@ public open class IntTensorAlgebra : TensorAlgebra { * @param shape array of integers defining the shape of the output tensor. * @return tensor with the [shape] shape and filled with [value]. */ - public fun full(value: Int, shape: IntArray): IntTensor { + public fun full(value: Int, shape: ShapeND): IntTensor { checkNotEmptyShape(shape) - val buffer = IntBuffer(shape.reduce(Int::times)) { value } + val buffer = IntBuffer(shape.linearSize) { value } return IntTensor(shape, buffer) } @@ -160,7 +161,7 @@ public open class IntTensorAlgebra : TensorAlgebra { * @param shape array of integers defining the shape of the output tensor. * @return tensor filled with the scalar value `0`, with the [shape] shape. */ - public fun zeros(shape: IntArray): IntTensor = full(0, shape) + public fun zeros(shape: ShapeND): IntTensor = full(0, shape) /** * Returns a tensor filled with the scalar value `0`, with the same shape as a given array. @@ -175,7 +176,7 @@ public open class IntTensorAlgebra : TensorAlgebra { * @param shape array of integers defining the shape of the output tensor. * @return tensor filled with the scalar value `1`, with the [shape] shape. */ - public fun ones(shape: IntArray): IntTensor = full(1, shape) + public fun ones(shape: ShapeND): IntTensor = full(1, shape) /** * Returns a tensor filled with the scalar value `1`, with the same shape as a given array. @@ -191,7 +192,7 @@ public open class IntTensorAlgebra : TensorAlgebra { * @return a 2-D tensor with ones on the diagonal and zeros elsewhere. */ public fun eye(n: Int): IntTensor { - val shape = intArrayOf(n, n) + val shape = ShapeND(n, n) val buffer = IntBuffer(n * n) { 0 } val res = IntTensor(shape, buffer) for (i in 0 until n) { @@ -249,32 +250,44 @@ public open class IntTensorAlgebra : TensorAlgebra { override fun StructureND.unaryMinus(): IntTensor = map { -it } - override fun Tensor.transposed(i: Int, j: Int): IntTensor { - // TODO change strides instead of changing content - val dt = asIntTensor() - val ii = dt.minusIndex(i) - val jj = dt.minusIndex(j) - checkTranspose(dt.dimension, ii, jj) - val n = dt.linearSize - val resBuffer = IntArray(n) - - val resShape = dt.shape.copyOf() - resShape[ii] = resShape[jj].also { resShape[jj] = resShape[ii] } - - val resTensor = IntTensor(resShape, resBuffer.asBuffer()) - - for (offset in 0 until n) { - val oldMultiIndex = dt.indices.index(offset) - val newMultiIndex = oldMultiIndex.copyOf() - newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] } - - val linearIndex = resTensor.indices.offset(newMultiIndex) - resTensor.source[linearIndex] = dt.source[offset] + override fun StructureND.transposed(i: Int, j: Int): Tensor { + val actualI = if (i >= 0) i else shape.size + i + val actualJ = if(j>=0) j else shape.size + j + return asIntTensor().permute( + shape.transposed(actualI, actualJ) + ) { originIndex -> + originIndex.copyOf().apply { + val ith = get(actualI) + val jth = get(actualJ) + set(actualI, jth) + set(actualJ, ith) + } } - return resTensor +// // TODO change strides instead of changing content +// val dt = asIntTensor() +// val ii = dt.minusIndex(i) +// val jj = dt.minusIndex(j) +// checkTranspose(dt.dimension, ii, jj) +// val n = dt.linearSize +// val resBuffer = IntArray(n) +// +// val resShape = dt.shape.toArray() +// resShape[ii] = resShape[jj].also { resShape[jj] = resShape[ii] } +// +// val resTensor = IntTensor(Shape(resShape), resBuffer.asBuffer()) +// +// for (offset in 0 until n) { +// val oldMultiIndex = dt.indices.index(offset) +// val newMultiIndex = oldMultiIndex.copyOf() +// newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] } +// +// val linearIndex = resTensor.indices.offset(newMultiIndex) +// resTensor.source[linearIndex] = dt.source[offset] +// } +// return resTensor } - override fun Tensor.view(shape: IntArray): IntTensor { + override fun Tensor.view(shape: ShapeND): IntTensor { checkView(asIntTensor(), shape) return IntTensor(shape, asIntTensor().source) } @@ -287,7 +300,7 @@ public open class IntTensorAlgebra : TensorAlgebra { } override fun diagonalEmbedding( - diagonalEntries: Tensor, + diagonalEntries: StructureND, offset: Int, dim1: Int, dim2: Int, @@ -311,11 +324,11 @@ public open class IntTensorAlgebra : TensorAlgebra { lessDim = greaterDim.also { greaterDim = lessDim } } - val resShape = diagonalEntries.shape.slice(0 until lessDim).toIntArray() + + val resShape = diagonalEntries.shape.slice(0 until lessDim) + intArrayOf(diagonalEntries.shape[n - 1] + abs(realOffset)) + - diagonalEntries.shape.slice(lessDim until greaterDim - 1).toIntArray() + + diagonalEntries.shape.slice(lessDim until greaterDim - 1) + intArrayOf(diagonalEntries.shape[n - 1] + abs(realOffset)) + - diagonalEntries.shape.slice(greaterDim - 1 until n - 1).toIntArray() + diagonalEntries.shape.slice(greaterDim - 1 until n - 1) val resTensor = zeros(resShape) for (i in 0 until diagonalEntries.asIntTensor().linearSize) { @@ -375,7 +388,7 @@ public open class IntTensorAlgebra : TensorAlgebra { check(tensors.isNotEmpty()) { "List must have at least 1 element" } val shape = tensors[0].shape check(tensors.all { it.shape contentEquals shape }) { "Tensors must have same shapes" } - val resShape = intArrayOf(tensors.size) + shape + val resShape = ShapeND(tensors.size) + shape // val resBuffer: List = tensors.flatMap { // it.asIntTensor().source.array.drop(it.asIntTensor().bufferStart) // .take(it.asIntTensor().linearSize) @@ -399,11 +412,11 @@ public open class IntTensorAlgebra : TensorAlgebra { ): IntTensor { check(dim < dimension) { "Dimension $dim out of range $dimension" } val resShape = if (keepDim) { - shape.take(dim).toIntArray() + intArrayOf(1) + shape.takeLast(dimension - dim - 1).toIntArray() + shape.first(dim) + intArrayOf(1) + shape.last(dimension - dim - 1) } else { - shape.take(dim).toIntArray() + shape.takeLast(dimension - dim - 1).toIntArray() + shape.first(dim) + shape.last(dimension - dim - 1) } - val resNumElements = resShape.reduce(Int::times) + val resNumElements = resShape.linearSize val init = foldFunction(IntArray(1) { 0 }) val resTensor = IntTensor( resShape, diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/TensorLinearStructure.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/TensorLinearStructure.kt deleted file mode 100644 index 729fc0d13..000000000 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/TensorLinearStructure.kt +++ /dev/null @@ -1,74 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.tensors.core - -import space.kscience.kmath.nd.Strides -import kotlin.math.max - -/** - * This [Strides] implementation follows the last dimension first convention - * For more information: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.strides.html - * - * @param shape the shape of the tensor. - */ -public class TensorLinearStructure(override val shape: IntArray) : Strides() { - override val strides: IntArray get() = stridesFromShape(shape) - - override fun index(offset: Int): IntArray = - indexFromOffset(offset, strides, shape.size) - - override val linearSize: Int get() = linearSizeOf(shape) - - override fun equals(other: Any?): Boolean { - if (this === other) return true - if (other == null || this::class != other::class) return false - - other as TensorLinearStructure - - if (!shape.contentEquals(other.shape)) return false - - return true - } - - override fun hashCode(): Int { - return shape.contentHashCode() - } - - public companion object { - - public fun linearSizeOf(shape: IntArray): Int = shape.reduce(Int::times) - - public fun stridesFromShape(shape: IntArray): IntArray { - val nDim = shape.size - val res = IntArray(nDim) - if (nDim == 0) - return res - - var current = nDim - 1 - res[current] = 1 - - while (current > 0) { - res[current - 1] = max(1, shape[current]) * res[current] - current-- - } - return res - } - - public fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArray { - val res = IntArray(nDim) - var current = offset - var strideIndex = 0 - - while (strideIndex < nDim) { - res[strideIndex] = (current / strides[strideIndex]) - current %= strides[strideIndex] - strideIndex++ - } - return res - } - } - -} \ No newline at end of file diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/broadcastUtils.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/broadcastUtils.kt index fee62c79c..0b0325a85 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/broadcastUtils.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/broadcastUtils.kt @@ -5,6 +5,8 @@ package space.kscience.kmath.tensors.core.internal +import space.kscience.kmath.misc.UnsafeKMathAPI +import space.kscience.kmath.nd.* import space.kscience.kmath.structures.asBuffer import space.kscience.kmath.tensors.core.DoubleTensor import kotlin.math.max @@ -12,7 +14,7 @@ import kotlin.math.max internal fun multiIndexBroadCasting(tensor: DoubleTensor, resTensor: DoubleTensor, linearSize: Int) { for (linearIndex in 0 until linearSize) { val totalMultiIndex = resTensor.indices.index(linearIndex) - val curMultiIndex = tensor.shape.copyOf() + val curMultiIndex = tensor.shape.toArray() val offset = totalMultiIndex.size - curMultiIndex.size @@ -30,7 +32,7 @@ internal fun multiIndexBroadCasting(tensor: DoubleTensor, resTensor: DoubleTenso } } -internal fun broadcastShapes(vararg shapes: IntArray): IntArray { +internal fun broadcastShapes(shapes: List): ShapeND { var totalDim = 0 for (shape in shapes) { totalDim = max(totalDim, shape.size) @@ -55,15 +57,15 @@ internal fun broadcastShapes(vararg shapes: IntArray): IntArray { } } - return totalShape + return ShapeND(totalShape) } -internal fun broadcastTo(tensor: DoubleTensor, newShape: IntArray): DoubleTensor { +internal fun broadcastTo(tensor: DoubleTensor, newShape: ShapeND): DoubleTensor { require(tensor.shape.size <= newShape.size) { "Tensor is not compatible with the new shape" } - val n = newShape.reduce { acc, i -> acc * i } + val n = newShape.linearSize val resTensor = DoubleTensor(newShape, DoubleArray(n).asBuffer()) for (i in tensor.shape.indices) { @@ -79,8 +81,8 @@ internal fun broadcastTo(tensor: DoubleTensor, newShape: IntArray): DoubleTensor } internal fun broadcastTensors(vararg tensors: DoubleTensor): List { - val totalShape = broadcastShapes(*(tensors.map { it.shape }).toTypedArray()) - val n = totalShape.reduce { acc, i -> acc * i } + val totalShape = broadcastShapes(tensors.map { it.shape }) + val n = totalShape.linearSize return tensors.map { tensor -> val resTensor = DoubleTensor(totalShape, DoubleArray(n).asBuffer()) @@ -100,12 +102,12 @@ internal fun broadcastOuterTensors(vararg tensors: DoubleTensor): List acc * i } + val totalShape = broadcastShapes(tensors.map { it.shape.slice(0..it.shape.size - 3) }) + val n = totalShape.linearSize return buildList { for (tensor in tensors) { - val matrixShape = tensor.shape.sliceArray(tensor.shape.size - 2 until tensor.shape.size).copyOf() + val matrixShape = tensor.shape.slice(tensor.shape.size - 2 until tensor.shape.size) val matrixSize = matrixShape[0] * matrixShape[1] val matrix = DoubleTensor(matrixShape, DoubleArray(matrixSize).asBuffer()) @@ -114,10 +116,11 @@ internal fun broadcastOuterTensors(vararg tensors: DoubleTensor): List 0) { "Illegal empty shape provided" } @@ -21,15 +25,15 @@ internal fun checkEmptyDoubleBuffer(buffer: DoubleArray) = check(buffer.isNotEmp "Illegal empty buffer provided" } -internal fun checkBufferShapeConsistency(shape: IntArray, buffer: DoubleArray) = - check(buffer.size == shape.reduce(Int::times)) { - "Inconsistent shape ${shape.toList()} for buffer of size ${buffer.size} provided" +internal fun checkBufferShapeConsistency(shape: ShapeND, buffer: DoubleArray) = + check(buffer.size == shape.linearSize) { + "Inconsistent shape $shape for buffer of size ${buffer.size} provided" } @PublishedApi internal fun checkShapesCompatible(a: StructureND, b: StructureND): Unit = check(a.shape contentEquals b.shape) { - "Incompatible shapes ${a.shape.toList()} and ${b.shape.toList()} " + "Incompatible shapes ${a.shape} and ${b.shape} " } internal fun checkTranspose(dim: Int, i: Int, j: Int) = @@ -37,10 +41,10 @@ internal fun checkTranspose(dim: Int, i: Int, j: Int) = "Cannot transpose $i to $j for a tensor of dim $dim" } -internal fun checkView(a: Tensor, shape: IntArray) = - check(a.shape.reduce(Int::times) == shape.reduce(Int::times)) +internal fun checkView(a: Tensor, shape: ShapeND) = + check(a.shape.linearSize == shape.linearSize) -internal fun checkSquareMatrix(shape: IntArray) { +internal fun checkSquareMatrix(shape: ShapeND) { val n = shape.size check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n instead" @@ -59,7 +63,7 @@ internal fun DoubleTensorAlgebra.checkSymmetric( internal fun DoubleTensorAlgebra.checkPositiveDefinite(tensor: DoubleTensor, epsilon: Double = 1e-6) { checkSymmetric(tensor, epsilon) for (mat in tensor.matrixSequence()) - check(mat.asDoubleTensor().detLU().value() > 0.0) { - "Tensor contains matrices which are not positive definite ${mat.asDoubleTensor().detLU().value()}" + check(detLU(mat.asDoubleTensor()).value() > 0.0) { + "Tensor contains matrices which are not positive definite ${detLU(mat.asDoubleTensor()).value()}" } } \ No newline at end of file diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/doubleTensorHelpers.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/doubleTensorHelpers.kt index c5910a436..a293c8da3 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/doubleTensorHelpers.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/doubleTensorHelpers.kt @@ -5,17 +5,15 @@ package space.kscience.kmath.tensors.core.internal -import space.kscience.kmath.nd.MutableStructure2D -import space.kscience.kmath.nd.Structure2D -import space.kscience.kmath.nd.as2D -import space.kscience.kmath.nd.get -import space.kscience.kmath.operations.asSequence +import space.kscience.kmath.nd.* import space.kscience.kmath.structures.DoubleBuffer -import space.kscience.kmath.structures.VirtualBuffer import space.kscience.kmath.structures.asBuffer import space.kscience.kmath.structures.indices -import space.kscience.kmath.tensors.core.* import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.eye +import space.kscience.kmath.tensors.core.BufferedTensor +import space.kscience.kmath.tensors.core.DoubleTensor +import space.kscience.kmath.tensors.core.OffsetDoubleBuffer +import space.kscience.kmath.tensors.core.copyToTensor import kotlin.math.abs import kotlin.math.max import kotlin.math.sqrt @@ -41,7 +39,7 @@ internal fun MutableStructure2D.jacobiHelper( source[i * shape[0] + j] = value } - fun maxOffDiagonal(matrix: BufferedTensor): Double { + fun maxOffDiagonal(matrix: DoubleTensor): Double { var maxOffDiagonalElement = 0.0 for (i in 0 until n - 1) { for (j in i + 1 until n) { @@ -51,7 +49,7 @@ internal fun MutableStructure2D.jacobiHelper( return maxOffDiagonalElement } - fun rotate(a: BufferedTensor, s: Double, tau: Double, i: Int, j: Int, k: Int, l: Int) { + fun rotate(a: DoubleTensor, s: Double, tau: Double, i: Int, j: Int, k: Int, l: Int) { val g = a[i, j] val h = a[k, l] a[i, j] = g - s * (h + g * tau) @@ -59,8 +57,8 @@ internal fun MutableStructure2D.jacobiHelper( } fun jacobiIteration( - a: BufferedTensor, - v: BufferedTensor, + a: DoubleTensor, + v: DoubleTensor, d: DoubleBuffer, z: DoubleBuffer, ) { @@ -154,13 +152,13 @@ internal fun List.concat(): DoubleBuffer { return array.asBuffer() } -internal val DoubleTensor.vectors: VirtualBuffer +internal val DoubleTensor.vectors: List get() { val n = shape.size val vectorOffset = shape[n - 1] - val vectorShape = intArrayOf(shape.last()) + val vectorShape = ShapeND(shape.last()) - return VirtualBuffer(linearSize / vectorOffset) { index -> + return List(linearSize / vectorOffset) { index -> val offset = index * vectorOffset DoubleTensor(vectorShape, source.view(offset, vectorShape.first())) } @@ -170,16 +168,16 @@ internal val DoubleTensor.vectors: VirtualBuffer internal fun DoubleTensor.vectorSequence(): Sequence = vectors.asSequence() -internal val DoubleTensor.matrices: VirtualBuffer +internal val DoubleTensor.matrices: List get() { val n = shape.size check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" } val matrixOffset = shape[n - 1] * shape[n - 2] - val matrixShape = intArrayOf(shape[n - 2], shape[n - 1]) + val matrixShape = ShapeND(shape[n - 2], shape[n - 1]) - val size = TensorLinearStructure.linearSizeOf(matrixShape) + val size = matrixShape.linearSize - return VirtualBuffer(linearSize / matrixOffset) { index -> + return List(linearSize / matrixOffset) { index -> val offset = index * matrixOffset DoubleTensor(matrixShape, source.view(offset, size)) } diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/intTensorHelpers.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/intTensorHelpers.kt index db289a090..35f0bf324 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/intTensorHelpers.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/intTensorHelpers.kt @@ -5,6 +5,9 @@ package space.kscience.kmath.tensors.core.internal +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.first +import space.kscience.kmath.nd.last import space.kscience.kmath.operations.asSequence import space.kscience.kmath.structures.IntBuffer import space.kscience.kmath.structures.VirtualBuffer @@ -32,20 +35,19 @@ internal fun List.concat(): IntBuffer { } -internal val IntTensor.vectors: VirtualBuffer - get() { - val n = shape.size - val vectorOffset = shape[n - 1] - val vectorShape = intArrayOf(shape.last()) +internal fun IntTensor.vectors(): VirtualBuffer { + val n = shape.size + val vectorOffset = shape[n - 1] + val vectorShape = shape.last(1) - return VirtualBuffer(linearSize / vectorOffset) { index -> - val offset = index * vectorOffset - IntTensor(vectorShape, source.view(offset, vectorShape.first())) - } + return VirtualBuffer(linearSize / vectorOffset) { index -> + val offset = index * vectorOffset + IntTensor(vectorShape, source.view(offset, vectorShape.first())) } +} -internal fun IntTensor.vectorSequence(): Sequence = vectors.asSequence() +internal fun IntTensor.vectorSequence(): Sequence = vectors().asSequence() internal val IntTensor.matrices: VirtualBuffer @@ -53,7 +55,7 @@ internal val IntTensor.matrices: VirtualBuffer val n = shape.size check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" } val matrixOffset = shape[n - 1] * shape[n - 2] - val matrixShape = intArrayOf(shape[n - 2], shape[n - 1]) + val matrixShape = ShapeND(shape[n - 2], shape[n - 1]) return VirtualBuffer(linearSize / matrixOffset) { index -> val offset = index * matrixOffset diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/linUtils.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/linUtils.kt index 9047ba29e..cf3697e76 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/linUtils.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/linUtils.kt @@ -7,6 +7,7 @@ package space.kscience.kmath.tensors.core.internal import space.kscience.kmath.nd.* import space.kscience.kmath.operations.invoke +import space.kscience.kmath.structures.DoubleBuffer import space.kscience.kmath.structures.IntBuffer import space.kscience.kmath.structures.asBuffer import space.kscience.kmath.structures.indices @@ -94,7 +95,7 @@ internal fun StructureND.setUpPivots(): IntTensor { pivotsShape[n - 2] = m + 1 return IntTensor( - pivotsShape, + ShapeND(pivotsShape), IntBuffer(pivotsShape.reduce(Int::times)) { 0 } ) } @@ -109,7 +110,7 @@ internal fun DoubleTensorAlgebra.computeLU( val pivotsTensor = tensor.setUpPivots() for ((lu, pivots) in luTensor.matrixSequence().zip(pivotsTensor.vectorSequence())) - if (luHelper(lu.as2D(), pivots.as1D(), epsilon)) + if (luHelper(lu.asDoubleTensor2D(), pivots.as1D(), epsilon)) return null return Pair(luTensor, pivotsTensor) @@ -210,23 +211,23 @@ internal fun DoubleTensorAlgebra.qrHelper( ) { checkSquareMatrix(matrix.shape) val n = matrix.shape[0] - val qM = q.as2D() + val qM = q.asDoubleTensor2D() val matrixT = matrix.transposed(0, 1) val qT = q.transposed(0, 1) for (j in 0 until n) { val v = matrixT.getTensor(j) - val vv = v.as1D() + val vv = v.asDoubleBuffer() if (j > 0) { for (i in 0 until j) { r[i, j] = (qT.getTensor(i) dot matrixT.getTensor(j)).value() for (k in 0 until n) { - val qTi = qT.getTensor(i).as1D() + val qTi = qT.getTensor(i).asDoubleBuffer() vv[k] = vv[k] - r[i, j] * qTi[k] } } } - r[j, j] = DoubleTensorAlgebra { (v dot v).sqrt().value() } + r[j, j] = DoubleTensorAlgebra { sqrt((v dot v)).value() } for (i in 0 until n) { qM[i, j] = vv[i] / r[j, j] } @@ -239,17 +240,17 @@ internal fun DoubleTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10) val b: DoubleTensor if (n > m) { b = a.transposed(0, 1).dot(a) - v = DoubleTensor(intArrayOf(m), getRandomUnitVector(m, 0)) + v = DoubleTensor(ShapeND(m), DoubleBuffer.randomUnitVector(m, 0)) } else { b = a.dot(a.transposed(0, 1)) - v = DoubleTensor(intArrayOf(n), getRandomUnitVector(n, 0)) + v = DoubleTensor(ShapeND(n), DoubleBuffer.randomUnitVector(n, 0)) } var lastV: DoubleTensor while (true) { lastV = v v = b.dot(lastV) - val norm = DoubleTensorAlgebra { (v dot v).sqrt().value() } + val norm = DoubleTensorAlgebra { sqrt((v dot v)).value() } v = v.times(1.0 / norm) if (abs(v.dot(lastV).value()) > 1 - epsilon) { return v @@ -274,7 +275,7 @@ internal fun DoubleTensorAlgebra.svdHelper( outerProduct[i * v.shape[0] + j] = u.getTensor(i).value() * v.getTensor(j).value() } } - a = a - singularValue.times(DoubleTensor(intArrayOf(u.shape[0], v.shape[0]), outerProduct.asBuffer())) + a = a - singularValue.times(DoubleTensor(ShapeND(u.shape[0], v.shape[0]), outerProduct.asBuffer())) } var v: DoubleTensor var u: DoubleTensor @@ -282,12 +283,12 @@ internal fun DoubleTensorAlgebra.svdHelper( if (n > m) { v = svd1d(a, epsilon) u = matrix.dot(v) - norm = DoubleTensorAlgebra { (u dot u).sqrt().value() } + norm = DoubleTensorAlgebra { sqrt((u dot u)).value() } u = u.times(1.0 / norm) } else { u = svd1d(a, epsilon) v = matrix.transposed(0, 1).dot(u) - norm = DoubleTensorAlgebra { (v dot v).sqrt().value() } + norm = DoubleTensorAlgebra { sqrt((v dot v)).value() } v = v.times(1.0 / norm) } diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/utils.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/utils.kt index daafdaa58..91fcc90ee 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/utils.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/utils.kt @@ -5,24 +5,25 @@ package space.kscience.kmath.tensors.core.internal -import space.kscience.kmath.nd.as1D +import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.nd.asList +import space.kscience.kmath.nd.last import space.kscience.kmath.operations.DoubleBufferOps.Companion.map -import space.kscience.kmath.operations.toMutableList +import space.kscience.kmath.random.RandomGenerator import space.kscience.kmath.samplers.GaussianSampler -import space.kscience.kmath.stat.RandomGenerator import space.kscience.kmath.structures.DoubleBuffer import space.kscience.kmath.tensors.core.BufferedTensor import space.kscience.kmath.tensors.core.DoubleTensor import kotlin.math.* -internal fun getRandomNormals(n: Int, seed: Long): DoubleBuffer { +internal fun DoubleBuffer.Companion.randomNormals(n: Int, seed: Long): DoubleBuffer { val distribution = GaussianSampler(0.0, 1.0) val generator = RandomGenerator.default(seed) return distribution.sample(generator).nextBufferBlocking(n) } -internal fun getRandomUnitVector(n: Int, seed: Long): DoubleBuffer { - val unnorm: DoubleBuffer = getRandomNormals(n, seed) +internal fun DoubleBuffer.Companion.randomUnitVector(n: Int, seed: Long): DoubleBuffer { + val unnorm: DoubleBuffer = randomNormals(n, seed) val norm = sqrt(unnorm.array.sumOf { it * it }) return unnorm.map { it / norm } } @@ -67,7 +68,8 @@ internal fun format(value: Double, digits: Int = 4): String = buildString { repeat(fLength - res.length) { append(' ') } } -internal fun DoubleTensor.toPrettyString(): String = buildString { +@OptIn(PerformancePitfall::class) +public fun DoubleTensor.toPrettyString(): String = buildString { var offset = 0 val shape = this@toPrettyString.shape val linearStructure = this@toPrettyString.indices @@ -85,14 +87,14 @@ internal fun DoubleTensor.toPrettyString(): String = buildString { charOffset += 1 } - val values = vector.as1D().toMutableList().map(::format) + val values = vector.elements().map { format(it.second) } values.joinTo(this, separator = ", ") append(']') charOffset -= 1 - index.reversed().zip(shape.reversed()).drop(1).forEach { (ind, maxInd) -> + index.reversed().zip(shape.asList().reversed()).drop(1).forEach { (ind, maxInd) -> if (ind != maxInd - 1) { return@forEach } @@ -101,7 +103,7 @@ internal fun DoubleTensor.toPrettyString(): String = buildString { } offset += vectorSize - if (this@toPrettyString.linearSize == offset) { + if (this@toPrettyString.indices.linearSize == offset) { break } diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt index 619d5c753..1733c1a7e 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt @@ -8,15 +8,15 @@ package space.kscience.kmath.tensors.core import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.Shape +import space.kscience.kmath.nd.ShapeND import kotlin.jvm.JvmName @JvmName("varArgOne") -public fun DoubleTensorAlgebra.one(vararg shape: Int): DoubleTensor = ones(intArrayOf(*shape)) +public fun DoubleTensorAlgebra.one(vararg shape: Int): DoubleTensor = ones(ShapeND(shape)) -public fun DoubleTensorAlgebra.one(shape: Shape): DoubleTensor = ones(shape) +public fun DoubleTensorAlgebra.one(shape: ShapeND): DoubleTensor = ones(shape) @JvmName("varArgZero") -public fun DoubleTensorAlgebra.zero(vararg shape: Int): DoubleTensor = zeros(intArrayOf(*shape)) +public fun DoubleTensorAlgebra.zero(vararg shape: Int): DoubleTensor = zeros(ShapeND(shape)) -public fun DoubleTensorAlgebra.zero(shape: Shape): DoubleTensor = zeros(shape) +public fun DoubleTensorAlgebra.zero(shape: ShapeND): DoubleTensor = zeros(shape) diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorOps.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorOps.kt new file mode 100644 index 000000000..e5dc55f68 --- /dev/null +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorOps.kt @@ -0,0 +1,370 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.tensors.core + +import space.kscience.kmath.nd.* +import space.kscience.kmath.operations.covariance +import space.kscience.kmath.structures.Buffer +import space.kscience.kmath.structures.DoubleBuffer +import space.kscience.kmath.tensors.api.Tensor +import space.kscience.kmath.tensors.core.internal.* +import kotlin.math.min +import kotlin.math.sign + + +/** + * Returns a tensor of random numbers drawn from normal distributions with `0.0` mean and `1.0` standard deviation. + * + * @param shape the desired shape for the output tensor. + * @param seed the random seed of the pseudo-random number generator. + * @return tensor of a given shape filled with numbers from the normal distribution + * with `0.0` mean and `1.0` standard deviation. + */ +public fun DoubleTensorAlgebra.randomNormal(shape: ShapeND, seed: Long = 0): DoubleTensor = + fromBuffer(shape, DoubleBuffer.randomNormals(shape.linearSize, seed)) + +/** + * Returns a tensor with the same shape as `input` of random numbers drawn from normal distributions + * with `0.0` mean and `1.0` standard deviation. + * + * @receiver the `input`. + * @param seed the random seed of the pseudo-random number generator. + * @return a tensor with the same shape as `input` filled with numbers from the normal distribution + * with `0.0` mean and `1.0` standard deviation. + */ +public fun DoubleTensorAlgebra.randomNormalLike(structure: WithShape, seed: Long = 0): DoubleTensor = + DoubleTensor(structure.shape, DoubleBuffer.randomNormals(structure.shape.linearSize, seed)) + +/** + * Concatenates a sequence of tensors with equal shapes along the first dimension. + * + * @param tensors the [List] of tensors with same shapes to concatenate + * @return tensor with concatenation result + */ +public fun stack(tensors: List>): DoubleTensor { + check(tensors.isNotEmpty()) { "List must have at least 1 element" } + val shape = tensors[0].shape + check(tensors.all { it.shape contentEquals shape }) { "Tensors must have same shapes" } + val resShape = ShapeND(tensors.size) + shape +// val resBuffer: List = tensors.flatMap { +// it.asDoubleTensor().source.array.drop(it.asDoubleTensor().bufferStart) +// .take(it.asDoubleTensor().linearSize) +// } + val resBuffer = tensors.map { it.asDoubleTensor().source }.concat() + return DoubleTensor(resShape, resBuffer) +} + +/** + * Computes the LU factorization of a matrix or batches of matrices `input`. + * Returns a tuple containing the LU factorization and pivots of `input`. + * + * @param epsilon permissible error when comparing the determinant of a matrix with zero default is 1e-9 + * @return pair of `factorization` and `pivots`. + * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor. + * The `pivots` has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows. + */ +public fun DoubleTensorAlgebra.luFactor( + structureND: StructureND, + epsilon: Double = 1e-9, +): Pair = + computeLU(structureND, epsilon) + ?: throw IllegalArgumentException("Tensor contains matrices which are singular at precision $epsilon") + + +/** + * Unpacks the data and pivots from a LU factorization of a tensor. + * Given a tensor [luTensor], return tensors `Triple(P, L, U)` satisfying `P dot luTensor = L dot U`, + * with `P` being a permutation matrix or batch of matrices, + * `L` being a lower triangular matrix or batch of matrices, + * `U` being an upper triangular matrix or batch of matrices. + * + * @param luTensor the packed LU factorization data + * @param pivotsTensor the packed LU factorization pivots + * @return triple of `P`, `L` and `U` tensors + */ +public fun DoubleTensorAlgebra.luPivot( + luTensor: StructureND, + pivotsTensor: Tensor, +): Triple { + checkSquareMatrix(luTensor.shape) + check( + luTensor.shape.first(luTensor.shape.size - 2) contentEquals pivotsTensor.shape.first(pivotsTensor.shape.size - 1) || + luTensor.shape.last() == pivotsTensor.shape.last() - 1 + ) { "Inappropriate shapes of input tensors" } + + val n = luTensor.shape.last() + val pTensor = zeroesLike(luTensor) + pTensor + .matrixSequence() + .zip(pivotsTensor.asIntTensor().vectorSequence()) + .forEach { (p, pivot) -> pivInit(p.asDoubleTensor2D(), pivot.as1D(), n) } + + val lTensor = zeroesLike(luTensor) + val uTensor = zeroesLike(luTensor) + + lTensor.matrixSequence() + .zip(uTensor.matrixSequence()) + .zip(luTensor.asDoubleTensor().matrixSequence()) + .forEach { (pairLU, lu) -> + val (l, u) = pairLU + luPivotHelper(l.asDoubleTensor2D(), u.asDoubleTensor2D(), lu.asDoubleTensor2D(), n) + } + + return Triple(pTensor, lTensor, uTensor) +} + + +/** + * LUP decomposition. + * + * Computes the LUP decomposition of a matrix or a batch of matrices. + * Given a tensor `input`, return tensors `Triple(P, L, U)` satisfying `P dot input == L dot U`, + * with `P` being a permutation matrix or batch of matrices, + * `L` being a lower triangular matrix or batch of matrices, + * `U` being an upper triangular matrix or batch of matrices. + * + * @param epsilon permissible error when comparing the determinant of a matrix with zero. + * @return triple of `P`, `L` and `U` tensors. + */ +public fun DoubleTensorAlgebra.lu( + structureND: StructureND, + epsilon: Double = 1e-9, +): Triple { + val (lu, pivots) = luFactor(structureND, epsilon) + return luPivot(lu, pivots) +} + + +/** + * QR decomposition. + * + * Computes the QR decomposition of a matrix or a batch of matrices, and returns a pair `Q to R` of tensors. + * Given a tensor `input`, return tensors `Q to R` satisfying `input == Q dot R`, + * with `Q` being an orthogonal matrix or batch of orthogonal matrices + * and `R` being an upper triangular matrix or batch of upper triangular matrices. + * + * @receiver the `input`. + * @param epsilon the permissible error when comparing tensors for equality. The default is 1e-6 + * Used when checking the positive definiteness of the input matrix or matrices. + * @return a pair of `Q` and `R` tensors. + */ +public fun DoubleTensorAlgebra.cholesky(structureND: StructureND, epsilon: Double = 1e-6): DoubleTensor { + checkSquareMatrix(structureND.shape) + checkPositiveDefinite(structureND.asDoubleTensor(), epsilon) + + val n = structureND.shape.last() + val lTensor = zeroesLike(structureND) + + for ((a, l) in structureND.asDoubleTensor().matrixSequence().zip(lTensor.matrixSequence())) + for (i in 0 until n) choleskyHelper(a.asDoubleTensor2D(), l.asDoubleTensor2D(), n) + + return lTensor +} + + +/** + * Singular Value Decomposition. + * + * Computes the singular value decomposition of either a matrix or batch of matrices `input`. + * The singular value decomposition is represented as a triple `Triple(U, S, V)`, + * such that `input == U dot diagonalEmbedding(S) dot V.transpose()`. + * If `input` is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as `input. + * + * @receiver the `input`. + * @param epsilon permissible error when calculating the dot product of vectors + * i.e., the precision with which the cosine approaches 1 in an iterative algorithm. + * @return a triple `Triple(U, S, V)`. + */ +public fun DoubleTensorAlgebra.svd( + structureND: StructureND, + epsilon: Double, +): Triple, StructureND, StructureND> { + val size = structureND.dimension + val commonShape = structureND.shape.slice(0 until size - 2) + val (n, m) = structureND.shape.slice(size - 2 until size) + val uTensor = zeros(commonShape + ShapeND(min(n, m), n)) + val sTensor = zeros(commonShape + ShapeND(min(n, m))) + val vTensor = zeros(commonShape + ShapeND(min(n, m), m)) + + val matrices = structureND.asDoubleTensor().matrices + val uTensors = uTensor.matrices + val sTensorVectors = sTensor.vectors + val vTensors = vTensor.matrices + + for (index in matrices.indices) { + val matrix = matrices[index] + val usv = Triple( + uTensors[index], + sTensorVectors[index], + vTensors[index] + ) + val matrixSize = matrix.shape.linearSize + val curMatrix = DoubleTensor( + matrix.shape, + matrix.source.view(0, matrixSize) + ) + svdHelper(curMatrix, usv, m, n, epsilon) + } + + return Triple(uTensor.transposed(), sTensor, vTensor.transposed()) +} + +/** + * Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices, + * represented by a pair `eigenvalues to eigenvectors`. + * + * @param epsilon the permissible error when comparing tensors for equality + * and when the cosine approaches 1 in the SVD algorithm. + * @return a pair `eigenvalues to eigenvectors`. + */ +public fun DoubleTensorAlgebra.symEigSvd( + structureND: StructureND, + epsilon: Double, +): Pair> { + //TODO optimize conversion + checkSymmetric(structureND.asDoubleTensor(), epsilon) + + fun MutableStructure2D.cleanSym(n: Int) { + for (i in 0 until n) { + for (j in 0 until n) { + if (i == j) { + this[i, j] = sign(this[i, j]) + } else { + this[i, j] = 0.0 + } + } + } + } + + val (u, s, v) = svd(structureND, epsilon) + val shp = s.shape + intArrayOf(1) + val utv = u.transposed() matmul v + val n = s.shape.last() + for (matrix in utv.matrixSequence()) { + matrix.asDoubleTensor2D().cleanSym(n) + } + + val eig = (utv dot s.asDoubleTensor().view(shp)).view(s.shape) + return eig to v +} + +public fun DoubleTensorAlgebra.symEigJacobi( + structureND: StructureND, + maxIteration: Int, + epsilon: Double, +): Pair { + //TODO optimize conversion + checkSymmetric(structureND.asDoubleTensor(), epsilon) + + val size = structureND.dimension + val eigenvectors = zeros(structureND.shape) + val eigenvalues = zeros(structureND.shape.slice(0 until size - 1)) + + var eigenvalueStart = 0 + var eigenvectorStart = 0 + for (matrix in structureND.asDoubleTensor().matrixSequence()) { + val matrix2D = matrix.asDoubleTensor2D() + val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon) + + for (i in 0 until matrix2D.rowNum) { + for (j in 0 until matrix2D.colNum) { + eigenvectors.source[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j] + } + } + + for (i in 0 until matrix2D.rowNum) { + eigenvalues.source[eigenvalueStart + i] = d[i] + } + + eigenvalueStart += structureND.shape.last() + eigenvectorStart += structureND.shape.last() * structureND.shape.last() + } + + return eigenvalues to eigenvectors +} + +/** + * Computes the determinant of a square matrix input, or of each square matrix in a batched input + * using LU factorization algorithm. + * + * @param epsilon the error in the LU algorithm—permissible error when comparing the determinant of a matrix + * with zero. + * @return the determinant. + */ +public fun DoubleTensorAlgebra.detLU(structureND: StructureND, epsilon: Double = 1e-9): DoubleTensor { + checkSquareMatrix(structureND.shape) + //TODO check for unnecessary copies + val luTensor = structureND.copyToTensor() + val pivotsTensor = structureND.setUpPivots() + + val n = structureND.shape.size + + val detTensorShape = ShapeND(IntArray(n - 1) { i -> structureND.shape[i] }.apply { + set(n - 2, 1) + }) + + val resBuffer = DoubleBuffer(detTensorShape.linearSize) { 0.0 } + + val detTensor = DoubleTensor( + detTensorShape, + resBuffer + ) + + luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).forEachIndexed { index, (lu, pivots) -> + resBuffer[index] = if (luHelper(lu.asDoubleTensor2D(), pivots.as1D(), epsilon)) + 0.0 else luMatrixDet(lu.asDoubleTensor2D(), pivots.as1D()) + } + + return detTensor +} + +/** + * Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input + * using LU factorization algorithm. + * Given a square matrix `a`, return the matrix `aInv` satisfying + * `a dot aInv == aInv dot a == eye(a.shape[0])`. + * + * @param epsilon error in the LU algorithm—permissible error when comparing the determinant of a matrix with zero + * @return the multiplicative inverse of a matrix. + */ +public fun DoubleTensorAlgebra.invLU(structureND: StructureND, epsilon: Double = 1e-9): DoubleTensor { + val (luTensor, pivotsTensor) = luFactor(structureND, epsilon) + val invTensor = zeroesLike(luTensor) + + //TODO replace sequence with a cycle + val seq = luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence()) + for ((luP, invMatrix) in seq) { + val (lu, pivots) = luP + luMatrixInv(lu.asDoubleTensor2D(), pivots.as1D(), invMatrix.asDoubleTensor2D()) + } + + return invTensor +} + +/** + * Returns the covariance matrix `M` of given vectors. + * + * `M[i, j]` contains covariance of `i`-th and `j`-th given vectors + * + * @param vectors the [List] of 1-dimensional tensors with same shape + * @return `M`. + */ +public fun DoubleTensorAlgebra.covariance(vectors: List>): DoubleTensor { + check(vectors.isNotEmpty()) { "List must have at least 1 element" } + val n = vectors.size + val m = vectors[0].size + check(vectors.all { it.size == m }) { "Vectors must have same shapes" } + val resTensor = DoubleTensor( + ShapeND(n, n), + DoubleBuffer(n * n) { 0.0 } + ) + for (i in 0 until n) { + for (j in 0 until n) { + resTensor[intArrayOf(i, j)] = bufferAlgebra.covariance(vectors[i], vectors[j]) + } + } + return resTensor +} \ No newline at end of file diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorTransform.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorTransform.kt index 118624440..3b0d15400 100644 --- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorTransform.kt +++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorTransform.kt @@ -5,8 +5,7 @@ package space.kscience.kmath.tensors.core -import space.kscience.kmath.nd.DoubleBufferND -import space.kscience.kmath.nd.StructureND +import space.kscience.kmath.nd.* import space.kscience.kmath.structures.DoubleBuffer import space.kscience.kmath.structures.asBuffer import space.kscience.kmath.tensors.api.Tensor @@ -17,12 +16,12 @@ import space.kscience.kmath.tensors.api.Tensor */ public fun StructureND.copyToTensor(): DoubleTensor = if (this is DoubleTensor) { DoubleTensor(shape, source.copy()) -} else if (this is DoubleBufferND && indices is TensorLinearStructure) { +} else if (this is DoubleBufferND && indices is RowStrides) { DoubleTensor(shape, buffer.copy()) } else { DoubleTensor( shape, - TensorLinearStructure(this.shape).map(this::get).toDoubleArray().asBuffer(), + RowStrides(this.shape).map(this::getDouble).toDoubleArray().asBuffer(), ) } @@ -35,7 +34,7 @@ public fun StructureND.toDoubleTensor(): DoubleTensor { } else { val tensor = DoubleTensorAlgebra.zeroesLike(this) indices.forEach { - tensor[it] = get(it).toDouble() + tensor[it] = getInt(it).toDouble() } return tensor } @@ -46,7 +45,7 @@ public fun StructureND.toDoubleTensor(): DoubleTensor { */ public fun StructureND.asDoubleTensor(): DoubleTensor = if (this is DoubleTensor) { this -} else if (this is DoubleBufferND && indices is TensorLinearStructure) { +} else if (this is DoubleBufferND && indices is RowStrides) { DoubleTensor(shape, buffer) } else { copyToTensor() @@ -58,7 +57,7 @@ public fun StructureND.asDoubleTensor(): DoubleTensor = if (this is Doub public fun StructureND.asIntTensor(): IntTensor = when (this) { is IntTensor -> this else -> IntTensor( - this.shape, - TensorLinearStructure(this.shape).map(this::get).toIntArray().asBuffer() + shape, + RowStrides(shape).map(this::getInt).toIntArray().asBuffer() ) } \ No newline at end of file diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt index 6a99b9ba8..73aed8a7b 100644 --- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt +++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt @@ -5,6 +5,8 @@ package space.kscience.kmath.tensors.core +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.contentEquals import space.kscience.kmath.operations.invoke import space.kscience.kmath.tensors.core.internal.broadcastOuterTensors import space.kscience.kmath.tensors.core.internal.broadcastShapes @@ -19,38 +21,38 @@ internal class TestBroadcasting { fun testBroadcastShapes() = DoubleTensorAlgebra { assertTrue( broadcastShapes( - intArrayOf(2, 3), intArrayOf(1, 3), intArrayOf(1, 1, 1) - ) contentEquals intArrayOf(1, 2, 3) + listOf(ShapeND(2, 3), ShapeND(1, 3), ShapeND(1, 1, 1)) + ) contentEquals ShapeND(1, 2, 3) ) assertTrue( broadcastShapes( - intArrayOf(6, 7), intArrayOf(5, 6, 1), intArrayOf(7), intArrayOf(5, 1, 7) - ) contentEquals intArrayOf(5, 6, 7) + listOf(ShapeND(6, 7), ShapeND(5, 6, 1), ShapeND(7), ShapeND(5, 1, 7)) + ) contentEquals ShapeND(5, 6, 7) ) } @Test fun testBroadcastTo() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) + val tensor1 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) val res = broadcastTo(tensor2, tensor1.shape) - assertTrue(res.shape contentEquals intArrayOf(2, 3)) + assertTrue(res.shape contentEquals ShapeND(2, 3)) assertTrue(res.source contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0)) } @Test fun testBroadcastTensors() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) - val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0)) + val tensor1 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) + val tensor3 = fromArray(ShapeND(1, 1, 1), doubleArrayOf(500.0)) val res = broadcastTensors(tensor1, tensor2, tensor3) - assertTrue(res[0].shape contentEquals intArrayOf(1, 2, 3)) - assertTrue(res[1].shape contentEquals intArrayOf(1, 2, 3)) - assertTrue(res[2].shape contentEquals intArrayOf(1, 2, 3)) + assertTrue(res[0].shape contentEquals ShapeND(1, 2, 3)) + assertTrue(res[1].shape contentEquals ShapeND(1, 2, 3)) + assertTrue(res[2].shape contentEquals ShapeND(1, 2, 3)) assertTrue(res[0].source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) assertTrue(res[1].source contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0)) @@ -59,15 +61,15 @@ internal class TestBroadcasting { @Test fun testBroadcastOuterTensors() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) - val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0)) + val tensor1 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) + val tensor3 = fromArray(ShapeND(1, 1, 1), doubleArrayOf(500.0)) val res = broadcastOuterTensors(tensor1, tensor2, tensor3) - assertTrue(res[0].shape contentEquals intArrayOf(1, 2, 3)) - assertTrue(res[1].shape contentEquals intArrayOf(1, 1, 3)) - assertTrue(res[2].shape contentEquals intArrayOf(1, 1, 1)) + assertTrue(res[0].shape contentEquals ShapeND(1, 2, 3)) + assertTrue(res[1].shape contentEquals ShapeND(1, 1, 3)) + assertTrue(res[2].shape contentEquals ShapeND(1, 1, 1)) assertTrue(res[0].source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) assertTrue(res[1].source contentEquals doubleArrayOf(10.0, 20.0, 30.0)) @@ -76,37 +78,37 @@ internal class TestBroadcasting { @Test fun testBroadcastOuterTensorsShapes() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(2, 1, 3, 2, 3), DoubleArray(2 * 1 * 3 * 2 * 3) { 0.0 }) - val tensor2 = fromArray(intArrayOf(4, 2, 5, 1, 3, 3), DoubleArray(4 * 2 * 5 * 1 * 3 * 3) { 0.0 }) - val tensor3 = fromArray(intArrayOf(1, 1), doubleArrayOf(500.0)) + val tensor1 = fromArray(ShapeND(2, 1, 3, 2, 3), DoubleArray(2 * 1 * 3 * 2 * 3) { 0.0 }) + val tensor2 = fromArray(ShapeND(4, 2, 5, 1, 3, 3), DoubleArray(4 * 2 * 5 * 1 * 3 * 3) { 0.0 }) + val tensor3 = fromArray(ShapeND(1, 1), doubleArrayOf(500.0)) val res = broadcastOuterTensors(tensor1, tensor2, tensor3) - assertTrue(res[0].shape contentEquals intArrayOf(4, 2, 5, 3, 2, 3)) - assertTrue(res[1].shape contentEquals intArrayOf(4, 2, 5, 3, 3, 3)) - assertTrue(res[2].shape contentEquals intArrayOf(4, 2, 5, 3, 1, 1)) + assertTrue(res[0].shape contentEquals ShapeND(4, 2, 5, 3, 2, 3)) + assertTrue(res[1].shape contentEquals ShapeND(4, 2, 5, 3, 3, 3)) + assertTrue(res[2].shape contentEquals ShapeND(4, 2, 5, 3, 1, 1)) } @Test fun testMinusTensor() = BroadcastDoubleTensorAlgebra.invoke { - val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) - val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0)) + val tensor1 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(1, 3), doubleArrayOf(10.0, 20.0, 30.0)) + val tensor3 = fromArray(ShapeND(1, 1, 1), doubleArrayOf(500.0)) val tensor21 = tensor2 - tensor1 val tensor31 = tensor3 - tensor1 val tensor32 = tensor3 - tensor2 - assertTrue(tensor21.shape contentEquals intArrayOf(2, 3)) + assertTrue(tensor21.shape contentEquals ShapeND(2, 3)) assertTrue(tensor21.source contentEquals doubleArrayOf(9.0, 18.0, 27.0, 6.0, 15.0, 24.0)) - assertTrue(tensor31.shape contentEquals intArrayOf(1, 2, 3)) + assertTrue(tensor31.shape contentEquals ShapeND(1, 2, 3)) assertTrue( tensor31.source contentEquals doubleArrayOf(499.0, 498.0, 497.0, 496.0, 495.0, 494.0) ) - assertTrue(tensor32.shape contentEquals intArrayOf(1, 1, 3)) + assertTrue(tensor32.shape contentEquals ShapeND(1, 1, 3)) assertTrue(tensor32.source contentEquals doubleArrayOf(490.0, 480.0, 470.0)) } diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleAnalyticTensorAlgebra.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleAnalyticTensorAlgebra.kt index 4bc2e3bdb..e4c2c40ea 100644 --- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleAnalyticTensorAlgebra.kt +++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleAnalyticTensorAlgebra.kt @@ -5,6 +5,7 @@ package space.kscience.kmath.tensors.core +import space.kscience.kmath.nd.ShapeND import space.kscience.kmath.operations.invoke import space.kscience.kmath.structures.asBuffer import kotlin.math.* @@ -13,7 +14,7 @@ import kotlin.test.assertTrue internal class TestDoubleAnalyticTensorAlgebra { - val shape = intArrayOf(2, 1, 3, 2) + val shape = ShapeND(2, 1, 3, 2) val buffer = doubleArrayOf( 27.1, 20.0, 19.84, 23.123, 3.0, 2.0, @@ -33,76 +34,76 @@ internal class TestDoubleAnalyticTensorAlgebra { @Test fun testExp() = DoubleTensorAlgebra { - assertTrue { tensor.exp() eq expectedTensor(::exp) } + assertTrue { exp(tensor) eq expectedTensor(::exp) } } @Test fun testLog() = DoubleTensorAlgebra { - assertTrue { tensor.ln() eq expectedTensor(::ln) } + assertTrue { ln(tensor) eq expectedTensor(::ln) } } @Test fun testSqrt() = DoubleTensorAlgebra { - assertTrue { tensor.sqrt() eq expectedTensor(::sqrt) } + assertTrue { sqrt(tensor) eq expectedTensor(::sqrt) } } @Test fun testCos() = DoubleTensorAlgebra { - assertTrue { tensor.cos() eq expectedTensor(::cos) } + assertTrue { cos(tensor) eq expectedTensor(::cos) } } @Test fun testCosh() = DoubleTensorAlgebra { - assertTrue { tensor.cosh() eq expectedTensor(::cosh) } + assertTrue { cosh(tensor) eq expectedTensor(::cosh) } } @Test fun testAcosh() = DoubleTensorAlgebra { - assertTrue { tensor.acosh() eq expectedTensor(::acosh) } + assertTrue { acosh(tensor) eq expectedTensor(::acosh) } } @Test fun testSin() = DoubleTensorAlgebra { - assertTrue { tensor.sin() eq expectedTensor(::sin) } + assertTrue { sin(tensor) eq expectedTensor(::sin) } } @Test fun testSinh() = DoubleTensorAlgebra { - assertTrue { tensor.sinh() eq expectedTensor(::sinh) } + assertTrue { sinh(tensor) eq expectedTensor(::sinh) } } @Test fun testAsinh() = DoubleTensorAlgebra { - assertTrue { tensor.asinh() eq expectedTensor(::asinh) } + assertTrue { asinh(tensor) eq expectedTensor(::asinh) } } @Test fun testTan() = DoubleTensorAlgebra { - assertTrue { tensor.tan() eq expectedTensor(::tan) } + assertTrue { tan(tensor) eq expectedTensor(::tan) } } @Test fun testAtan() = DoubleTensorAlgebra { - assertTrue { tensor.atan() eq expectedTensor(::atan) } + assertTrue { atan(tensor) eq expectedTensor(::atan) } } @Test fun testTanh() = DoubleTensorAlgebra { - assertTrue { tensor.tanh() eq expectedTensor(::tanh) } + assertTrue { tanh(tensor) eq expectedTensor(::tanh) } } @Test fun testCeil() = DoubleTensorAlgebra { - assertTrue { tensor.ceil() eq expectedTensor(::ceil) } + assertTrue { ceil(tensor) eq expectedTensor(::ceil) } } @Test fun testFloor() = DoubleTensorAlgebra { - assertTrue { tensor.floor() eq expectedTensor(::floor) } + assertTrue { floor(tensor) eq expectedTensor(::floor) } } - val shape2 = intArrayOf(2, 2) + val shape2 = ShapeND(2, 2) val buffer2 = doubleArrayOf( 1.0, 2.0, -3.0, 4.0 @@ -114,13 +115,13 @@ internal class TestDoubleAnalyticTensorAlgebra { assertTrue { tensor2.min() == -3.0 } assertTrue { tensor2.min(0, true) eq fromArray( - intArrayOf(1, 2), + ShapeND(1, 2), doubleArrayOf(-3.0, 2.0) ) } assertTrue { tensor2.min(1, false) eq fromArray( - intArrayOf(2), + ShapeND(2), doubleArrayOf(1.0, -3.0) ) } @@ -131,13 +132,13 @@ internal class TestDoubleAnalyticTensorAlgebra { assertTrue { tensor2.max() == 4.0 } assertTrue { tensor2.max(0, true) eq fromArray( - intArrayOf(1, 2), + ShapeND(1, 2), doubleArrayOf(1.0, 4.0) ) } assertTrue { tensor2.max(1, false) eq fromArray( - intArrayOf(2), + ShapeND(2), doubleArrayOf(2.0, 4.0) ) } @@ -148,13 +149,13 @@ internal class TestDoubleAnalyticTensorAlgebra { assertTrue { tensor2.sum() == 4.0 } assertTrue { tensor2.sum(0, true) eq fromArray( - intArrayOf(1, 2), + ShapeND(1, 2), doubleArrayOf(-2.0, 6.0) ) } assertTrue { tensor2.sum(1, false) eq fromArray( - intArrayOf(2), + ShapeND(2), doubleArrayOf(3.0, 1.0) ) } @@ -162,16 +163,16 @@ internal class TestDoubleAnalyticTensorAlgebra { @Test fun testMean() = DoubleTensorAlgebra { - assertTrue { tensor2.mean() == 1.0 } + assertTrue { mean(tensor2) == 1.0 } assertTrue { - tensor2.mean(0, true) eq fromArray( - intArrayOf(1, 2), + mean(tensor2, 0, true) eq fromArray( + ShapeND(1, 2), doubleArrayOf(-1.0, 3.0) ) } assertTrue { - tensor2.mean(1, false) eq fromArray( - intArrayOf(2), + mean(tensor2, 1, false) eq fromArray( + ShapeND(2), doubleArrayOf(1.5, 0.5) ) } diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt index 1c23cff18..cbd7b9887 100644 --- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt +++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt @@ -5,6 +5,8 @@ package space.kscience.kmath.tensors.core +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.contentEquals import space.kscience.kmath.operations.invoke import space.kscience.kmath.tensors.core.internal.svd1d import kotlin.math.abs @@ -17,7 +19,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { @Test fun testDetLU() = DoubleTensorAlgebra { val tensor = fromArray( - intArrayOf(2, 2, 2), + ShapeND(2, 2, 2), doubleArrayOf( 1.0, 3.0, 1.0, 2.0, @@ -27,13 +29,13 @@ internal class TestDoubleLinearOpsTensorAlgebra { ) val expectedTensor = fromArray( - intArrayOf(2, 1), + ShapeND(2, 1), doubleArrayOf( -1.0, -7.0 ) ) - val detTensor = tensor.detLU() + val detTensor = detLU(tensor) assertTrue(detTensor.eq(expectedTensor)) @@ -43,7 +45,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { fun testDet() = DoubleTensorAlgebra { val expectedValue = 0.019827417 val m = fromArray( - intArrayOf(3, 3), doubleArrayOf( + ShapeND(3, 3), doubleArrayOf( 2.1843, 1.4391, -0.4845, 1.4391, 1.7772, 0.4055, -0.4845, 0.4055, 0.7519 @@ -57,7 +59,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { fun testDetSingle() = DoubleTensorAlgebra { val expectedValue = 48.151623 val m = fromArray( - intArrayOf(1, 1), doubleArrayOf( + ShapeND(1, 1), doubleArrayOf( expectedValue ) ) @@ -68,7 +70,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { @Test fun testInvLU() = DoubleTensorAlgebra { val tensor = fromArray( - intArrayOf(2, 2, 2), + ShapeND(2, 2, 2), doubleArrayOf( 1.0, 0.0, 0.0, 2.0, @@ -78,7 +80,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { ) val expectedTensor = fromArray( - intArrayOf(2, 2, 2), doubleArrayOf( + ShapeND(2, 2, 2), doubleArrayOf( 1.0, 0.0, 0.0, 0.5, 0.0, 1.0, @@ -86,20 +88,20 @@ internal class TestDoubleLinearOpsTensorAlgebra { ) ) - val invTensor = tensor.invLU() + val invTensor = invLU(tensor) assertTrue(invTensor.eq(expectedTensor)) } @Test fun testScalarProduct() = DoubleTensorAlgebra { - val a = fromArray(intArrayOf(3), doubleArrayOf(1.8, 2.5, 6.8)) - val b = fromArray(intArrayOf(3), doubleArrayOf(5.5, 2.6, 6.4)) + val a = fromArray(ShapeND(3), doubleArrayOf(1.8, 2.5, 6.8)) + val b = fromArray(ShapeND(3), doubleArrayOf(5.5, 2.6, 6.4)) assertEquals(a.dot(b).value(), 59.92) } @Test fun testQR() = DoubleTensorAlgebra { - val shape = intArrayOf(2, 2, 2) + val shape = ShapeND(2, 2, 2) val buffer = doubleArrayOf( 1.0, 3.0, 1.0, 2.0, @@ -109,7 +111,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { val tensor = fromArray(shape, buffer) - val (q, r) = tensor.qr() + val (q, r) = qr(tensor) assertTrue { q.shape contentEquals shape } assertTrue { r.shape contentEquals shape } @@ -120,7 +122,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { @Test fun testLU() = DoubleTensorAlgebra { - val shape = intArrayOf(2, 2, 2) + val shape = ShapeND(2, 2, 2) val buffer = doubleArrayOf( 1.0, 3.0, 1.0, 2.0, @@ -129,7 +131,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { ) val tensor = fromArray(shape, buffer) - val (p, l, u) = tensor.lu() + val (p, l, u) = lu(tensor) assertTrue { p.shape contentEquals shape } assertTrue { l.shape contentEquals shape } @@ -140,45 +142,45 @@ internal class TestDoubleLinearOpsTensorAlgebra { @Test fun testCholesky() = DoubleTensorAlgebra { - val tensor = randomNormal(intArrayOf(2, 5, 5), 0) + val tensor = randomNormal(ShapeND(2, 5, 5), 0) val sigma = (tensor matmul tensor.transposed()) + diagonalEmbedding( - fromArray(intArrayOf(2, 5), DoubleArray(10) { 0.1 }) + fromArray(ShapeND(2, 5), DoubleArray(10) { 0.1 }) ) - val low = sigma.cholesky() + val low = cholesky(sigma) val sigmChol = low matmul low.transposed() assertTrue(sigma.eq(sigmChol)) } @Test fun testSVD1D() = DoubleTensorAlgebra { - val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) val res = svd1d(tensor2) - assertTrue(res.shape contentEquals intArrayOf(2)) + assertTrue(res.shape contentEquals ShapeND(2)) assertTrue { abs(abs(res.source[0]) - 0.386) < 0.01 } assertTrue { abs(abs(res.source[1]) - 0.922) < 0.01 } } @Test fun testSVD() = DoubleTensorAlgebra { - testSVDFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))) - testSVDFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0))) + testSVDFor(fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))) + testSVDFor(fromArray(ShapeND(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0))) } @Test fun testBatchedSVD() = DoubleTensorAlgebra { - val tensor = randomNormal(intArrayOf(2, 5, 3), 0) - val (tensorU, tensorS, tensorV) = tensor.svd() + val tensor = randomNormal(ShapeND(2, 5, 3), 0) + val (tensorU, tensorS, tensorV) = svd(tensor) val tensorSVD = tensorU matmul (diagonalEmbedding(tensorS) matmul tensorV.transposed()) assertTrue(tensor.eq(tensorSVD)) } @Test fun testBatchedSymEig() = DoubleTensorAlgebra { - val tensor = randomNormal(shape = intArrayOf(2, 3, 3), 0) + val tensor = randomNormal(shape = ShapeND(2, 3, 3), 0) val tensorSigma = tensor + tensor.transposed() - val (tensorS, tensorV) = tensorSigma.symEig() + val (tensorS, tensorV) = symEig(tensorSigma) val tensorSigmaCalc = tensorV matmul (diagonalEmbedding(tensorS) matmul tensorV.transposed()) assertTrue(tensorSigma.eq(tensorSigmaCalc)) } @@ -188,7 +190,7 @@ internal class TestDoubleLinearOpsTensorAlgebra { private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor, epsilon: Double = 1e-10) { - val svd = tensor.svd() + val svd = svd(tensor) val tensorSVD = svd.first .dot( diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensor.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensor.kt index c87cf2a68..d01ae124b 100644 --- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensor.kt +++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensor.kt @@ -11,6 +11,7 @@ import space.kscience.kmath.operations.invoke import space.kscience.kmath.structures.DoubleBuffer import space.kscience.kmath.structures.toDoubleArray import space.kscience.kmath.tensors.core.internal.matrixSequence +import space.kscience.kmath.testutils.assertBufferEquals import kotlin.test.Test import kotlin.test.assertEquals import kotlin.test.assertTrue @@ -20,14 +21,14 @@ internal class TestDoubleTensor { @Test fun testValue() = DoubleTensorAlgebra { val value = 12.5 - val tensor = fromArray(intArrayOf(1), doubleArrayOf(value)) + val tensor = fromArray(ShapeND(1), doubleArrayOf(value)) assertEquals(tensor.value(), value) } @OptIn(PerformancePitfall::class) @Test fun testStrides() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(2, 2), doubleArrayOf(3.5, 5.8, 58.4, 2.4)) + val tensor = fromArray(ShapeND(2, 2), doubleArrayOf(3.5, 5.8, 58.4, 2.4)) assertEquals(tensor[intArrayOf(0, 1)], 5.8) assertTrue( tensor.elements().map { it.second }.toList() @@ -37,8 +38,8 @@ internal class TestDoubleTensor { @Test fun testGet() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(1, 2, 2), doubleArrayOf(3.5, 5.8, 58.4, 2.4)) - val matrix = tensor.getTensor(0).as2D() + val tensor = fromArray(ShapeND(1, 2, 2), doubleArrayOf(3.5, 5.8, 58.4, 2.4)) + val matrix = tensor.getTensor(0).asDoubleTensor2D() assertEquals(matrix[0, 1], 5.8) val vector = tensor.getTensor(0, 1).as1D() @@ -52,8 +53,8 @@ internal class TestDoubleTensor { tensor.matrixSequence().forEach { val a = it.asDoubleTensor() - val secondRow = a.getTensor(1).as1D() - val secondColumn = a.transposed(0, 1).getTensor(1).as1D() + val secondRow = a.getTensor(1).asDoubleBuffer() + val secondColumn = a.transposed(0, 1).getTensor(1).asDoubleBuffer() assertEquals(secondColumn[0], 77.89) assertEquals(secondRow[1], secondColumn[1]) } @@ -66,7 +67,7 @@ internal class TestDoubleTensor { val doubleArray = DoubleBuffer(1.0, 2.0, 3.0) // create ND buffers, no data is copied - val ndArray: MutableBufferND = DoubleBufferND(DefaultStrides(intArrayOf(3)), doubleArray) + val ndArray: MutableBufferND = DoubleBufferND(ColumnStrides(ShapeND(3)), doubleArray) // map to tensors val tensorArray = ndArray.asDoubleTensor() // Data is copied because of strides change. @@ -86,6 +87,23 @@ internal class TestDoubleTensor { tensorArray[intArrayOf(0)] = 55.9 assertEquals(ndArray[intArrayOf(0)], 1.0) + } + @Test + fun test2D() = with(DoubleTensorAlgebra) { + val tensor: DoubleTensor = structureND(ShapeND(3, 3)) { (i, j) -> (i - j).toDouble() } + //println(tensor.toPrettyString()) + val tensor2d = tensor.asDoubleTensor2D() + assertBufferEquals(DoubleBuffer(1.0, 0.0, -1.0), tensor2d.rows[1]) + assertBufferEquals(DoubleBuffer(-2.0, -1.0, 0.0), tensor2d.columns[2]) + } + + @Test + fun testMatrixIteration() = with(DoubleTensorAlgebra) { + val tensor = structureND(ShapeND(3, 3, 3, 3)) { index -> index.sum().toDouble() } + tensor.forEachMatrix { index, matrix -> + println(index.joinToString { it.toString() }) + println(matrix) + } } } diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt index 67bebb9a7..cae01bed8 100644 --- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt +++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt @@ -6,6 +6,8 @@ package space.kscience.kmath.tensors.core +import space.kscience.kmath.nd.ShapeND +import space.kscience.kmath.nd.contentEquals import space.kscience.kmath.nd.get import space.kscience.kmath.operations.invoke import space.kscience.kmath.testutils.assertBufferEquals @@ -18,62 +20,62 @@ internal class TestDoubleTensorAlgebra { @Test fun testDoublePlus() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(2), doubleArrayOf(1.0, 2.0)) + val tensor = fromArray(ShapeND(2), doubleArrayOf(1.0, 2.0)) val res = 10.0 + tensor assertTrue(res.source contentEquals doubleArrayOf(11.0, 12.0)) } @Test fun testDoubleDiv() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(2), doubleArrayOf(2.0, 4.0)) + val tensor = fromArray(ShapeND(2), doubleArrayOf(2.0, 4.0)) val res = 2.0 / tensor assertTrue(res.source contentEquals doubleArrayOf(1.0, 0.5)) } @Test fun testDivDouble() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(2), doubleArrayOf(10.0, 5.0)) + val tensor = fromArray(ShapeND(2), doubleArrayOf(10.0, 5.0)) val res = tensor / 2.5 assertTrue(res.source contentEquals doubleArrayOf(4.0, 2.0)) } @Test fun testTranspose1x1() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(1), doubleArrayOf(0.0)) + val tensor = fromArray(ShapeND(1), doubleArrayOf(0.0)) val res = tensor.transposed(0, 0) - assertTrue(res.source contentEquals doubleArrayOf(0.0)) - assertTrue(res.shape contentEquals intArrayOf(1)) + assertTrue(res.asDoubleTensor().source contentEquals doubleArrayOf(0.0)) + assertTrue(res.shape contentEquals ShapeND(1)) } @Test fun testTranspose3x2() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor = fromArray(ShapeND(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) val res = tensor.transposed(1, 0) - assertTrue(res.source contentEquals doubleArrayOf(1.0, 3.0, 5.0, 2.0, 4.0, 6.0)) - assertTrue(res.shape contentEquals intArrayOf(2, 3)) + assertTrue(res.asDoubleTensor().source contentEquals doubleArrayOf(1.0, 3.0, 5.0, 2.0, 4.0, 6.0)) + assertTrue(res.shape contentEquals ShapeND(2, 3)) } @Test fun testTranspose1x2x3() = DoubleTensorAlgebra { - val tensor = fromArray(intArrayOf(1, 2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor = fromArray(ShapeND(1, 2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) val res01 = tensor.transposed(0, 1) val res02 = tensor.transposed(-3, 2) val res12 = tensor.transposed() - assertTrue(res01.shape contentEquals intArrayOf(2, 1, 3)) - assertTrue(res02.shape contentEquals intArrayOf(3, 2, 1)) - assertTrue(res12.shape contentEquals intArrayOf(1, 3, 2)) + assertTrue(res01.shape contentEquals ShapeND(2, 1, 3)) + assertTrue(res02.shape contentEquals ShapeND(3, 2, 1)) + assertTrue(res12.shape contentEquals ShapeND(1, 3, 2)) - assertTrue(res01.source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - assertTrue(res02.source contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0)) - assertTrue(res12.source contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0)) + assertTrue(res01.asDoubleTensor().source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + assertTrue(res02.asDoubleTensor().source contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0)) + assertTrue(res12.asDoubleTensor().source contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0)) } @Test fun testLinearStructure() = DoubleTensorAlgebra { - val shape = intArrayOf(3) + val shape = ShapeND(3) val tensorA = full(value = -4.5, shape = shape) val tensorB = full(value = 10.9, shape = shape) val tensorC = full(value = 789.3, shape = shape) @@ -105,28 +107,28 @@ internal class TestDoubleTensorAlgebra { @Test fun testDot() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor11 = fromArray(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor2 = fromArray(intArrayOf(3), doubleArrayOf(10.0, 20.0, 30.0)) - val tensor3 = fromArray(intArrayOf(1, 1, 3), doubleArrayOf(-1.0, -2.0, -3.0)) - val tensor4 = fromArray(intArrayOf(2, 3, 3), (1..18).map { it.toDouble() }.toDoubleArray()) - val tensor5 = fromArray(intArrayOf(2, 3, 3), (1..18).map { 1 + it.toDouble() }.toDoubleArray()) + val tensor1 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor11 = fromArray(ShapeND(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(3), doubleArrayOf(10.0, 20.0, 30.0)) + val tensor3 = fromArray(ShapeND(1, 1, 3), doubleArrayOf(-1.0, -2.0, -3.0)) + val tensor4 = fromArray(ShapeND(2, 3, 3), (1..18).map { it.toDouble() }.toDoubleArray()) + val tensor5 = fromArray(ShapeND(2, 3, 3), (1..18).map { 1 + it.toDouble() }.toDoubleArray()) val res12 = tensor1.dot(tensor2) assertTrue(res12.source contentEquals doubleArrayOf(140.0, 320.0)) - assertTrue(res12.shape contentEquals intArrayOf(2)) + assertTrue(res12.shape contentEquals ShapeND(2)) val res32 = tensor3.matmul(tensor2) assertTrue(res32.source contentEquals doubleArrayOf(-140.0)) - assertTrue(res32.shape contentEquals intArrayOf(1, 1)) + assertTrue(res32.shape contentEquals ShapeND(1, 1)) val res22 = tensor2.dot(tensor2) assertTrue(res22.source contentEquals doubleArrayOf(1400.0)) - assertTrue(res22.shape contentEquals intArrayOf(1)) + assertTrue(res22.shape contentEquals ShapeND(1)) val res11 = tensor1.dot(tensor11) assertTrue(res11.source contentEquals doubleArrayOf(22.0, 28.0, 49.0, 64.0)) - assertTrue(res11.shape contentEquals intArrayOf(2, 2)) + assertTrue(res11.shape contentEquals ShapeND(2, 2)) val res45 = tensor4.matmul(tensor5) assertTrue( @@ -135,44 +137,44 @@ internal class TestDoubleTensorAlgebra { 468.0, 501.0, 534.0, 594.0, 636.0, 678.0, 720.0, 771.0, 822.0 ) ) - assertTrue(res45.shape contentEquals intArrayOf(2, 3, 3)) + assertTrue(res45.shape contentEquals ShapeND(2, 3, 3)) } @Test fun testDiagonalEmbedding() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(3), doubleArrayOf(10.0, 20.0, 30.0)) - val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor3 = zeros(intArrayOf(2, 3, 4, 5)) + val tensor1 = fromArray(ShapeND(3), doubleArrayOf(10.0, 20.0, 30.0)) + val tensor2 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor3 = zeros(ShapeND(2, 3, 4, 5)) assertTrue( diagonalEmbedding(tensor3, 0, 3, 4).shape contentEquals - intArrayOf(2, 3, 4, 5, 5) + ShapeND(2, 3, 4, 5, 5) ) assertTrue( diagonalEmbedding(tensor3, 1, 3, 4).shape contentEquals - intArrayOf(2, 3, 4, 6, 6) + ShapeND(2, 3, 4, 6, 6) ) assertTrue( diagonalEmbedding(tensor3, 2, 0, 3).shape contentEquals - intArrayOf(7, 2, 3, 7, 4) + ShapeND(7, 2, 3, 7, 4) ) val diagonal1 = diagonalEmbedding(tensor1, 0, 1, 0) - assertTrue(diagonal1.shape contentEquals intArrayOf(3, 3)) + assertTrue(diagonal1.shape contentEquals ShapeND(3, 3)) assertTrue( diagonal1.source contentEquals doubleArrayOf(10.0, 0.0, 0.0, 0.0, 20.0, 0.0, 0.0, 0.0, 30.0) ) val diagonal1Offset = diagonalEmbedding(tensor1, 1, 1, 0) - assertTrue(diagonal1Offset.shape contentEquals intArrayOf(4, 4)) + assertTrue(diagonal1Offset.shape contentEquals ShapeND(4, 4)) assertTrue( diagonal1Offset.source contentEquals doubleArrayOf(0.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0.0, 20.0, 0.0, 0.0, 0.0, 0.0, 30.0, 0.0) ) val diagonal2 = diagonalEmbedding(tensor2, 1, 0, 2) - assertTrue(diagonal2.shape contentEquals intArrayOf(4, 2, 4)) + assertTrue(diagonal2.shape contentEquals ShapeND(4, 2, 4)) assertTrue( diagonal2.source contentEquals doubleArrayOf( @@ -186,9 +188,9 @@ internal class TestDoubleTensorAlgebra { @Test fun testEq() = DoubleTensorAlgebra { - val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) - val tensor3 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 5.0)) + val tensor1 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor2 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)) + val tensor3 = fromArray(ShapeND(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 5.0)) assertTrue(tensor1 eq tensor1) assertTrue(tensor1 eq tensor2) @@ -202,7 +204,7 @@ internal class TestDoubleTensorAlgebra { val l = tensor.getTensor(0).map { it + 1.0 } val r = tensor.getTensor(1).map { it - 1.0 } val res = l + r - assertTrue { intArrayOf(5, 5) contentEquals res.shape } + assertTrue { ShapeND(5, 5) contentEquals res.shape } assertEquals(2.0, res[4, 4]) } } diff --git a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPath.kt b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPath.kt index e90e3de41..1ba9936ee 100644 --- a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPath.kt +++ b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPath.kt @@ -13,74 +13,80 @@ import kotlin.math.acos import kotlin.math.cos import kotlin.math.sin -internal fun Pose2D.getLeftCircle(radius: Double): Circle2D = getTangentCircles(radius).first +internal fun DubinsPose2D.getLeftCircle(radius: Double): Circle2D = getTangentCircles(radius).first -internal fun Pose2D.getRightCircle(radius: Double): Circle2D = getTangentCircles(radius).second +internal fun DubinsPose2D.getRightCircle(radius: Double): Circle2D = getTangentCircles(radius).second -internal fun Pose2D.getTangentCircles(radius: Double): Pair = with(Euclidean2DSpace) { - val dX = radius * cos(theta) - val dY = radius * sin(theta) +internal fun DubinsPose2D.getTangentCircles(radius: Double): Pair = with(Euclidean2DSpace) { + val dX = radius * cos(bearing) + val dY = radius * sin(bearing) return Circle2D(vector(x - dX, y + dY), radius) to Circle2D(vector(x + dX, y - dY), radius) } -internal fun leftOuterTangent(a: Circle2D, b: Circle2D): StraightSegment = outerTangent(a, b, ArcSegment.Direction.LEFT) +internal fun leftOuterTangent(a: Circle2D, b: Circle2D): StraightTrajectory2D = + outerTangent(a, b, CircleTrajectory2D.Direction.LEFT) -internal fun rightOuterTangent(a: Circle2D, b: Circle2D): StraightSegment = outerTangent(a, b, - ArcSegment.Direction.RIGHT +internal fun rightOuterTangent(a: Circle2D, b: Circle2D): StraightTrajectory2D = outerTangent( + a, b, + CircleTrajectory2D.Direction.RIGHT ) -private fun outerTangent(a: Circle2D, b: Circle2D, side: ArcSegment.Direction): StraightSegment = with(Euclidean2DSpace){ - val centers = StraightSegment(a.center, b.center) - val p1 = when (side) { - ArcSegment.Direction.LEFT -> vector( - a.center.x - a.radius * cos(centers.theta), - a.center.y + a.radius * sin(centers.theta) - ) - ArcSegment.Direction.RIGHT -> vector( - a.center.x + a.radius * cos(centers.theta), - a.center.y - a.radius * sin(centers.theta) +private fun outerTangent(a: Circle2D, b: Circle2D, side: CircleTrajectory2D.Direction): StraightTrajectory2D = + with(Euclidean2DSpace) { + val centers = StraightTrajectory2D(a.center, b.center) + val p1 = when (side) { + CircleTrajectory2D.Direction.LEFT -> vector( + a.center.x - a.radius * cos(centers.bearing), + a.center.y + a.radius * sin(centers.bearing) + ) + + CircleTrajectory2D.Direction.RIGHT -> vector( + a.center.x + a.radius * cos(centers.bearing), + a.center.y - a.radius * sin(centers.bearing) + ) + } + return StraightTrajectory2D( + p1, + vector(p1.x + (centers.end.x - centers.start.x), p1.y + (centers.end.y - centers.start.y)) ) } - return StraightSegment( - p1, - vector(p1.x + (centers.end.x - centers.start.x), p1.y + (centers.end.y - centers.start.y)) - ) -} -internal fun leftInnerTangent(base: Circle2D, direction: Circle2D): StraightSegment? = - innerTangent(base, direction, ArcSegment.Direction.LEFT) +internal fun leftInnerTangent(base: Circle2D, direction: Circle2D): StraightTrajectory2D? = + innerTangent(base, direction, CircleTrajectory2D.Direction.LEFT) -internal fun rightInnerTangent(base: Circle2D, direction: Circle2D): StraightSegment? = - innerTangent(base, direction, ArcSegment.Direction.RIGHT) +internal fun rightInnerTangent(base: Circle2D, direction: Circle2D): StraightTrajectory2D? = + innerTangent(base, direction, CircleTrajectory2D.Direction.RIGHT) -private fun innerTangent(base: Circle2D, direction: Circle2D, side: ArcSegment.Direction): StraightSegment? = with(Euclidean2DSpace){ - val centers = StraightSegment(base.center, direction.center) - if (centers.length < base.radius * 2) return null - val angle = theta( - when (side) { - ArcSegment.Direction.LEFT -> centers.theta + acos(base.radius * 2 / centers.length) - ArcSegment.Direction.RIGHT -> centers.theta - acos(base.radius * 2 / centers.length) - } - ) - val dX = base.radius * sin(angle) - val dY = base.radius * cos(angle) - val p1 = vector(base.center.x + dX, base.center.y + dY) - val p2 = vector(direction.center.x - dX, direction.center.y - dY) - return StraightSegment(p1, p2) -} +private fun innerTangent(base: Circle2D, direction: Circle2D, side: CircleTrajectory2D.Direction): StraightTrajectory2D? = + with(Euclidean2DSpace) { + val centers = StraightTrajectory2D(base.center, direction.center) + if (centers.length < base.radius * 2) return null + val angle = theta( + when (side) { + CircleTrajectory2D.Direction.LEFT -> centers.bearing + acos(base.radius * 2 / centers.length) + CircleTrajectory2D.Direction.RIGHT -> centers.bearing - acos(base.radius * 2 / centers.length) + } + ) + val dX = base.radius * sin(angle) + val dY = base.radius * cos(angle) + val p1 = vector(base.center.x + dX, base.center.y + dY) + val p2 = vector(direction.center.x - dX, direction.center.y - dY) + return StraightTrajectory2D(p1, p2) + } internal fun theta(theta: Double): Double = (theta + (2 * PI)) % (2 * PI) +@Suppress("DuplicatedCode") public class DubinsPath( - public val a: ArcSegment, - public val b: Trajectory, - public val c: ArcSegment, -) : CompositeTrajectory(listOf(a,b,c)) { + public val a: CircleTrajectory2D, + public val b: Trajectory2D, + public val c: CircleTrajectory2D, +) : CompositeTrajectory2D(listOf(a, b, c)) { public val type: TYPE = TYPE.valueOf( arrayOf( a.direction.name[0], - if (b is ArcSegment) b.direction.name[0] else 'S', + if (b is CircleTrajectory2D) b.direction.name[0] else 'S', c.direction.name[0] ).toCharArray().concatToString() ) @@ -91,8 +97,8 @@ public class DubinsPath( public companion object { public fun all( - start: Pose2D, - end: Pose2D, + start: DubinsPose2D, + end: DubinsPose2D, turningRadius: Double, ): List = listOfNotNull( rlr(start, end, turningRadius), @@ -103,90 +109,132 @@ public class DubinsPath( lsr(start, end, turningRadius) ) - public fun shortest(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath = + public fun shortest(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath = all(start, end, turningRadius).minBy { it.length } - public fun rlr(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? = with(Euclidean2DSpace){ + public fun rlr(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath? = with(Euclidean2DSpace) { val c1 = start.getRightCircle(turningRadius) val c2 = end.getRightCircle(turningRadius) - val centers = StraightSegment(c1.center, c2.center) + val centers = StraightTrajectory2D(c1.center, c2.center) if (centers.length > turningRadius * 4) return null - var theta = theta(centers.theta - acos(centers.length / (turningRadius * 4))) - var dX = turningRadius * sin(theta) - var dY = turningRadius * cos(theta) - val p = vector(c1.center.x + dX * 2, c1.center.y + dY * 2) - val e = Circle2D(p, turningRadius) - val p1 = vector(c1.center.x + dX, c1.center.y + dY) - theta = theta(centers.theta + acos(centers.length / (turningRadius * 4))) - dX = turningRadius * sin(theta) - dY = turningRadius * cos(theta) - val p2 = vector(e.center.x + dX, e.center.y + dY) - val a1 = ArcSegment.of(c1.center, start, p1, ArcSegment.Direction.RIGHT) - val a2 = ArcSegment.of(e.center, p1, p2, ArcSegment.Direction.LEFT) - val a3 = ArcSegment.of(c2.center, p2, end, ArcSegment.Direction.RIGHT) - return DubinsPath(a1, a2, a3) + val firstVariant = run { + var theta = theta(centers.bearing - acos(centers.length / (turningRadius * 4))) + var dX = turningRadius * sin(theta) + var dY = turningRadius * cos(theta) + val p = vector(c1.center.x + dX * 2, c1.center.y + dY * 2) + val e = Circle2D(p, turningRadius) + val p1 = vector(c1.center.x + dX, c1.center.y + dY) + theta = theta(centers.bearing + acos(centers.length / (turningRadius * 4))) + dX = turningRadius * sin(theta) + dY = turningRadius * cos(theta) + val p2 = vector(e.center.x + dX, e.center.y + dY) + val a1 = CircleTrajectory2D.of(c1.center, start, p1, CircleTrajectory2D.Direction.RIGHT) + val a2 = CircleTrajectory2D.of(e.center, p1, p2, CircleTrajectory2D.Direction.LEFT) + val a3 = CircleTrajectory2D.of(c2.center, p2, end, CircleTrajectory2D.Direction.RIGHT) + DubinsPath(a1, a2, a3) + } + + val secondVariant = run { + var theta = theta(centers.bearing + acos(centers.length / (turningRadius * 4))) + var dX = turningRadius * sin(theta) + var dY = turningRadius * cos(theta) + val p = vector(c1.center.x + dX * 2, c1.center.y + dY * 2) + val e = Circle2D(p, turningRadius) + val p1 = vector(c1.center.x + dX, c1.center.y + dY) + theta = theta(centers.bearing - acos(centers.length / (turningRadius * 4))) + dX = turningRadius * sin(theta) + dY = turningRadius * cos(theta) + val p2 = vector(e.center.x + dX, e.center.y + dY) + val a1 = CircleTrajectory2D.of(c1.center, start, p1, CircleTrajectory2D.Direction.RIGHT) + val a2 = CircleTrajectory2D.of(e.center, p1, p2, CircleTrajectory2D.Direction.LEFT) + val a3 = CircleTrajectory2D.of(c2.center, p2, end, CircleTrajectory2D.Direction.RIGHT) + DubinsPath(a1, a2, a3) + } + + return if (firstVariant.length < secondVariant.length) firstVariant else secondVariant } - public fun lrl(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath?= with(Euclidean2DSpace) { + public fun lrl(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath? = with(Euclidean2DSpace) { val c1 = start.getLeftCircle(turningRadius) val c2 = end.getLeftCircle(turningRadius) - val centers = StraightSegment(c1.center, c2.center) + val centers = StraightTrajectory2D(c1.center, c2.center) if (centers.length > turningRadius * 4) return null - var theta = theta(centers.theta + acos(centers.length / (turningRadius * 4))) - var dX = turningRadius * sin(theta) - var dY = turningRadius * cos(theta) - val p = vector(c1.center.x + dX * 2, c1.center.y + dY * 2) - val e = Circle2D(p, turningRadius) - val p1 = vector(c1.center.x + dX, c1.center.y + dY) - theta = theta(centers.theta - acos(centers.length / (turningRadius * 4))) - dX = turningRadius * sin(theta) - dY = turningRadius * cos(theta) - val p2 = vector(e.center.x + dX, e.center.y + dY) - val a1 = ArcSegment.of(c1.center, start, p1, ArcSegment.Direction.LEFT) - val a2 = ArcSegment.of(e.center, p1, p2, ArcSegment.Direction.RIGHT) - val a3 = ArcSegment.of(c2.center, p2, end, ArcSegment.Direction.LEFT) - return DubinsPath(a1, a2, a3) + val firstVariant = run { + var theta = theta(centers.bearing + acos(centers.length / (turningRadius * 4))) + var dX = turningRadius * sin(theta) + var dY = turningRadius * cos(theta) + val p = vector(c1.center.x + dX * 2, c1.center.y + dY * 2) + val e = Circle2D(p, turningRadius) + val p1 = vector(c1.center.x + dX, c1.center.y + dY) + theta = theta(centers.bearing - acos(centers.length / (turningRadius * 4))) + dX = turningRadius * sin(theta) + dY = turningRadius * cos(theta) + val p2 = vector(e.center.x + dX, e.center.y + dY) + val a1 = CircleTrajectory2D.of(c1.center, start, p1, CircleTrajectory2D.Direction.LEFT) + val a2 = CircleTrajectory2D.of(e.center, p1, p2, CircleTrajectory2D.Direction.RIGHT) + val a3 = CircleTrajectory2D.of(c2.center, p2, end, CircleTrajectory2D.Direction.LEFT) + DubinsPath(a1, a2, a3) + } + + val secondVariant = run{ + var theta = theta(centers.bearing - acos(centers.length / (turningRadius * 4))) + var dX = turningRadius * sin(theta) + var dY = turningRadius * cos(theta) + val p = vector(c1.center.x + dX * 2, c1.center.y + dY * 2) + val e = Circle2D(p, turningRadius) + val p1 = vector(c1.center.x + dX, c1.center.y + dY) + theta = theta(centers.bearing + acos(centers.length / (turningRadius * 4))) + dX = turningRadius * sin(theta) + dY = turningRadius * cos(theta) + val p2 = vector(e.center.x + dX, e.center.y + dY) + val a1 = CircleTrajectory2D.of(c1.center, start, p1, CircleTrajectory2D.Direction.LEFT) + val a2 = CircleTrajectory2D.of(e.center, p1, p2, CircleTrajectory2D.Direction.RIGHT) + val a3 = CircleTrajectory2D.of(c2.center, p2, end, CircleTrajectory2D.Direction.LEFT) + DubinsPath(a1, a2, a3) + } + + return if (firstVariant.length < secondVariant.length) firstVariant else secondVariant } - public fun rsr(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath { + public fun rsr(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath { val c1 = start.getRightCircle(turningRadius) val c2 = end.getRightCircle(turningRadius) val s = leftOuterTangent(c1, c2) - val a1 = ArcSegment.of(c1.center, start, s.start, ArcSegment.Direction.RIGHT) - val a3 = ArcSegment.of(c2.center, s.end, end, ArcSegment.Direction.RIGHT) + val a1 = CircleTrajectory2D.of(c1.center, start, s.start, CircleTrajectory2D.Direction.RIGHT) + val a3 = CircleTrajectory2D.of(c2.center, s.end, end, CircleTrajectory2D.Direction.RIGHT) return DubinsPath(a1, s, a3) } - public fun lsl(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath { + public fun lsl(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath { val c1 = start.getLeftCircle(turningRadius) val c2 = end.getLeftCircle(turningRadius) val s = rightOuterTangent(c1, c2) - val a1 = ArcSegment.of(c1.center, start, s.start, ArcSegment.Direction.LEFT) - val a3 = ArcSegment.of(c2.center, s.end, end, ArcSegment.Direction.LEFT) + val a1 = CircleTrajectory2D.of(c1.center, start, s.start, CircleTrajectory2D.Direction.LEFT) + val a3 = CircleTrajectory2D.of(c2.center, s.end, end, CircleTrajectory2D.Direction.LEFT) return DubinsPath(a1, s, a3) } - public fun rsl(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? { + public fun rsl(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath? { val c1 = start.getRightCircle(turningRadius) val c2 = end.getLeftCircle(turningRadius) val s = rightInnerTangent(c1, c2) if (s == null || c1.center.distanceTo(c2.center) < turningRadius * 2) return null - val a1 = ArcSegment.of(c1.center, start, s.start, ArcSegment.Direction.RIGHT) - val a3 = ArcSegment.of(c2.center, s.end, end, ArcSegment.Direction.LEFT) + val a1 = CircleTrajectory2D.of(c1.center, start, s.start, CircleTrajectory2D.Direction.RIGHT) + val a3 = CircleTrajectory2D.of(c2.center, s.end, end, CircleTrajectory2D.Direction.LEFT) return DubinsPath(a1, s, a3) } - public fun lsr(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? { + public fun lsr(start: DubinsPose2D, end: DubinsPose2D, turningRadius: Double): DubinsPath? { val c1 = start.getLeftCircle(turningRadius) val c2 = end.getRightCircle(turningRadius) val s = leftInnerTangent(c1, c2) if (s == null || c1.center.distanceTo(c2.center) < turningRadius * 2) return null - val a1 = ArcSegment.of(c1.center, start, s.start, ArcSegment.Direction.LEFT) - val a3 = ArcSegment.of(c2.center, s.end, end, ArcSegment.Direction.RIGHT) + val a1 = CircleTrajectory2D.of(c1.center, start, s.start, CircleTrajectory2D.Direction.LEFT) + val a3 = CircleTrajectory2D.of(c2.center, s.end, end, CircleTrajectory2D.Direction.RIGHT) return DubinsPath(a1, s, a3) } } diff --git a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPose2D.kt b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPose2D.kt new file mode 100644 index 000000000..5aa8c1455 --- /dev/null +++ b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/DubinsPose2D.kt @@ -0,0 +1,36 @@ +/* + * Copyright 2018-2022 KMath contributors. + * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. + */ + +package space.kscience.kmath.trajectory + +import space.kscience.kmath.geometry.DoubleVector2D +import space.kscience.kmath.geometry.Vector +import kotlin.math.atan2 + +/** + * Combination of [Vector] and its view angle (clockwise from positive y-axis direction) + */ +public interface DubinsPose2D : DoubleVector2D { + public val coordinate: DoubleVector2D + public val bearing: Double +} + +public class PhaseVector2D( + override val coordinate: DoubleVector2D, + public val velocity: DoubleVector2D, +) : DubinsPose2D, DoubleVector2D by coordinate { + override val bearing: Double get() = atan2(velocity.x, velocity.y) +} + +private class DubinsPose2DImpl( + override val coordinate: DoubleVector2D, + override val bearing: Double, +) : DubinsPose2D, DoubleVector2D by coordinate{ + + override fun toString(): String = "Pose2D(x=$x, y=$y, bearing=$bearing)" +} + + +public fun DubinsPose2D(coordinate: DoubleVector2D, theta: Double): DubinsPose2D = DubinsPose2DImpl(coordinate, theta) \ No newline at end of file diff --git a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Pose2D.kt b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Pose2D.kt deleted file mode 100644 index 788cf57af..000000000 --- a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Pose2D.kt +++ /dev/null @@ -1,33 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.trajectory - -import space.kscience.kmath.geometry.DoubleVector2D -import space.kscience.kmath.geometry.Vector -import kotlin.math.atan2 - -/** - * Combination of [Vector] and its view angle - */ -public interface Pose2D: DoubleVector2D{ - public val coordinate: DoubleVector2D - public val theta: Double -} - -public class PhaseVector2D( - override val coordinate: DoubleVector2D, - public val velocity: DoubleVector2D -): Pose2D, DoubleVector2D by coordinate{ - override val theta: Double get() = atan2(velocity.y, velocity.x) -} - -internal class Pose2DImpl( - override val coordinate: DoubleVector2D, - override val theta: Double -) : Pose2D, DoubleVector2D by coordinate - - -public fun Pose2D(coordinate: DoubleVector2D, theta: Double): Pose2D = Pose2DImpl(coordinate, theta) \ No newline at end of file diff --git a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Trajectory.kt b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Trajectory2D.kt similarity index 50% rename from kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Trajectory.kt rename to kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Trajectory2D.kt index 03b0fcec9..3fcf4365d 100644 --- a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Trajectory.kt +++ b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/Trajectory2D.kt @@ -8,58 +8,61 @@ package space.kscience.kmath.trajectory import space.kscience.kmath.geometry.Circle2D import space.kscience.kmath.geometry.DoubleVector2D import space.kscience.kmath.geometry.Euclidean2DSpace.distanceTo -import space.kscience.kmath.geometry.circumference import kotlin.math.PI import kotlin.math.atan2 -public sealed interface Trajectory { +public sealed interface Trajectory2D { public val length: Double } /** * Straight path segment. The order of start and end defines the direction */ -public data class StraightSegment( - internal val start: DoubleVector2D, - internal val end: DoubleVector2D, -) : Trajectory { +public data class StraightTrajectory2D( + public val start: DoubleVector2D, + public val end: DoubleVector2D, +) : Trajectory2D { override val length: Double get() = start.distanceTo(end) - internal val theta: Double get() = theta(atan2(end.x - start.x, end.y - start.y)) + public val bearing: Double get() = theta(atan2(end.x - start.x, end.y - start.y)) } /** * An arc segment */ -public data class ArcSegment( +public data class CircleTrajectory2D( public val circle: Circle2D, - public val start: Pose2D, - public val end: Pose2D, -) : Trajectory { + public val start: DubinsPose2D, + public val end: DubinsPose2D, +) : Trajectory2D { public enum class Direction { LEFT, RIGHT } - override val length: Double by lazy { - val angle: Double = theta( + /** + * Arc length in radians + */ + val arcLength: Double + get() = theta( if (direction == Direction.LEFT) { - start.theta - end.theta + start.bearing - end.bearing } else { - end.theta - start.theta + end.bearing - start.bearing } ) - val proportion = angle / (2 * PI) - circle.circumference * proportion + + override val length: Double by lazy { + circle.radius * arcLength } - internal val direction: Direction by lazy { + public val direction: Direction by lazy { if (start.y < circle.center.y) { - if (start.theta > PI) Direction.RIGHT else Direction.LEFT + if (start.bearing > PI) Direction.RIGHT else Direction.LEFT } else if (start.y > circle.center.y) { - if (start.theta < PI) Direction.RIGHT else Direction.LEFT + if (start.bearing < PI) Direction.RIGHT else Direction.LEFT } else { - if (start.theta == 0.0) { + if (start.bearing == 0.0) { if (start.x < circle.center.x) Direction.RIGHT else Direction.LEFT } else { if (start.x > circle.center.x) Direction.RIGHT else Direction.LEFT @@ -68,12 +71,17 @@ public data class ArcSegment( } public companion object { - public fun of(center: DoubleVector2D, start: DoubleVector2D, end: DoubleVector2D, direction: Direction): ArcSegment { + public fun of( + center: DoubleVector2D, + start: DoubleVector2D, + end: DoubleVector2D, + direction: Direction, + ): CircleTrajectory2D { fun calculatePose( vector: DoubleVector2D, theta: Double, direction: Direction, - ): Pose2D = Pose2D( + ): DubinsPose2D = DubinsPose2D( vector, when (direction) { Direction.LEFT -> theta(theta - PI / 2) @@ -81,16 +89,20 @@ public data class ArcSegment( } ) - val s1 = StraightSegment(center, start) - val s2 = StraightSegment(center, end) - val pose1 = calculatePose(start, s1.theta, direction) - val pose2 = calculatePose(end, s2.theta, direction) - return ArcSegment(Circle2D(center, s1.length), pose1, pose2) + val s1 = StraightTrajectory2D(center, start) + val s2 = StraightTrajectory2D(center, end) + val pose1 = calculatePose(start, s1.bearing, direction) + val pose2 = calculatePose(end, s2.bearing, direction) + val trajectory = CircleTrajectory2D(Circle2D(center, s1.length), pose1, pose2) + if(trajectory.direction != direction){ + error("Trajectory direction mismatch") + } + return trajectory } } } -public open class CompositeTrajectory(public val segments: Collection) : Trajectory { +public open class CompositeTrajectory2D(public val segments: Collection) : Trajectory2D { override val length: Double get() = segments.sumOf { it.length } } diff --git a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/TrajectoryCost.kt b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/TrajectoryCost.kt deleted file mode 100644 index 3782a9a32..000000000 --- a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/TrajectoryCost.kt +++ /dev/null @@ -1,14 +0,0 @@ -/* - * Copyright 2018-2022 KMath contributors. - * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file. - */ - -package space.kscience.kmath.trajectory - -public fun interface TrajectoryCost { - public fun estimate(trajectory: Trajectory): Double - - public companion object{ - public val length: TrajectoryCost = TrajectoryCost { it.length } - } -} \ No newline at end of file diff --git a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/route.kt b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/route.kt index 2e8e43be9..56350835d 100644 --- a/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/route.kt +++ b/kmath-trajectory/src/commonMain/kotlin/space/kscience/kmath/trajectory/route.kt @@ -12,5 +12,5 @@ public fun interface MaxCurvature { public fun DubinsPath.Companion.shortest( start: PhaseVector2D, end: PhaseVector2D, - computer: MaxCurvature, -): DubinsPath = shortest(start, end, computer.compute(start)) + maxCurvature: MaxCurvature, +): DubinsPath = shortest(start, end, maxCurvature.compute(start)) diff --git a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/dubins/DubinsTests.kt b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/dubins/DubinsTests.kt index 166567475..5bbf8c294 100644 --- a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/dubins/DubinsTests.kt +++ b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/dubins/DubinsTests.kt @@ -16,11 +16,11 @@ class DubinsTests { @Test fun dubinsTest() = with(Euclidean2DSpace){ - val straight = StraightSegment(vector(0.0, 0.0), vector(100.0, 100.0)) + val straight = StraightTrajectory2D(vector(0.0, 0.0), vector(100.0, 100.0)) val lineP1 = straight.shift(1, 10.0).inverse() - val start = Pose2D(straight.end, straight.theta) - val end = Pose2D(lineP1.start, lineP1.theta) + val start = DubinsPose2D(straight.end, straight.bearing) + val end = DubinsPose2D(lineP1.start, lineP1.bearing) val radius = 2.0 val dubins = DubinsPath.all(start, end, radius) @@ -45,14 +45,14 @@ class DubinsTests { assertTrue(end.equalsFloat(path.c.end)) // Not working, theta double precision inaccuracy - if (path.b is ArcSegment) { - val b = path.b as ArcSegment + if (path.b is CircleTrajectory2D) { + val b = path.b as CircleTrajectory2D assertTrue(path.a.end.equalsFloat(b.start)) assertTrue(path.c.start.equalsFloat(b.end)) - } else if (path.b is StraightSegment) { - val b = path.b as StraightSegment - assertTrue(path.a.end.equalsFloat(Pose2D(b.start, b.theta))) - assertTrue(path.c.start.equalsFloat(Pose2D(b.end, b.theta))) + } else if (path.b is StraightTrajectory2D) { + val b = path.b as StraightTrajectory2D + assertTrue(path.a.end.equalsFloat(DubinsPose2D(b.start, b.bearing))) + assertTrue(path.c.start.equalsFloat(DubinsPose2D(b.end, b.bearing))) } } } diff --git a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/Math.kt b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/math.kt similarity index 59% rename from kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/Math.kt rename to kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/math.kt index 3b2535cee..4599f30f8 100644 --- a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/Math.kt +++ b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/math.kt @@ -15,14 +15,14 @@ const val maxFloatDelta = 0.000001 fun Double.radiansToDegrees() = this * 180 / PI fun Double.equalFloat(other: Double) = abs(this - other) < maxFloatDelta -fun Pose2D.equalsFloat(other: Pose2D) = x.equalFloat(other.x) && y.equalFloat(other.y) && theta.equalFloat(other.theta) +fun DubinsPose2D.equalsFloat(other: DubinsPose2D) = x.equalFloat(other.x) && y.equalFloat(other.y) && bearing.equalFloat(other.bearing) -fun StraightSegment.inverse() = StraightSegment(end, start) -fun StraightSegment.shift(shift: Int, width: Double): StraightSegment = with(Euclidean2DSpace){ - val dX = width * sin(inverse().theta) - val dY = width * sin(theta) +fun StraightTrajectory2D.inverse() = StraightTrajectory2D(end, start) +fun StraightTrajectory2D.shift(shift: Int, width: Double): StraightTrajectory2D = with(Euclidean2DSpace){ + val dX = width * sin(inverse().bearing) + val dY = width * sin(bearing) - return StraightSegment( + return StraightTrajectory2D( vector(start.x - dX * shift, start.y - dY * shift), vector(end.x - dX * shift, end.y - dY * shift) ) diff --git a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/ArcTests.kt b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/ArcTests.kt index 86c79a5d6..af1444ade 100644 --- a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/ArcTests.kt +++ b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/ArcTests.kt @@ -8,7 +8,7 @@ package space.kscience.kmath.trajectory.segments import space.kscience.kmath.geometry.Circle2D import space.kscience.kmath.geometry.Euclidean2DSpace import space.kscience.kmath.geometry.circumference -import space.kscience.kmath.trajectory.ArcSegment +import space.kscience.kmath.trajectory.CircleTrajectory2D import space.kscience.kmath.trajectory.radiansToDegrees import kotlin.test.Test import kotlin.test.assertEquals @@ -18,9 +18,9 @@ class ArcTests { @Test fun arcTest() = with(Euclidean2DSpace){ val circle = Circle2D(vector(0.0, 0.0), 2.0) - val arc = ArcSegment.of(circle.center, vector(-2.0, 0.0), vector(0.0, 2.0), ArcSegment.Direction.RIGHT) + val arc = CircleTrajectory2D.of(circle.center, vector(-2.0, 0.0), vector(0.0, 2.0), CircleTrajectory2D.Direction.RIGHT) assertEquals(circle.circumference / 4, arc.length, 1.0) - assertEquals(0.0, arc.start.theta.radiansToDegrees()) - assertEquals(90.0, arc.end.theta.radiansToDegrees()) + assertEquals(0.0, arc.start.bearing.radiansToDegrees()) + assertEquals(90.0, arc.end.bearing.radiansToDegrees()) } } diff --git a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/LineTests.kt b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/LineTests.kt index c5e88c1f1..03320a3df 100644 --- a/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/LineTests.kt +++ b/kmath-trajectory/src/commonTest/kotlin/space/kscience/kmath/trajectory/segments/LineTests.kt @@ -6,7 +6,7 @@ package space.kscience.kmath.trajectory.segments import space.kscience.kmath.geometry.Euclidean2DSpace -import space.kscience.kmath.trajectory.StraightSegment +import space.kscience.kmath.trajectory.StraightTrajectory2D import space.kscience.kmath.trajectory.radiansToDegrees import kotlin.math.pow import kotlin.math.sqrt @@ -17,21 +17,21 @@ class LineTests { @Test fun lineTest() = with(Euclidean2DSpace){ - val straight = StraightSegment(vector(0.0, 0.0), vector(100.0, 100.0)) + val straight = StraightTrajectory2D(vector(0.0, 0.0), vector(100.0, 100.0)) assertEquals(sqrt(100.0.pow(2) + 100.0.pow(2)), straight.length) - assertEquals(45.0, straight.theta.radiansToDegrees()) + assertEquals(45.0, straight.bearing.radiansToDegrees()) } @Test fun lineAngleTest() = with(Euclidean2DSpace){ //val zero = Vector2D(0.0, 0.0) - val north = StraightSegment(Euclidean2DSpace.zero, vector(0.0, 2.0)) - assertEquals(0.0, north.theta.radiansToDegrees()) - val east = StraightSegment(Euclidean2DSpace.zero, vector(2.0, 0.0)) - assertEquals(90.0, east.theta.radiansToDegrees()) - val south = StraightSegment(Euclidean2DSpace.zero, vector(0.0, -2.0)) - assertEquals(180.0, south.theta.radiansToDegrees()) - val west = StraightSegment(Euclidean2DSpace.zero, vector(-2.0, 0.0)) - assertEquals(270.0, west.theta.radiansToDegrees()) + val north = StraightTrajectory2D(zero, vector(0.0, 2.0)) + assertEquals(0.0, north.bearing.radiansToDegrees()) + val east = StraightTrajectory2D(zero, vector(2.0, 0.0)) + assertEquals(90.0, east.bearing.radiansToDegrees()) + val south = StraightTrajectory2D(zero, vector(0.0, -2.0)) + assertEquals(180.0, south.bearing.radiansToDegrees()) + val west = StraightTrajectory2D(zero, vector(-2.0, 0.0)) + assertEquals(270.0, west.bearing.radiansToDegrees()) } } diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt index 493af54c9..8533c9d32 100644 --- a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt +++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt @@ -9,6 +9,7 @@ package space.kscience.kmath.viktor import org.jetbrains.bio.viktor.F64Array import space.kscience.kmath.misc.PerformancePitfall +import space.kscience.kmath.misc.UnsafeKMathAPI import space.kscience.kmath.misc.UnstableKMathAPI import space.kscience.kmath.nd.* import space.kscience.kmath.operations.DoubleField @@ -31,32 +32,36 @@ public open class ViktorFieldOpsND : override val elementAlgebra: DoubleField get() = DoubleField - override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND = - F64Array(*shape).apply { - DefaultStrides(shape).asSequence().forEach { index -> + @OptIn(UnsafeKMathAPI::class) + override fun structureND(shape: ShapeND, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND = + F64Array(*shape.asArray()).apply { + ColumnStrides(shape).asSequence().forEach { index -> set(value = DoubleField.initializer(index), indices = index) } }.asStructure() override fun StructureND.unaryMinus(): StructureND = -1 * this + @OptIn(UnsafeKMathAPI::class) @PerformancePitfall override fun StructureND.map(transform: DoubleField.(Double) -> Double): ViktorStructureND = - F64Array(*shape).apply { - DefaultStrides(shape).asSequence().forEach { index -> + F64Array(*shape.asArray()).apply { + ColumnStrides(ShapeND(shape)).asSequence().forEach { index -> set(value = DoubleField.transform(this@map[index]), indices = index) } }.asStructure() + @OptIn(UnsafeKMathAPI::class) @PerformancePitfall override fun StructureND.mapIndexed( transform: DoubleField.(index: IntArray, Double) -> Double, - ): ViktorStructureND = F64Array(*shape).apply { - DefaultStrides(shape).asSequence().forEach { index -> + ): ViktorStructureND = F64Array(*shape.asArray()).apply { + ColumnStrides(ShapeND(shape)).asSequence().forEach { index -> set(value = DoubleField.transform(index, this@mapIndexed[index]), indices = index) } }.asStructure() + @OptIn(UnsafeKMathAPI::class) @PerformancePitfall override fun zip( left: StructureND, @@ -64,8 +69,8 @@ public open class ViktorFieldOpsND : transform: DoubleField.(Double, Double) -> Double, ): ViktorStructureND { require(left.shape.contentEquals(right.shape)) - return F64Array(*left.shape).apply { - DefaultStrides(left.shape).asSequence().forEach { index -> + return F64Array(*left.shape.asArray()).apply { + ColumnStrides(left.shape).asSequence().forEach { index -> set(value = DoubleField.transform(left[index], right[index]), indices = index) } }.asStructure() @@ -119,13 +124,17 @@ public val DoubleField.viktorAlgebra: ViktorFieldOpsND get() = ViktorFieldOpsND @OptIn(UnstableKMathAPI::class) public open class ViktorFieldND( - override val shape: Shape, + private val shapeAsArray: IntArray, ) : ViktorFieldOpsND(), FieldND, NumbersAddOps> { - override val zero: ViktorStructureND by lazy { F64Array.full(init = 0.0, shape = shape).asStructure() } - override val one: ViktorStructureND by lazy { F64Array.full(init = 1.0, shape = shape).asStructure() } + + override val shape: ShapeND = ShapeND(shapeAsArray) + + + override val zero: ViktorStructureND by lazy { F64Array.full(init = 0.0, shape = shapeAsArray).asStructure() } + override val one: ViktorStructureND by lazy { F64Array.full(init = 1.0, shape = shapeAsArray).asStructure() } override fun number(value: Number): ViktorStructureND = - F64Array.full(init = value.toDouble(), shape = shape).asStructure() + F64Array.full(init = value.toDouble(), shape = shapeAsArray).asStructure() } public fun DoubleField.viktorAlgebra(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape) diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt index c9749d41a..085790355 100644 --- a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt +++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt @@ -7,22 +7,25 @@ package space.kscience.kmath.viktor import org.jetbrains.bio.viktor.F64Array import space.kscience.kmath.misc.PerformancePitfall -import space.kscience.kmath.nd.DefaultStrides +import space.kscience.kmath.nd.ColumnStrides import space.kscience.kmath.nd.MutableStructureND +import space.kscience.kmath.nd.ShapeND @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE") public class ViktorStructureND(public val f64Buffer: F64Array) : MutableStructureND { - override val shape: IntArray get() = f64Buffer.shape + override val shape: ShapeND get() = ShapeND(f64Buffer.shape) + @OptIn(PerformancePitfall::class) override inline fun get(index: IntArray): Double = f64Buffer.get(*index) + @OptIn(PerformancePitfall::class) override inline fun set(index: IntArray, value: Double) { f64Buffer.set(*index, value = value) } @PerformancePitfall override fun elements(): Sequence> = - DefaultStrides(shape).asSequence().map { it to get(it) } + ColumnStrides(shape).asSequence().map { it to get(it) } } public fun F64Array.asStructure(): ViktorStructureND = ViktorStructureND(this) diff --git a/settings.gradle.kts b/settings.gradle.kts index f53232f44..23af18d31 100644 --- a/settings.gradle.kts +++ b/settings.gradle.kts @@ -26,7 +26,6 @@ include( ":kmath-core", ":kmath-coroutines", ":kmath-functions", - ":kmath-polynomial", ":kmath-histograms", ":kmath-commons", ":kmath-viktor",