From 45ed45bd137bb5e5f7547333ca72bf6b3d90b46d Mon Sep 17 00:00:00 2001
From: Gleb Minaev <43728100+lounres@users.noreply.github.com>
Date: Tue, 5 Jul 2022 03:41:52 +0300
Subject: [PATCH] Finish tests generation for numbered utilities. Also: -
Optimize a bit labeled and numbered differentiation. - Fixed bugs in numbered
anti-differentiation.
---
.../kscience/kmath/functions/labeledUtil.kt | 12 +-
.../kscience/kmath/functions/numberedUtil.kt | 24 +-
.../functions/NumberedPolynomialUtilTest.kt | 2816 ++++++++++++++++-
3 files changed, 2823 insertions(+), 29 deletions(-)
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt
index 4002eb25a..4e799cb43 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt
@@ -148,7 +148,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
variable: Symbol,
): LabeledPolynomial<C> = algebra {
LabeledPolynomial<C>(
- buildMap(coefficients.size) {
+ buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= 1u }) {
coefficients
.forEach { (degs, c) ->
if (variable !in degs) return@forEach
@@ -179,7 +179,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
): LabeledPolynomial<C> = algebra {
if (order == 0u) return this@nthDerivativeWithRespectTo
LabeledPolynomial<C>(
- buildMap(coefficients.size) {
+ buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= order }) {
coefficients
.forEach { (degs, c) ->
if (degs.getOrElse(variable) { 0u } < order) return@forEach
@@ -213,7 +213,13 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
LabeledPolynomial<C>(
- buildMap(coefficients.size) {
+ 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
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt
index 9397c1956..9d88cd648 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt
@@ -352,7 +352,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
variable: Int,
): NumberedPolynomial<C> = ring {
NumberedPolynomial<C>(
- buildMap(coefficients.size) {
+ buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= 1u }) {
coefficients
.forEach { (degs, c) ->
if (degs.lastIndex < variable) return@forEach
@@ -382,7 +382,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
): NumberedPolynomial<C> = ring {
if (order == 0u) return this@nthDerivativeWithRespectTo
NumberedPolynomial<C>(
- buildMap(coefficients.size) {
+ buildMap(coefficients.count { it.key.getOrElse(variable) { 0u } >= order }) {
coefficients
.forEach { (degs, c) ->
if (degs.lastIndex < variable) return@forEach
@@ -451,8 +451,8 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
coefficients
.forEach { (degs, c) ->
put(
- List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u },
- c / multiplyByDoubling(one, degs[variable])
+ List(max(variable + 1, degs.size)) { degs.getOrElse(it) { 0u } + if (it != variable) 0u else 1u },
+ c / multiplyByDoubling(one, degs.getOrElse(variable) { 0u } + 1u)
)
}
}
@@ -474,9 +474,9 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectT
coefficients
.forEach { (degs, c) ->
put(
- List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order },
- degs[variable].let { deg ->
- (deg downTo deg - order + 1u)
+ 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) }
}
)
@@ -501,11 +501,11 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectT
coefficients
.forEach { (degs, c) ->
put(
- List(max(maxRespectedVariable + 1, degs.size)) { degs[it] + filteredVariablesAndOrders.getOrElse(it) { 0u } },
- filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
- degs[index].let { deg ->
- (deg downTo deg - order + 1u)
- .fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) }
+ 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) }
}
}
)
diff --git a/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt b/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt
index 9e49f1315..1b87d3fcf 100644
--- a/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt
+++ b/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt
@@ -5,6 +5,7 @@
package space.kscience.kmath.functions
+import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.asBuffer
import space.kscience.kmath.test.misc.Rational
@@ -8832,7 +8833,7 @@ class NumberedPolynomialUtilTest {
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>())
+ ).substituteFully(RationalField, bufferOf())
}
assertFailsWithTypeAndMessage<IllegalArgumentException>(
fullSubstitutionExceptionMessage,
@@ -9200,37 +9201,2824 @@ class NumberedPolynomialUtilTest {
listOf(1u, 2u) to Rational(-5, 5),
listOf(2u, 2u) to Rational(-7, 8),
)
- ).substituteFully(RationalField, bufferOf<Rational>())
+ ).substituteFully(RationalField, bufferOf())
}
}
@Test
- @Ignore
+ @OptIn(UnstableKMathAPI::class)
fun test_Polynomial_derivativeWithRespectTo_variable() {
- // TODO
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(-2),
+ listOf(1u) to Rational(2),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).derivativeWithRespectTo(RationalField, 0),
+ "test 1"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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
- @Ignore
+ @OptIn(UnstableKMathAPI::class)
fun test_Polynomial_nthDerivativeWithRespectTo_variable_order() {
- // TODO
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(-2),
+ listOf(1u) to Rational(2),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 0, 1u),
+ "test 1"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 0, 0u),
+ "test 2"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(2),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 0, 2u),
+ "test 3"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 0, 3u),
+ "test 4"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 0, 4u),
+ "test 5"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 1, 0u),
+ "test 6"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 1, 1u),
+ "test 7"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, 1, 2u),
+ "test 8"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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
- @Ignore
+ @OptIn(UnstableKMathAPI::class)
fun test_Polynomial_nthDerivativeWithRespectTo_variablesAndOrders() {
- // TODO
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(-2),
+ listOf(1u) to Rational(2),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 1u)),
+ "test 1"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 0u)),
+ "test 2"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(2),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, mapOf(0 to 4u)),
+ "test 5"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, mapOf(1 to 2u)),
+ "test 8"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthDerivativeWithRespectTo(RationalField, mapOf()),
+ "test 9"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(-2),
+ listOf(1u) to Rational(2),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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
- @Ignore
+ @OptIn(UnstableKMathAPI::class)
fun test_Polynomial_antiderivativeWithRespectTo_variable() {
- // TODO
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf(1u) to Rational(1),
+ listOf(2u) to Rational(-1),
+ listOf(3u) to Rational(1, 3),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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
- @Ignore
+ @OptIn(UnstableKMathAPI::class)
fun test_Polynomial_nthAntiderivativeWithRespectTo_variable_order() {
- // TODO
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf(1u) to Rational(1),
+ listOf(2u) to Rational(-1),
+ listOf(3u) to Rational(1, 3),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthAntiderivativeWithRespectTo(RationalField, 0, 1u),
+ "test 1"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthAntiderivativeWithRespectTo(RationalField, 0, 4u),
+ "test 5"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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
- @Ignore
+ @OptIn(UnstableKMathAPI::class)
fun test_Polynomial_nthAntiderivativeWithRespectTo_variablesAndOrders() {
- // TODO
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf(1u) to Rational(1),
+ listOf(2u) to Rational(-1),
+ listOf(3u) to Rational(1, 3),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthAntiderivativeWithRespectTo(RationalField, mapOf(0 to 1u)),
+ "test 1"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthAntiderivativeWithRespectTo(RationalField, 0, 4u),
+ "test 5"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ).nthAntiderivativeWithRespectTo(RationalField, 1, 2u),
+ "test 8"
+ )
+ assertEquals(
+ NumberedPolynomialAsIs(
+ listOf<UInt>() to Rational(1),
+ listOf(1u) to Rational(-2),
+ listOf(2u) to Rational(1),
+ ),
+ NumberedPolynomialAsIs(
+ listOf<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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<UInt>() 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"
+ )
}
}
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