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Feature: Polynomials and rational functions #469

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lounres merged 132 commits from feature/polynomials into dev 2022-07-28 18:04:06 +03:00
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5 changed files with 816 additions and 146 deletions
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150
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt
View File

@ -77,63 +77,63 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
* Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial.
*/
public override operator fun Symbol.plus(other: Int): LabeledPolynomial<C> =
if (other == 0) LabeledPolynomialAsIs(mapOf(
if (other == 0) LabeledPolynomialAsIs(
mapOf(this@plus to 1U) to constantOne,
))
else LabeledPolynomialAsIs(mapOf(
)
else LabeledPolynomialAsIs(
mapOf(this@plus to 1U) to constantOne,
emptyMap<Symbol, UInt>() to constantOne * other,
))
)
/**
* Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial.
*/
public override operator fun Symbol.minus(other: Int): LabeledPolynomial<C> =
if (other == 0) LabeledPolynomialAsIs(mapOf(
mapOf(this@minus to 1U) to -constantOne,
))
else LabeledPolynomialAsIs(mapOf(
mapOf(this@minus to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to constantOne * other,
))
if (other == 0) LabeledPolynomialAsIs(
mapOf(this@minus to 1U) to constantOne,
)
else LabeledPolynomialAsIs(
mapOf(this@minus to 1U) to constantOne,
emptyMap<Symbol, UInt>() to constantOne * -other,
)
/**
* Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial.
*/
public override operator fun Symbol.times(other: Int): LabeledPolynomial<C> =
if (other == 0) zero
else LabeledPolynomialAsIs(mapOf(
else LabeledPolynomialAsIs(
mapOf(this to 1U) to constantOne * other,
))
)
/**
* Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial.
*/
public override operator fun Int.plus(other: Symbol): LabeledPolynomial<C> =
if (this == 0) LabeledPolynomialAsIs(mapOf(
if (this == 0) LabeledPolynomialAsIs(
mapOf(other to 1U) to constantOne,
))
else LabeledPolynomialAsIs(mapOf(
)
else LabeledPolynomialAsIs(
mapOf(other to 1U) to constantOne,
emptyMap<Symbol, UInt>() to constantOne * this@plus,
))
)
/**
* Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial.
*/
public override operator fun Int.minus(other: Symbol): LabeledPolynomial<C> =
if (this == 0) LabeledPolynomialAsIs(mapOf(
if (this == 0) LabeledPolynomialAsIs(
mapOf(other to 1U) to -constantOne,
))
else LabeledPolynomialAsIs(mapOf(
)
else LabeledPolynomialAsIs(
mapOf(other to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to constantOne * this@minus,
))
)
/**
* Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial.
*/
public override operator fun Int.times(other: Symbol): LabeledPolynomial<C> =
if (this == 0) zero
else LabeledPolynomialAsIs(mapOf(
else LabeledPolynomialAsIs(
mapOf(other to 1U) to constantOne * this@times,
))
)
/**
* Returns sum of the polynomial and the integer represented as a polynomial.
@ -143,7 +143,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
public override operator fun LabeledPolynomial<C>.plus(other: Int): LabeledPolynomial<C> =
if (other == 0) this
else with(coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to other.asConstant()))
if (isEmpty()) other.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -161,7 +161,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
public override operator fun LabeledPolynomial<C>.minus(other: Int): LabeledPolynomial<C> =
if (other == 0) this
else with(coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to (-other).asConstant()))
if (isEmpty()) (-other).asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -180,7 +180,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
when(other) {
0 -> zero
1 -> this
else -> LabeledPolynomial(
else -> LabeledPolynomialAsIs(
coefficients
.toMutableMap()
.apply {
@ -197,7 +197,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
public override operator fun Int.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
if (this == 0) other
else with(other.coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@plus.asConstant()))
if (isEmpty()) this@plus.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -215,7 +215,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
public override operator fun Int.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
if (this == 0) -other
else with(other.coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@minus.asConstant()))
if (isEmpty()) this@minus.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -236,7 +236,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
when(this) {
0 -> zero
1 -> other
else -> LabeledPolynomial(
else -> LabeledPolynomialAsIs(
other.coefficients
.toMutableMap()
.apply {
@ -245,65 +245,60 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Converts the integer [value] to polynomial.
*/
public override fun number(value: Int): LabeledPolynomial<C> = number(constantNumber(value))
/**
* Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial.
*/
public override operator fun Symbol.plus(other: C): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(this@plus to 1U) to constantOne,
emptyMap<Symbol, UInt>() to other,
))
)
/**
* Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial.
*/
public override operator fun Symbol.minus(other: C): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
mapOf(this@minus to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to other,
))
LabeledPolynomialAsIs(
mapOf(this@minus to 1U) to constantOne,
emptyMap<Symbol, UInt>() to -other,
)
/**
* Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial.
*/
public override operator fun Symbol.times(other: C): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(this@times to 1U) to other,
))
)
/**
* Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial.
*/
public override operator fun C.plus(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(other to 1U) to constantOne,
emptyMap<Symbol, UInt>() to this@plus,
))
)
/**
* Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial.
*/
public override operator fun C.minus(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(other to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to this@minus,
))
)
/**
* Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial.
*/
public override operator fun C.times(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(other to 1U) to this@times,
))
)
/**
* Returns sum of the constant represented as a polynomial and the polynomial.
*/
override operator fun C.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@plus))
if (isEmpty()) this@plus.asLabeledPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -318,7 +313,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
*/
override operator fun C.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@minus))
if (isEmpty()) this@minus.asLabeledPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -347,7 +342,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
*/
override operator fun LabeledPolynomial<C>.plus(other: C): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to other))
if (isEmpty()) other.asLabeledPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -362,7 +357,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
*/
override operator fun LabeledPolynomial<C>.minus(other: C): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to other))
if (isEmpty()) other.asLabeledPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -387,60 +382,59 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
/**
* Converts the constant [value] to polynomial.
*/
public override fun number(value: C): LabeledPolynomial<C> =
LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to value))
public override fun number(value: C): LabeledPolynomial<C> = value.asLabeledPolynomial()
/**
* Represents the variable as a monic monomial.
*/
public override operator fun Symbol.unaryPlus(): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(this to 1U) to constantOne,
))
)
/**
* Returns negation of representation of the variable as a monic monomial.
*/
public override operator fun Symbol.unaryMinus(): LabeledPolynomial<C> =
LabeledPolynomialAsIs(mapOf(
LabeledPolynomialAsIs(
mapOf(this to 1U) to -constantOne,
))
)
/**
* Returns sum of the variables represented as monic monomials.
*/
public override operator fun Symbol.plus(other: Symbol): LabeledPolynomial<C> =
if (this == other) LabeledPolynomialAsIs(mapOf(
if (this == other) LabeledPolynomialAsIs(
mapOf(this to 1U) to constantOne * 2
))
else LabeledPolynomialAsIs(mapOf(
)
else LabeledPolynomialAsIs(
mapOf(this to 1U) to constantOne,
mapOf(other to 1U) to constantOne,
))
)
/**
* Returns difference between the variables represented as monic monomials.
*/
public override operator fun Symbol.minus(other: Symbol): LabeledPolynomial<C> =
if (this == other) zero
else LabeledPolynomialAsIs(mapOf(
else LabeledPolynomialAsIs(
mapOf(this to 1U) to constantOne,
mapOf(other to 1U) to -constantOne,
))
)
/**
* Returns product of the variables represented as monic monomials.
*/
public override operator fun Symbol.times(other: Symbol): LabeledPolynomial<C> =
if (this == other) LabeledPolynomialAsIs(mapOf(
if (this == other) LabeledPolynomialAsIs(
mapOf(this to 2U) to constantOne
))
else LabeledPolynomialAsIs(mapOf(
)
else LabeledPolynomialAsIs(
mapOf(this to 1U, other to 1U) to constantOne,
))
)
/**
* Returns sum of the variable represented as a monic monomial and the polynomial.
*/
public override operator fun Symbol.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(this@plus to 1u) to constantOne))
if (isEmpty()) this@plus.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -455,15 +449,15 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
*/
public override operator fun Symbol.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(this@minus to 1u) to constantOne))
if (isEmpty()) this@minus.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
val degs = mapOf(this@minus to 1U)
val theVariableDegs = mapOf(this@minus to 1U)
forEach { (degs, c) -> if(degs != degs) this[degs] = -c }
forEach { (degs, c) -> if(degs != theVariableDegs) this[degs] = -c }
this[degs] = constantOne - getOrElse(degs) { constantZero }
this[theVariableDegs] = constantOne - getOrElse(theVariableDegs) { constantZero }
}
)
}
@ -481,7 +475,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
*/
public override operator fun LabeledPolynomial<C>.plus(other: Symbol): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(other to 1u) to constantOne))
if (isEmpty()) other.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
@ -496,13 +490,13 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
*/
public override operator fun LabeledPolynomial<C>.minus(other: Symbol): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(other to 1u) to constantOne))
if (isEmpty()) other.asPolynomial()
else LabeledPolynomialAsIs(
toMutableMap()
.apply {
val degs = mapOf(other to 1U)
this[degs] = constantOne - getOrElse(degs) { constantZero }
this[degs] = getOrElse(degs) { constantZero } - constantOne
}
)
}
@ -560,11 +554,11 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
/**
* Instance of zero polynomial (zero of the polynomial ring).
*/
override val zero: LabeledPolynomial<C> = LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to constantZero))
override val zero: LabeledPolynomial<C> = LabeledPolynomialAsIs()
/**
* Instance of unit polynomial (unit of the polynomial ring).
*/
override val one: LabeledPolynomial<C> = LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to constantOne))
override val one: LabeledPolynomial<C> = constantOne.asLabeledPolynomial()
/**
* Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is

5
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListPolynomial.kt
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@ -172,11 +172,6 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Converts the integer [value] to polynomial.
*/
public override fun number(value: Int): ListPolynomial<C> = number(constantNumber(value))
/**
* Returns sum of the constant represented as a polynomial and the polynomial.
*/

5
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt
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@ -169,11 +169,6 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Converts the integer [value] to polynomial.
*/
public override fun number(value: Int): NumberedPolynomial<C> = number(constantNumber(value))
/**
* Returns sum of the constant represented as a polynomial and the polynomial.
*/

2
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
View File

@ -112,7 +112,7 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
/**
* Converts the integer [value] to polynomial.
*/
public fun number(value: Int): P = one * value
public fun number(value: Int): P = number(constantNumber(value))
/**
* Converts the integer to polynomial.
*/

800
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt
View File

@ -3,6 +3,8 @@
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
@file:Suppress("LocalVariableName")
package space.kscience.kmath.functions
import space.kscience.kmath.expressions.Symbol
@ -26,34 +28,118 @@ class LabeledPolynomialTest {
val o = Rational(0)
@Test
@Ignore
fun test_Variable_Int_plus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(5),
mapOf(x to 1u) to Rational(1),
),
x + 5,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(1),
),
x + 0,
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Int_minus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-5),
mapOf(x to 1u) to Rational(1),
),
x - 5,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(1),
),
x - 0,
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Int_times() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(5),
),
x * 5,
"test 1"
)
assertSame(
zero,
x * 0,
"test 2"
)
}
}
@Test
@Ignore
fun test_Int_Variable_plus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(5),
mapOf(x to 1u) to Rational(1),
),
5 + x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(1),
),
0 + x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Int_Variable_minus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(5),
mapOf(x to 1u) to Rational(-1),
),
5 - x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(-1),
),
0 - x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Int_Variable_times() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(5),
),
5 * x,
"test 1"
)
assertSame(
zero,
0 * x,
"test 2"
)
}
}
@Test
fun test_Polynomial_Int_plus() {
@ -516,34 +602,126 @@ class LabeledPolynomialTest {
}
}
@Test
@Ignore
fun test_Variable_Constant_plus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(5),
mapOf(x to 1u) to Rational(1),
),
x + Rational(5),
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(0),
mapOf(x to 1u) to Rational(1),
),
x + Rational(0),
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Constant_minus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-5),
mapOf(x to 1u) to Rational(1),
),
x - Rational(5),
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(0),
mapOf(x to 1u) to Rational(1),
),
x - Rational(0),
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Constant_times() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(5),
),
x * Rational(5),
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(0),
),
x * Rational(0),
"test 2"
)
}
}
@Test
@Ignore
fun test_Constant_Variable_plus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(5),
mapOf(x to 1u) to Rational(1),
),
Rational(5) + x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(0),
mapOf(x to 1u) to Rational(1),
),
Rational(0) + x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Constant_Variable_minus() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(5),
mapOf(x to 1u) to Rational(-1),
),
Rational(5) - x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(0),
mapOf(x to 1u) to Rational(-1),
),
Rational(0) - x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Constant_Variable_times() {
// TODO
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(5),
),
Rational(5) * x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(0),
),
Rational(0) * x,
"test 2"
)
}
}
@Test
fun test_Polynomial_Constant_plus() {
@ -1068,59 +1246,567 @@ class LabeledPolynomialTest {
}
}
@Test
@Ignore
fun test_Variable_unaryPlus(){
// TODO
fun test_Variable_unaryPlus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(1),
),
+x
)
}
}
@Test
@Ignore
fun test_Variable_unaryMinus(){
// TODO
fun test_Variable_unaryMinus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(-1),
),
-x
)
}
}
@Test
@Ignore
fun test_Variable_Variable_plus(){
// TODO
fun test_Variable_Variable_plus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(1),
mapOf(y to 1u) to Rational(1),
),
x + y,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(2),
),
x + x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Variable_minus(){
// TODO
fun test_Variable_Variable_minus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(1),
mapOf(y to 1u) to Rational(-1),
),
x - y,
"test 1"
)
assertSame(
zero,
x - x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Variable_times(){
// TODO
fun test_Variable_Variable_times() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u, y to 1u) to Rational(1),
),
x * y,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 2u) to Rational(1),
),
x * x,
"test 2"
)
}
}
@Test
@Ignore
fun test_Variable_Polynomial_plus(){
// TODO
fun test_Variable_Polynomial_plus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(7, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
x + LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(6, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
y + LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 2"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
mapOf(iota to 1u) to Rational(1),
),
iota + LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 3"
)
}
}
@Test
@Ignore
fun test_Variable_Polynomial_minus(){
// TODO
fun test_Variable_Polynomial_minus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(16, 4),
mapOf(x to 1u) to Rational(-1, 3),
mapOf(x to 2u) to Rational(-3, 8),
mapOf(y to 1u) to Rational(1, 7),
mapOf(x to 1u, y to 1u) to Rational(15, 3),
mapOf(x to 2u, y to 1u) to Rational(-6, 5),
mapOf(y to 2u) to Rational(13, 3),
mapOf(x to 1u, y to 2u) to Rational(-13, 4),
mapOf(x to 2u, y to 2u) to Rational(-11, 8),
),
x - LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(16, 4),
mapOf(x to 1u) to Rational(-4, 3),
mapOf(x to 2u) to Rational(-3, 8),
mapOf(y to 1u) to Rational(8, 7),
mapOf(x to 1u, y to 1u) to Rational(15, 3),
mapOf(x to 2u, y to 1u) to Rational(-6, 5),
mapOf(y to 2u) to Rational(13, 3),
mapOf(x to 1u, y to 2u) to Rational(-13, 4),
mapOf(x to 2u, y to 2u) to Rational(-11, 8),
),
y - LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 2"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(16, 4),
mapOf(x to 1u) to Rational(-4, 3),
mapOf(x to 2u) to Rational(-3, 8),
mapOf(y to 1u) to Rational(1, 7),
mapOf(x to 1u, y to 1u) to Rational(15, 3),
mapOf(x to 2u, y to 1u) to Rational(-6, 5),
mapOf(y to 2u) to Rational(13, 3),
mapOf(x to 1u, y to 2u) to Rational(-13, 4),
mapOf(x to 2u, y to 2u) to Rational(-11, 8),
mapOf(iota to 1u) to Rational(1),
),
iota - LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 3"
)
}
}
@Test
@Ignore
fun test_Variable_Polynomial_times(){
// TODO
fun test_Variable_Polynomial_times() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(-16, 4),
mapOf(x to 2u) to Rational(4, 3),
mapOf(x to 3u) to Rational(3, 8),
mapOf(x to 1u, y to 1u) to Rational(-1, 7),
mapOf(x to 2u, y to 1u) to Rational(-15, 3),
mapOf(x to 3u, y to 1u) to Rational(6, 5),
mapOf(x to 1u, y to 2u) to Rational(-13, 3),
mapOf(x to 2u, y to 2u) to Rational(13, 4),
mapOf(x to 3u, y to 2u) to Rational(11, 8),
),
x * LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(y to 1u) to Rational(-16, 4),
mapOf(x to 1u, y to 1u) to Rational(4, 3),
mapOf(x to 2u, y to 1u) to Rational(3, 8),
mapOf(y to 2u) to Rational(-1, 7),
mapOf(x to 1u, y to 2u) to Rational(-15, 3),
mapOf(x to 2u, y to 2u) to Rational(6, 5),
mapOf(y to 3u) to Rational(-13, 3),
mapOf(x to 1u, y to 3u) to Rational(13, 4),
mapOf(x to 2u, y to 3u) to Rational(11, 8),
),
y * LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 2"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(iota to 1u) to Rational(-16, 4),
mapOf(x to 1u, iota to 1u) to Rational(4, 3),
mapOf(x to 2u, iota to 1u) to Rational(3, 8),
mapOf(y to 1u, iota to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u, iota to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u, iota to 1u) to Rational(6, 5),
mapOf(y to 2u, iota to 1u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u, iota to 1u) to Rational(13, 4),
mapOf(x to 2u, y to 2u, iota to 1u) to Rational(11, 8),
),
iota * LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
"test 3"
)
}
}
@Test
@Ignore
fun test_Polynomial_Variable_plus(){
// TODO
fun test_Polynomial_Variable_plus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(7, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) + x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(6, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) + y,
"test 2"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
mapOf(iota to 1u) to Rational(1),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) + iota,
"test 3"
)
}
}
@Test
@Ignore
fun test_Polynomial_Variable_minus(){
// TODO
fun test_Polynomial_Variable_minus() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(1, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) - x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-8, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) - y,
"test 2"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
mapOf(iota to 1u) to Rational(-1),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) - iota,
"test 3"
)
}
}
@Test
@Ignore
fun test_Polynomial_Variable_times(){
// TODO
fun test_Polynomial_Variable_times() {
RationalField.labeledPolynomialSpace {
assertEquals(
LabeledPolynomialAsIs(
mapOf(x to 1u) to Rational(-16, 4),
mapOf(x to 2u) to Rational(4, 3),
mapOf(x to 3u) to Rational(3, 8),
mapOf(x to 1u, y to 1u) to Rational(-1, 7),
mapOf(x to 2u, y to 1u) to Rational(-15, 3),
mapOf(x to 3u, y to 1u) to Rational(6, 5),
mapOf(x to 1u, y to 2u) to Rational(-13, 3),
mapOf(x to 2u, y to 2u) to Rational(13, 4),
mapOf(x to 3u, y to 2u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) * x,
"test 1"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(y to 1u) to Rational(-16, 4),
mapOf(x to 1u, y to 1u) to Rational(4, 3),
mapOf(x to 2u, y to 1u) to Rational(3, 8),
mapOf(y to 2u) to Rational(-1, 7),
mapOf(x to 1u, y to 2u) to Rational(-15, 3),
mapOf(x to 2u, y to 2u) to Rational(6, 5),
mapOf(y to 3u) to Rational(-13, 3),
mapOf(x to 1u, y to 3u) to Rational(13, 4),
mapOf(x to 2u, y to 3u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) * y,
"test 2"
)
assertEquals(
LabeledPolynomialAsIs(
mapOf(iota to 1u) to Rational(-16, 4),
mapOf(x to 1u, iota to 1u) to Rational(4, 3),
mapOf(x to 2u, iota to 1u) to Rational(3, 8),
mapOf(y to 1u, iota to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u, iota to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u, iota to 1u) to Rational(6, 5),
mapOf(y to 2u, iota to 1u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u, iota to 1u) to Rational(13, 4),
mapOf(x to 2u, y to 2u, iota to 1u) to Rational(11, 8),
),
LabeledPolynomialAsIs(
mapOf<Symbol, UInt>() to Rational(-16, 4),
mapOf(x to 1u) to Rational(4, 3),
mapOf(x to 2u) to Rational(3, 8),
mapOf(y to 1u) to Rational(-1, 7),
mapOf(x to 1u, y to 1u) to Rational(-15, 3),
mapOf(x to 2u, y to 1u) to Rational(6, 5),
mapOf(y to 2u) to Rational(-13, 3),
mapOf(x to 1u, y to 2u) to Rational(13, 4),
mapOf(x to 2u, y to 2u) to Rational(11, 8),
) * iota,
"test 3"
)
}
}
@Test
fun test_Polynomial_unaryMinus() {