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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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kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt
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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.ScaleOperations
import kotlin.math.max
/**
* Represents multivariate polynomials with labeled variables.
*
* @param C Ring in which the polynomial is considered.
*/
public data class LabeledPolynomial<C>
internal constructor(
/**
* Map that collects coefficients of the polynomial. Every non-zero monomial
* `a x_1^{d_1} ... x_n^{d_n}` is represented as pair "key-value" in the map, where value is coefficients `a` and
* key is map that associates variables in the monomial with multiplicity of them occurring in the monomial.
* For example polynomial
* ```
* 5 a^2 c^3 - 6 b + 0 b c
* ```
* has coefficients represented as
* ```
* mapOf(
* mapOf(
* a to 2,
* c to 3
* ) to 5,
* mapOf(
* b to 1
* ) to (-6)
* )
* ```
* where `a`, `b` and `c` are corresponding [Symbol] objects.
*/
public val coefficients: Map<Map<Symbol, UInt>, C>
) : Polynomial<C> {
override fun toString(): String = "LabeledPolynomial$coefficients"
}
/**
* Space of polynomials.
*
* @param C the type of operated polynomials.
* @param A the intersection of [Ring] of [C] and [ScaleOperations] of [C].
* @param ring the [A] instance.
*/
public class LabeledPolynomialSpace<C, A : Ring<C>>(
public override val ring: A,
) : MultivariatePolynomialSpace<C, Symbol, LabeledPolynomial<C>>, PolynomialSpaceOverRing<C, LabeledPolynomial<C>, A> {
public override operator fun Symbol.plus(other: Int): LabeledPolynomial<C> =
if (other == 0) LabeledPolynomial<C>(mapOf(
mapOf(this@plus to 1U) to constantOne,
))
else LabeledPolynomial<C>(mapOf(
mapOf(this@plus to 1U) to constantOne,
emptyMap<Symbol, UInt>() to constantOne * other,
))
public override operator fun Symbol.minus(other: Int): LabeledPolynomial<C> =
if (other == 0) LabeledPolynomial<C>(mapOf(
mapOf(this@minus to 1U) to -constantOne,
))
else LabeledPolynomial<C>(mapOf(
mapOf(this@minus to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to constantOne * other,
))
public override operator fun Symbol.times(other: Int): LabeledPolynomial<C> =
if (other == 0) zero
else LabeledPolynomial<C>(mapOf(
mapOf(this to 1U) to constantOne * other,
))
public override operator fun Int.plus(other: Symbol): LabeledPolynomial<C> =
if (this == 0) LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to constantOne,
))
else LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to constantOne,
emptyMap<Symbol, UInt>() to constantOne * this@plus,
))
public override operator fun Int.minus(other: Symbol): LabeledPolynomial<C> =
if (this == 0) LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to -constantOne,
))
else LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to constantOne * this@minus,
))
public override operator fun Int.times(other: Symbol): LabeledPolynomial<C> =
if (this == 0) zero
else LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to constantOne * this@times,
))
/**
* Returns sum of the polynomial and the integer represented as polynomial.
*
* The operation is equivalent to adding [other] copies of unit polynomial to [this].
*/
public override operator fun LabeledPolynomial<C>.plus(other: Int): LabeledPolynomial<C> =
if (other == 0) this
else with(coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to other.asConstant()))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyMap<Symbol, UInt>()
this[degs] = getOrElse(degs) { constantZero } + other
}
)
}
/**
* Returns difference between the polynomial and the integer represented as polynomial.
*
* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
*/
public override operator fun LabeledPolynomial<C>.minus(other: Int): LabeledPolynomial<C> =
if (other == 0) this
else with(coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to (-other).asConstant()))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyMap<Symbol, UInt>()
this[degs] = getOrElse(degs) { constantZero } - other
}
)
}
/**
* Returns product of the polynomial and the integer represented as polynomial.
*
* The operation is equivalent to sum of [other] copies of [this].
*/
public override operator fun LabeledPolynomial<C>.times(other: Int): LabeledPolynomial<C> =
if (other == 0) zero
else LabeledPolynomial(
coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this[degs]!! * other
}
)
/**
* Returns sum of the integer represented as polynomial and the polynomial.
*
* The operation is equivalent to adding [this] copies of unit polynomial to [other].
*/
public override operator fun Int.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
if (this == 0) other
else with(other.coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@plus.asConstant()))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyMap<Symbol, UInt>()
this[degs] = this@plus + getOrElse(degs) { constantZero }
}
)
}
/**
* Returns difference between the integer represented as polynomial and the polynomial.
*
* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
*/
public override operator fun Int.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
if (this == 0) other
else with(other.coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@minus.asConstant()))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyMap<Symbol, UInt>()
this[degs] = this@minus - getOrElse(degs) { constantZero }
}
)
}
/**
* Returns product of the integer represented as polynomial and the polynomial.
*
* The operation is equivalent to sum of [this] copies of [other].
*/
public override operator fun Int.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
if (this == 0) zero
else LabeledPolynomial(
other.coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this@times * this[degs]!!
}
)
/**
* Converts the integer [value] to polynomial.
*/
public override fun number(value: Int): LabeledPolynomial<C> = number(constantNumber(value))
public override operator fun C.plus(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to constantOne,
emptyMap<Symbol, UInt>() to this@plus,
))
public override operator fun C.minus(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to this@minus,
))
public override operator fun C.times(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(other to 1U) to this@times,
))
public override operator fun Symbol.plus(other: C): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(this@plus to 1U) to constantOne,
emptyMap<Symbol, UInt>() to other,
))
public override operator fun Symbol.minus(other: C): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(this@minus to 1U) to -constantOne,
emptyMap<Symbol, UInt>() to other,
))
public override operator fun Symbol.times(other: C): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(this@times to 1U) to other,
))
/**
* Returns sum of the constant represented as polynomial and the polynomial.
*/
override operator fun C.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@plus))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyMap<Symbol, UInt>()
this[degs] = this@plus + getOrElse(degs) { constantZero }
}
)
}
/**
* Returns difference between the constant represented as polynomial and the polynomial.
*/
override operator fun C.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@minus))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
val degs = emptyMap<Symbol, UInt>()
this[degs] = this@minus - getOrElse(degs) { constantZero }
}
)
}
/**
* Returns product of the constant represented as polynomial and the polynomial.
*/
override operator fun C.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
LabeledPolynomial<C>(
other.coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this@times * this[degs]!!
}
)
/**
* Returns sum of the constant represented as polynomial and the polynomial.
*/
override operator fun LabeledPolynomial<C>.plus(other: C): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to other))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyMap<Symbol, UInt>()
this[degs] = getOrElse(degs) { constantZero } + other
}
)
}
/**
* Returns difference between the constant represented as polynomial and the polynomial.
*/
override operator fun LabeledPolynomial<C>.minus(other: C): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to other))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
val degs = emptyMap<Symbol, UInt>()
this[degs] = getOrElse(degs) { constantZero } - other
}
)
}
/**
* Returns product of the constant represented as polynomial and the polynomial.
*/
override operator fun LabeledPolynomial<C>.times(other: C): LabeledPolynomial<C> =
LabeledPolynomial<C>(
coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this[degs]!! * other
}
)
/**
* Converts the constant [value] to polynomial.
*/
public override fun number(value: C): LabeledPolynomial<C> =
LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to value))
public override operator fun Symbol.unaryPlus(): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(this to 1U) to constantOne,
))
public override operator fun Symbol.unaryMinus(): LabeledPolynomial<C> =
LabeledPolynomial<C>(mapOf(
mapOf(this to 1U) to -constantOne,
))
public override operator fun Symbol.plus(other: Symbol): LabeledPolynomial<C> =
if (this == other) LabeledPolynomial<C>(mapOf(
mapOf(this to 1U) to constantOne * 2
))
else LabeledPolynomial<C>(mapOf(
mapOf(this to 1U) to constantOne,
mapOf(other to 1U) to constantOne,
))
public override operator fun Symbol.minus(other: Symbol): LabeledPolynomial<C> =
if (this == other) zero
else LabeledPolynomial<C>(mapOf(
mapOf(this to 1U) to constantOne,
mapOf(other to 1U) to -constantOne,
))
public override operator fun Symbol.times(other: Symbol): LabeledPolynomial<C> =
if (this == other) LabeledPolynomial<C>(mapOf(
mapOf(this to 2U) to constantOne
))
else LabeledPolynomial<C>(mapOf(
mapOf(this to 1U, other to 1U) to constantOne,
))
public override operator fun Symbol.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@plus to 1u) to constantOne))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = mapOf(this@plus to 1U)
this[degs] = constantOne + getOrElse(degs) { constantZero }
}
)
}
public override operator fun Symbol.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@minus to 1u) to constantOne))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
val degs = mapOf(this@minus to 1U)
this[degs] = constantOne - getOrElse(degs) { constantZero }
}
)
}
public override operator fun Symbol.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
LabeledPolynomial<C>(
other.coefficients
.mapKeys { (degs, _) -> degs.toMutableMap().also{ it[this] = if (this in it) it[this]!! + 1U else 1U } }
)
public override operator fun LabeledPolynomial<C>.plus(other: Symbol): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to constantOne))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = mapOf(other to 1U)
this[degs] = constantOne + getOrElse(degs) { constantZero }
}
)
}
public override operator fun LabeledPolynomial<C>.minus(other: Symbol): LabeledPolynomial<C> =
with(coefficients) {
if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to constantOne))
else LabeledPolynomial<C>(
toMutableMap()
.apply {
val degs = mapOf(other to 1U)
this[degs] = constantOne - getOrElse(degs) { constantZero }
}
)
}
public override operator fun LabeledPolynomial<C>.times(other: Symbol): LabeledPolynomial<C> =
LabeledPolynomial<C>(
coefficients
.mapKeys { (degs, _) -> degs.toMutableMap().also{ it[other] = if (other in it) it[other]!! + 1U else 1U } }
)
/**
* Returns negation of the polynomial.
*/
override fun LabeledPolynomial<C>.unaryMinus(): LabeledPolynomial<C> =
LabeledPolynomial<C>(
coefficients.mapValues { -it.value }
)
/**
* Returns sum of the polynomials.
*/
override operator fun LabeledPolynomial<C>.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
LabeledPolynomial<C>(
buildMap(coefficients.size + other.coefficients.size) {
other.coefficients.mapValuesTo(this) { it.value }
other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
}
)
/**
* Returns difference of the polynomials.
*/
override operator fun LabeledPolynomial<C>.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
LabeledPolynomial<C>(
buildMap(coefficients.size + other.coefficients.size) {
other.coefficients.mapValuesTo(this) { it.value }
other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
}
)
/**
* Returns product of the polynomials.
*/
override operator fun LabeledPolynomial<C>.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
LabeledPolynomial<C>(
buildMap(coefficients.size * other.coefficients.size) {
for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
val degs = degs1.toMutableMap()
degs2.mapValuesTo(degs) { (variable, deg) -> degs.getOrElse(variable) { 0u } + deg }
val c = c1 * c2
this[degs] = if (degs in this) this[degs]!! + c else c
}
}
)
/**
* Instance of zero polynomial (zero of the polynomial ring).
*/
override val zero: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to constantZero))
/**
* Instance of unit polynomial (unit of the polynomial ring).
*/
override val one: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to constantOne))
/**
* Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
* zero, degree is -1.
*/
override val LabeledPolynomial<C>.degree: Int
get() = coefficients.entries.maxOfOrNull { (degs, c) -> degs.values.sum().toInt() } ?: -1
/**
* Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents
* in which they are appeared in the polynomial.
*
* As consequence all values in the map are positive integers. Also, if the polynomial is constant, the map is empty.
* And keys of the map is the same as in [variables].
*/
public override val LabeledPolynomial<C>.degrees: Map<Symbol, UInt>
get() =
buildMap {
coefficients.entries.forEach { (degs, _) ->
degs.mapValuesTo(this) { (variable, deg) ->
max(getOrElse(variable) { 0u }, deg)
}
}
}
/**
* Counts degree of the polynomial by the specified [variable].
*/
public override fun LabeledPolynomial<C>.degreeBy(variable: Symbol): UInt =
coefficients.entries.maxOfOrNull { (degs, _) -> degs.getOrElse(variable) { 0u } } ?: 0u
/**
* Counts degree of the polynomial by the specified [variables].
*/
public override fun LabeledPolynomial<C>.degreeBy(variables: Collection<Symbol>): UInt =
coefficients.entries.maxOfOrNull { (degs, _) -> degs.filterKeys { it in variables }.values.sum() } ?: 0u
/**
* Set of all variables that appear in the polynomial in positive exponents.
*/
public override val LabeledPolynomial<C>.variables: Set<Symbol>
get() =
buildSet {
coefficients.entries.forEach { (degs, _) -> addAll(degs.keys) }
}
/**
* Count of all variables that appear in the polynomial in positive exponents.
*/
public override val LabeledPolynomial<C>.countOfVariables: Int get() = variables.size
// @Suppress("NOTHING_TO_INLINE")
// public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, C>): LabeledPolynomial<C> = this.substitute(ring, argument)
// @Suppress("NOTHING_TO_INLINE")
// @JvmName("substitutePolynomial")
// public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, LabeledPolynomial<C>>): LabeledPolynomial<C> = this.substitute(ring, argument)
//
// @Suppress("NOTHING_TO_INLINE")
// public inline fun LabeledPolynomial<C>.asFunction(): (Map<Symbol, C>) -> LabeledPolynomial<C> = { this.substitute(ring, it) }
// @Suppress("NOTHING_TO_INLINE")
// public inline fun LabeledPolynomial<C>.asFunctionOnConstants(): (Map<Symbol, C>) -> LabeledPolynomial<C> = { this.substitute(ring, it) }
// @Suppress("NOTHING_TO_INLINE")
// public inline fun LabeledPolynomial<C>.asFunctionOnPolynomials(): (Map<Symbol, LabeledPolynomial<C>>) -> LabeledPolynomial<C> = { this.substitute(ring, it) }
//
// @Suppress("NOTHING_TO_INLINE")
// public inline operator fun LabeledPolynomial<C>.invoke(argument: Map<Symbol, C>): LabeledPolynomial<C> = this.substitute(ring, argument)
// @Suppress("NOTHING_TO_INLINE")
// @JvmName("invokePolynomial")
// public inline operator fun LabeledPolynomial<C>.invoke(argument: Map<Symbol, LabeledPolynomial<C>>): LabeledPolynomial<C> = this.substitute(ring, argument)
}

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kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledRationalFunction.kt
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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.invoke
public class LabeledRationalFunction<C>(
public override val numerator: LabeledPolynomial<C>,
public override val denominator: LabeledPolynomial<C>
) : RationalFunction<C, LabeledPolynomial<C>> {
override fun toString(): String = "LabeledRationalFunction${numerator.coefficients}/${denominator.coefficients}"
}
public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
public val ring: A,
) :
MultivariateRationalFunctionalSpaceOverMultivariatePolynomialSpace<
C,
Symbol,
LabeledPolynomial<C>,
LabeledRationalFunction<C>,
LabeledPolynomialSpace<C, A>,
>,
MultivariatePolynomialSpaceOfFractions<
C,
Symbol,
LabeledPolynomial<C>,
LabeledRationalFunction<C>,
>() {
override val polynomialRing : LabeledPolynomialSpace<C, A> = LabeledPolynomialSpace(ring)
override fun constructRationalFunction(
numerator: LabeledPolynomial<C>,
denominator: LabeledPolynomial<C>
): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(numerator, denominator)
/**
* Instance of zero rational function (zero of the rational functions ring).
*/
public override val zero: LabeledRationalFunction<C> = LabeledRationalFunction<C>(polynomialZero, polynomialOne)
/**
* Instance of unit polynomial (unit of the rational functions ring).
*/
public override val one: LabeledRationalFunction<C> = LabeledRationalFunction<C>(polynomialOne, polynomialOne)
// TODO: Разобрать
// operator fun invoke(arg: Map<Symbol, C>): LabeledRationalFunction<C> =
// LabeledRationalFunction(
// numerator(arg),
// denominator(arg)
// )
//
// @JvmName("invokeLabeledPolynomial")
// operator fun invoke(arg: Map<Symbol, LabeledPolynomial<C>>): LabeledRationalFunction<C> =
// LabeledRationalFunction(
// numerator(arg),
// denominator(arg)
// )
//
// @JvmName("invokeLabeledRationalFunction")
// operator fun invoke(arg: Map<Symbol, LabeledRationalFunction<C>>): LabeledRationalFunction<C> {
// var num = numerator invokeRFTakeNumerator arg
// var den = denominator invokeRFTakeNumerator arg
// for (variable in variables) if (variable in arg) {
// val degreeDif = degrees[variable]!!
// if (degreeDif > 0)
// den = multiplyByPower(den, arg[variable]!!.denominator, degreeDif)
// else
// num = multiplyByPower(num, arg[variable]!!.denominator, -degreeDif)
// }
// return LabeledRationalFunction(num, den)
// }
//
// override fun toString(): String = toString(emptyMap())
//
// fun toString(names: Map<Symbol, String> = emptyMap()): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toString(names)
// else -> "${numerator.toStringWithBrackets(names)}/${denominator.toStringWithBrackets(names)}"
// }
//
// fun toString(namer: (Symbol) -> String): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toString(namer)
// else -> "${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)}"
// }
//
// fun toStringWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toStringWithBrackets(names)
// else -> "(${numerator.toStringWithBrackets(names)}/${denominator.toStringWithBrackets(names)})"
// }
//
// fun toStringWithBrackets(namer: (Symbol) -> String): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toStringWithBrackets(namer)
// else -> "(${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)})"
// }
//
// fun toReversedString(names: Map<Symbol, String> = emptyMap()): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedString(names)
// else -> "${numerator.toReversedStringWithBrackets(names)}/${denominator.toReversedStringWithBrackets(names)}"
// }
//
// fun toReversedString(namer: (Symbol) -> String): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedString(namer)
// else -> "${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)}"
// }
//
// fun toReversedStringWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedStringWithBrackets(names)
// else -> "(${numerator.toReversedStringWithBrackets(names)}/${denominator.toReversedStringWithBrackets(names)})"
// }
//
// fun toReversedStringWithBrackets(namer: (Symbol) -> String): String =
// when (true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedStringWithBrackets(namer)
// else -> "(${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)})"
// }
}

80
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListPolynomial.kt
View File

@ -8,23 +8,19 @@ package space.kscience.kmath.functions
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.ScaleOperations
import space.kscience.kmath.operations.invoke
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.experimental.ExperimentalTypeInference
import kotlin.jvm.JvmName
import kotlin.math.max
import kotlin.math.min
/**
* Polynomial model without fixation on specific context they are applied to.
* Represents univariate polynomial that stores its coefficients in a [List].
*
* @param coefficients constant is the leftmost coefficient.
*/
public data class ListPolynomial<C>(
/**
* List that collects coefficients of the polynomial. Every monomial `a x^d` is represented as a coefficients
* `a` placed into the list with index `d`. For example coefficients of polynomial `5 x^2 - 6` can be represented as
* List that contains coefficients of the polynomial. Every monomial `a x^d` is stored as a coefficient `a` placed
* into the list at index `d`. For example, coefficients of a polynomial `5 x^2 - 6` can be represented as
* ```
* listOf(
* -6, // -6 +
@ -42,26 +38,28 @@ public data class ListPolynomial<C>(
* 0, // 0 x^4
* )
* ```
* It is recommended not to put extra zeros at end of the list (as for `0x^3` and `0x^4` in the example), but is not
* prohibited.
* It is not prohibited to put extra zeros at end of the list (as for `0x^3` and `0x^4` in the example). But the
* longer the coefficients list the worse performance of arithmetical operations performed on it. Thus, it is
* recommended not to put (or even to remove) extra (or useless) coefficients at the end of the coefficients list.
*/
public val coefficients: List<C>
) : Polynomial<C> {
override fun toString(): String = "Polynomial$coefficients"
override fun toString(): String = "ListPolynomial$coefficients"
}
/**
* Space of univariate polynomials constructed over ring.
* Arithmetic context for univariate polynomials with coefficients stored as a [List] constructed with the given [ring]
* of constants.
*
* @param C the type of constants. Polynomials have them as a coefficients in their terms.
* @param A type of underlying ring of constants. It's [Ring] of [C].
* @param C the type of constants. Polynomials have them a coefficients in their terms.
* @param A type of provided underlying ring of constants. It's [Ring] of [C].
* @param ring underlying ring of constants of type [A].
*/
public open class ListPolynomialSpace<C, A : Ring<C>>(
public override val ring: A,
) : PolynomialSpaceOverRing<C, ListPolynomial<C>, A> {
/**
* Returns sum of the polynomial and the integer represented as polynomial.
* Returns sum of the polynomial and the integer represented as a polynomial.
*
* The operation is equivalent to adding [other] copies of unit polynomial to [this].
*/
@ -79,7 +77,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
}
)
/**
* Returns difference between the polynomial and the integer represented as polynomial.
* Returns difference between the polynomial and the integer represented as a polynomial.
*
* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
*/
@ -97,7 +95,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
}
)
/**
* Returns product of the polynomial and the integer represented as polynomial.
* Returns product of the polynomial and the integer represented as a polynomial.
*
* The operation is equivalent to sum of [other] copies of [this].
*/
@ -112,7 +110,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
/**
* Returns sum of the integer represented as polynomial and the polynomial.
* Returns sum of the integer represented as a polynomial and the polynomial.
*
* The operation is equivalent to adding [this] copies of unit polynomial to [other].
*/
@ -130,7 +128,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
}
)
/**
* Returns difference between the integer represented as polynomial and the polynomial.
* Returns difference between the integer represented as a polynomial and the polynomial.
*
* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
*/
@ -150,7 +148,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
}
)
/**
* Returns product of the integer represented as polynomial and the polynomial.
* Returns product of the integer represented as a polynomial and the polynomial.
*
* The operation is equivalent to sum of [this] copies of [other].
*/
@ -170,7 +168,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
public override fun number(value: Int): ListPolynomial<C> = number(constantNumber(value))
/**
* Returns sum of the constant represented as polynomial and the polynomial.
* Returns sum of the constant represented as a polynomial and the polynomial.
*/
public override operator fun C.plus(other: ListPolynomial<C>): ListPolynomial<C> =
with(other.coefficients) {
@ -186,7 +184,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Returns difference between the constant represented as polynomial and the polynomial.
* Returns difference between the constant represented as a polynomial and the polynomial.
*/
public override operator fun C.minus(other: ListPolynomial<C>): ListPolynomial<C> =
with(other.coefficients) {
@ -204,7 +202,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Returns product of the constant represented as polynomial and the polynomial.
* Returns product of the constant represented as a polynomial and the polynomial.
*/
public override operator fun C.times(other: ListPolynomial<C>): ListPolynomial<C> =
ListPolynomial(
@ -216,7 +214,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
/**
* Returns sum of the constant represented as polynomial and the polynomial.
* Returns sum of the constant represented as a polynomial and the polynomial.
*/
public override operator fun ListPolynomial<C>.plus(other: C): ListPolynomial<C> =
with(coefficients) {
@ -232,7 +230,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Returns difference between the constant represented as polynomial and the polynomial.
* Returns difference between the constant represented as a polynomial and the polynomial.
*/
public override operator fun ListPolynomial<C>.minus(other: C): ListPolynomial<C> =
with(coefficients) {
@ -248,7 +246,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
)
}
/**
* Returns product of the constant represented as polynomial and the polynomial.
* Returns product of the constant represented as a polynomial and the polynomial.
*/
public override operator fun ListPolynomial<C>.times(other: C): ListPolynomial<C> =
ListPolynomial(
@ -262,7 +260,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
/**
* Converts the constant [value] to polynomial.
*/
public override fun number(value: C): ListPolynomial<C> = ListPolynomial(value)
public override fun number(value: C): ListPolynomial<C> = ListPolynomial(listOf(value))
/**
* Returns negation of the polynomial.
@ -321,9 +319,9 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
*/
override val zero: ListPolynomial<C> = ListPolynomial(emptyList())
/**
* Instance of unit constant (unit of the underlying ring).
* Instance of unit polynomial (unit of the polynomial ring).
*/
override val one: ListPolynomial<C> = ListPolynomial(listOf(constantOne))
override val one: ListPolynomial<C> by lazy { ListPolynomial(listOf(constantOne)) }
/**
* Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
@ -331,23 +329,43 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
*/
public override val ListPolynomial<C>.degree: Int get() = coefficients.lastIndex
// TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
// [ListPolynomialSpace] as a context receiver
/**
* Evaluates value of [this] polynomial on provided argument.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.substitute(argument: C): C = this.substitute(ring, argument)
/**
* Substitutes provided polynomial [argument] into [this] polynomial.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.substitute(argument: ListPolynomial<C>): ListPolynomial<C> = this.substitute(ring, argument)
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunction(): (C) -> C = { this.substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunctionOnConstants(): (C) -> C = { this.substitute(ring, it) }
public inline fun ListPolynomial<C>.asFunctionOfConstant(): (C) -> C = { this.substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunctionOnPolynomials(): (ListPolynomial<C>) -> ListPolynomial<C> = { this.substitute(ring, it) }
public inline fun ListPolynomial<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListPolynomial<C> = { this.substitute(ring, it) }
/**
* Evaluates the polynomial for the given value [argument].
* Evaluates value of [this] polynomial on provided [argument].
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListPolynomial<C>.invoke(argument: C): C = this.substitute(ring, argument)
/**
* Evaluates value of [this] polynomial on provided [argument].
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListPolynomial<C>.invoke(argument: ListPolynomial<C>): ListPolynomial<C> = this.substitute(ring, argument)
}

158
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt
View File

@ -8,13 +8,23 @@ package space.kscience.kmath.functions
import space.kscience.kmath.operations.Ring
/**
* Represents rational function that stores its numerator and denominator as [ListPolynomial]s.
*/
public data class ListRationalFunction<C>(
public override val numerator: ListPolynomial<C>,
public override val denominator: ListPolynomial<C>
) : RationalFunction<C, ListPolynomial<C>> {
override fun toString(): String = "RationalFunction${numerator.coefficients}/${denominator.coefficients}"
override fun toString(): String = "ListRationalFunction${numerator.coefficients}/${denominator.coefficients}"
}
/**
* Arithmetic context for univariate rational functions with numerator and denominator represented as [ListPolynomial]s.
*
* @param C the type of constants. Polynomials have them a coefficients in their terms.
* @param A type of provided underlying ring of constants. It's [Ring] of [C].
* @param ring underlying ring of constants of type [A].
*/
public class ListRationalFunctionSpace<C, A : Ring<C>> (
public val ring: A,
) :
@ -30,76 +40,98 @@ public class ListRationalFunctionSpace<C, A : Ring<C>> (
ListRationalFunction<C>,
>() {
/**
* Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations.
*/
override val polynomialRing : ListPolynomialSpace<C, A> = ListPolynomialSpace(ring)
/**
* Constructor of [ListRationalFunction] from numerator and denominator [ListPolynomial].
*/
override fun constructRationalFunction(numerator: ListPolynomial<C>, denominator: ListPolynomial<C>): ListRationalFunction<C> =
ListRationalFunction(numerator, denominator)
// TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
// [ListPolynomialSpace] as a context receiver
/**
* Instance of zero rational function (zero of the rational functions ring).
* Evaluates value of [this] polynomial on provided argument.
*/
public override val zero: ListRationalFunction<C> = ListRationalFunction(polynomialZero, polynomialOne)
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.substitute(argument: C): C = this.substitute(ring, argument)
/**
* Instance of unit polynomial (unit of the rational functions ring).
* Substitutes provided polynomial [argument] into [this] polynomial.
*/
public override val one: ListRationalFunction<C> = ListRationalFunction(polynomialOne, polynomialOne)
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.substitute(argument: ListPolynomial<C>): ListPolynomial<C> = this.substitute(ring, argument)
/**
* Substitutes provided rational function [argument] into [this] polynomial.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.substitute(argument: ListRationalFunction<C>): ListRationalFunction<C> = this.substitute(ring, argument)
/**
* Substitutes provided polynomial [argument] into [this] rational function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListRationalFunction<C>.substitute(argument: ListPolynomial<C>): ListRationalFunction<C> = this.substitute(ring, argument)
/**
* Substitutes provided rational function [argument] into [this] rational function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListRationalFunction<C>.substitute(argument: ListRationalFunction<C>): ListRationalFunction<C> = this.substitute(ring, argument)
// TODO: Разобрать
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunction(): (C) -> C = { this.substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunctionOfConstant(): (C) -> C = { this.substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListPolynomial<C> = { this.substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListPolynomial<C>.asFunctionOfRationalFunction(): (ListRationalFunction<C>) -> ListRationalFunction<C> = { this.substitute(ring, it) }
/**
* Represent [this] rational function as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListRationalFunction<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListRationalFunction<C> = { this.substitute(ring, it) }
/**
* Represent [this] rational function as a regular context-less function.
*/
@Suppress("NOTHING_TO_INLINE")
public inline fun ListRationalFunction<C>.asFunctionOfRationalFunction(): (ListRationalFunction<C>) -> ListRationalFunction<C> = { this.substitute(ring, it) }
// operator fun invoke(arg: UnivariatePolynomial<T>): RationalFunction<T> =
// RationalFunction(
// numerator(arg),
// denominator(arg)
// )
//
// operator fun invoke(arg: RationalFunction<T>): RationalFunction<T> {
// val num = numerator invokeRFTakeNumerator arg
// val den = denominator invokeRFTakeNumerator arg
// val degreeDif = numeratorDegree - denominatorDegree
// return if (degreeDif > 0)
// RationalFunction(
// num,
// multiplyByPower(den, arg.denominator, degreeDif)
// )
// else
// RationalFunction(
// multiplyByPower(num, arg.denominator, -degreeDif),
// den
// )
// }
//
// override fun toString(): String = toString(UnivariatePolynomial.variableName)
//
// fun toString(withVariableName: String = UnivariatePolynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toString(withVariableName)
// else -> "${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)}"
// }
//
// fun toStringWithBrackets(withVariableName: String = UnivariatePolynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toStringWithBrackets(withVariableName)
// else -> "(${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)})"
// }
//
// fun toReversedString(withVariableName: String = UnivariatePolynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedString(withVariableName)
// else -> "${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)}"
// }
//
// fun toReversedStringWithBrackets(withVariableName: String = UnivariatePolynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedStringWithBrackets(withVariableName)
// else -> "(${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)})"
// }
//
// fun removeZeros() =
// RationalFunction(
// numerator.removeZeros(),
// denominator.removeZeros()
// )
/**
* Evaluates value of [this] polynomial on provided argument.
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListPolynomial<C>.invoke(argument: C): C = this.substitute(ring, argument)
/**
* Evaluates value of [this] polynomial on provided argument.
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListPolynomial<C>.invoke(argument: ListPolynomial<C>): ListPolynomial<C> = this.substitute(ring, argument)
/**
* Evaluates value of [this] polynomial on provided argument.
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListPolynomial<C>.invoke(argument: ListRationalFunction<C>): ListRationalFunction<C> = this.substitute(ring, argument)
/**
* Evaluates value of [this] rational function on provided argument.
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListRationalFunction<C>.invoke(argument: ListPolynomial<C>): ListRationalFunction<C> = this.substitute(ring, argument)
/**
* Evaluates value of [this] rational function on provided argument.
*/
@Suppress("NOTHING_TO_INLINE")
public inline operator fun ListRationalFunction<C>.invoke(argument: ListRationalFunction<C>): ListRationalFunction<C> = this.substitute(ring, argument)
}

389
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt
View File

@ -1,389 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.ScaleOperations
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.experimental.ExperimentalTypeInference
import kotlin.jvm.JvmName
import kotlin.math.max
/**
* Polynomial model without fixation on specific context they are applied to.
*
* @param C the type of constants.
*/
public data class NumberedPolynomial<C>
internal constructor(
/**
* Map that collects coefficients of the polynomial. Every monomial `a x_1^{d_1} ... x_n^{d_n}` is represented as
* pair "key-value" in the map, where value is coefficients `a` and
* key is list that associates index of every variable in the monomial with multiplicity of the variable occurring
* in the monomial. For example coefficients of polynomial `5 x_1^2 x_3^3 - 6 x_2` can be represented as
* ```
* mapOf(
* listOf(2, 0, 3) to 5,
* listOf(0, 1) to (-6),
* )
* ```
* and also as
* ```
* mapOf(
* listOf(2, 0, 3) to 5,
* listOf(0, 1) to (-6),
* listOf(0, 1, 1) to 0,
* )
* ```
* It is recommended not to put zero monomials into the map, but is not prohibited. Lists of degrees always do not
* contain any zeros on end, but can contain zeros on start or anywhere in middle.
*/
public val coefficients: Map<List<UInt>, C>
) : Polynomial<C> {
override fun toString(): String = "NumberedPolynomial$coefficients"
}
/**
* Space of polynomials.
*
* @param C the type of operated polynomials.
* @param A the intersection of [Ring] of [C] and [ScaleOperations] of [C].
* @param ring the [A] instance.
*/
public open class NumberedPolynomialSpace<C, A : Ring<C>>(
public final override val ring: A,
) : PolynomialSpaceOverRing<C, NumberedPolynomial<C>, A> {
/**
* Returns sum of the polynomial and the integer represented as polynomial.
*
* The operation is equivalent to adding [other] copies of unit polynomial to [this].
*/
public override operator fun NumberedPolynomial<C>.plus(other: Int): NumberedPolynomial<C> =
if (other == 0) this
else
NumberedPolynomial(
coefficients
.toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = getOrElse(degs) { constantZero } + other
}
)
/**
* Returns difference between the polynomial and the integer represented as polynomial.
*
* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
*/
public override operator fun NumberedPolynomial<C>.minus(other: Int): NumberedPolynomial<C> =
if (other == 0) this
else
NumberedPolynomial(
coefficients
.toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = getOrElse(degs) { constantZero } - other
}
)
/**
* Returns product of the polynomial and the integer represented as polynomial.
*
* The operation is equivalent to sum of [other] copies of [this].
*/
public override operator fun NumberedPolynomial<C>.times(other: Int): NumberedPolynomial<C> =
if (other == 0) zero
else NumberedPolynomial<C>(
coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this[degs]!! * other
}
)
/**
* Returns sum of the integer represented as polynomial and the polynomial.
*
* The operation is equivalent to adding [this] copies of unit polynomial to [other].
*/
public override operator fun Int.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
if (this == 0) other
else
NumberedPolynomial(
other.coefficients
.toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = this@plus + getOrElse(degs) { constantZero }
}
)
/**
* Returns difference between the integer represented as polynomial and the polynomial.
*
* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
*/
public override operator fun Int.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
if (this == 0) other
else
NumberedPolynomial(
other.coefficients
.toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = this@minus - getOrElse(degs) { constantZero }
}
)
/**
* Returns product of the integer represented as polynomial and the polynomial.
*
* The operation is equivalent to sum of [this] copies of [other].
*/
public override operator fun Int.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
if (this == 0) zero
else NumberedPolynomial(
other.coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this@times * this[degs]!!
}
)
/**
* Converts the integer [value] to polynomial.
*/
public override fun number(value: Int): NumberedPolynomial<C> = number(constantNumber(value))
/**
* Returns sum of the constant represented as polynomial and the polynomial.
*/
override operator fun C.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this@plus))
else NumberedPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = this@plus + getOrElse(degs) { constantZero }
}
)
}
/**
* Returns difference between the constant represented as polynomial and the polynomial.
*/
override operator fun C.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
with(other.coefficients) {
if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this@minus))
else NumberedPolynomial<C>(
toMutableMap()
.apply {
forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
val degs = emptyList<UInt>()
this[degs] = this@minus - getOrElse(degs) { constantZero }
}
)
}
/**
* Returns product of the constant represented as polynomial and the polynomial.
*/
override operator fun C.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
NumberedPolynomial<C>(
other.coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this@times * this[degs]!!
}
)
/**
* Returns sum of the constant represented as polynomial and the polynomial.
*/
override operator fun NumberedPolynomial<C>.plus(other: C): NumberedPolynomial<C> =
with(coefficients) {
if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to other))
else NumberedPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = getOrElse(degs) { constantZero } + other
}
)
}
/**
* Returns difference between the constant represented as polynomial and the polynomial.
*/
override operator fun NumberedPolynomial<C>.minus(other: C): NumberedPolynomial<C> =
with(coefficients) {
if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to other))
else NumberedPolynomial<C>(
toMutableMap()
.apply {
val degs = emptyList<UInt>()
this[degs] = getOrElse(degs) { constantZero } - other
}
)
}
/**
* Returns product of the constant represented as polynomial and the polynomial.
*/
override operator fun NumberedPolynomial<C>.times(other: C): NumberedPolynomial<C> =
NumberedPolynomial<C>(
coefficients
.toMutableMap()
.apply {
for (degs in keys) this[degs] = this[degs]!! * other
}
)
/**
* Converts the constant [value] to polynomial.
*/
public override fun number(value: C): NumberedPolynomial<C> =
NumberedPolynomial(mapOf(emptyList<UInt>() to value))
/**
* Returns negation of the polynomial.
*/
override fun NumberedPolynomial<C>.unaryMinus(): NumberedPolynomial<C> =
NumberedPolynomial<C>(
coefficients.mapValues { -it.value }
)
/**
* Returns sum of the polynomials.
*/
override operator fun NumberedPolynomial<C>.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
NumberedPolynomial<C>(
buildMap(coefficients.size + other.coefficients.size) {
other.coefficients.mapValuesTo(this) { it.value }
other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
}
)
/**
* Returns difference of the polynomials.
*/
override operator fun NumberedPolynomial<C>.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
NumberedPolynomial<C>(
buildMap(coefficients.size + other.coefficients.size) {
other.coefficients.mapValuesTo(this) { it.value }
other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
}
)
/**
* Returns product of the polynomials.
*/
override operator fun NumberedPolynomial<C>.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
NumberedPolynomial<C>(
buildMap(coefficients.size * other.coefficients.size) {
for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
val degs =
(0..max(degs1.lastIndex, degs2.lastIndex))
.map { degs1.getOrElse(it) { 0U } + degs2.getOrElse(it) { 0U } }
val c = c1 * c2
this[degs] = if (degs in this) this[degs]!! + c else c
}
}
)
/**
* Instance of zero polynomial (zero of the polynomial ring).
*/
override val zero: NumberedPolynomial<C> = NumberedPolynomial<C>(emptyMap())
/**
* Instance of unit polynomial (unit of the polynomial ring).
*/
override val one: NumberedPolynomial<C> =
NumberedPolynomial<C>(
mapOf(
emptyList<UInt>() to constantOne // 1 * x_1^0 * x_2^0 * ...
)
)
/**
* Maximal index (ID) of variable occurring in the polynomial with positive power. If there is no such variable,
* the result is `-1`.
*/
public val NumberedPolynomial<C>.lastVariable: Int
get() = coefficients.entries.maxOfOrNull { (degs, _) -> degs.lastIndex } ?: -1
/**
* Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
* zero, degree is -1.
*/
override val NumberedPolynomial<C>.degree: Int
get() = coefficients.entries.maxOfOrNull { (degs, _) -> degs.sum().toInt() } ?: -1
/**
* List that associates indices of variables (that appear in the polynomial in positive exponents) with their most
* exponents in which the variables are appeared in the polynomial.
*
* As consequence all values in the list are non-negative integers. Also, if the polynomial is constant, the list is empty.
* And last index of the list is [lastVariable].
*/
public val NumberedPolynomial<C>.degrees: List<UInt>
get() =
MutableList(lastVariable + 1) { 0u }.apply {
coefficients.entries.forEach { (degs, _) ->
degs.forEachIndexed { index, deg ->
this[index] = max(this[index], deg)
}
}
}
/**
* Counts degree of the polynomial by the specified [variable].
*/
public fun NumberedPolynomial<C>.degreeBy(variable: Int): UInt =
coefficients.entries.maxOfOrNull { (degs, _) -> degs.getOrElse(variable) { 0u } } ?: 0u
/**
* Counts degree of the polynomial by the specified [variables].
*/
public fun NumberedPolynomial<C>.degreeBy(variables: Collection<Int>): UInt =
coefficients.entries.maxOfOrNull { (degs, _) ->
degs.withIndex().filter { (index, _) -> index in variables }.sumOf { it.value }
} ?: 0u
/**
* Count of variables occurring in the polynomial with positive power. If there is no such variable,
* the result is `0`.
*/
public val NumberedPolynomial<C>.countOfVariables: Int
get() =
MutableList(lastVariable + 1) { false }.apply {
coefficients.entries.forEach { (degs, _) ->
degs.forEachIndexed { index, deg ->
if (deg != 0u) this[index] = true
}
}
}.count { it }
@Suppress("NOTHING_TO_INLINE")
public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, C>): NumberedPolynomial<C> = this.substitute(ring, argument)
@Suppress("NOTHING_TO_INLINE")
@JvmName("substitutePolynomial")
public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = this.substitute(ring, argument)
@Suppress("NOTHING_TO_INLINE")
public inline fun NumberedPolynomial<C>.asFunction(): (Map<Int, C>) -> NumberedPolynomial<C> = { this.substitute(ring, it) }
@Suppress("NOTHING_TO_INLINE")
public inline fun NumberedPolynomial<C>.asFunctionOnConstants(): (Map<Int, C>) -> NumberedPolynomial<C> = { this.substitute(ring, it) }
@Suppress("NOTHING_TO_INLINE")
public inline fun NumberedPolynomial<C>.asFunctionOnPolynomials(): (Map<Int, NumberedPolynomial<C>>) -> NumberedPolynomial<C> = { this.substitute(ring, it) }
@Suppress("NOTHING_TO_INLINE")
public inline operator fun NumberedPolynomial<C>.invoke(argument: Map<Int, C>): NumberedPolynomial<C> = this.substitute(ring, argument)
@Suppress("NOTHING_TO_INLINE")
@JvmName("invokePolynomial")
public inline operator fun NumberedPolynomial<C>.invoke(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = this.substitute(ring, argument)
// FIXME: Move to other constructors with context receiver
public fun C.asNumberedPolynomial() : NumberedPolynomial<C> = NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this))
}

188
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedRationalFunction.kt
View File

@ -1,188 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.invoke
import kotlin.math.max
public class NumberedRationalFunction<C> internal constructor(
public override val numerator: NumberedPolynomial<C>,
public override val denominator: NumberedPolynomial<C>
) : RationalFunction<C, NumberedPolynomial<C>> {
override fun toString(): String = "NumberedRationalFunction${numerator.coefficients}/${denominator.coefficients}"
}
public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
public val ring: A,
) :
RationalFunctionalSpaceOverPolynomialSpace<
C,
NumberedPolynomial<C>,
NumberedRationalFunction<C>,
NumberedPolynomialSpace<C, A>,
>,
PolynomialSpaceOfFractions<
C,
NumberedPolynomial<C>,
NumberedRationalFunction<C>,
>() {
override val polynomialRing : NumberedPolynomialSpace<C, A> = NumberedPolynomialSpace(ring)
override fun constructRationalFunction(
numerator: NumberedPolynomial<C>,
denominator: NumberedPolynomial<C>
): NumberedRationalFunction<C> =
NumberedRationalFunction(numerator, denominator)
/**
* Instance of zero rational function (zero of the rational functions ring).
*/
public override val zero: NumberedRationalFunction<C> = NumberedRationalFunction(polynomialZero, polynomialOne)
/**
* Instance of unit polynomial (unit of the rational functions ring).
*/
public override val one: NumberedRationalFunction<C> = NumberedRationalFunction(polynomialOne, polynomialOne)
/**
* Maximal index (ID) of variable occurring in the polynomial with positive power. If there is no such variable,
* the result is `-1`.
*/
public val NumberedPolynomial<C>.lastVariable: Int get() = polynomialRing { lastVariable }
/**
* List that associates indices of variables (that appear in the polynomial in positive exponents) with their most
* exponents in which the variables are appeared in the polynomial.
*
* As consequence all values in the list are non-negative integers. Also, if the polynomial is constant, the list is empty.
* And last index of the list is [lastVariable].
*/
public val NumberedPolynomial<C>.degrees: List<UInt> get() = polynomialRing { degrees }
/**
* Counts degree of the polynomial by the specified [variable].
*/
public fun NumberedPolynomial<C>.degreeBy(variable: Int): UInt = polynomialRing { degreeBy(variable) }
/**
* Counts degree of the polynomial by the specified [variables].
*/
public fun NumberedPolynomial<C>.degreeBy(variables: Collection<Int>): UInt = polynomialRing { degreeBy(variables) }
/**
* Count of variables occurring in the polynomial with positive power. If there is no such variable,
* the result is `0`.
*/
public val NumberedPolynomial<C>.countOfVariables: Int get() = polynomialRing { countOfVariables }
/**
* Count of all variables that appear in the polynomial in positive exponents.
*/
public val NumberedRationalFunction<C>.lastVariable: Int
get() = polynomialRing { max(numerator.lastVariable, denominator.lastVariable) }
/**
* Count of variables occurring in the rational function with positive power. If there is no such variable,
* the result is `0`.
*/
public val NumberedRationalFunction<C>.countOfVariables: Int
get() =
MutableList(lastVariable + 1) { false }.apply {
numerator.coefficients.entries.forEach { (degs, _) ->
degs.forEachIndexed { index, deg ->
if (deg != 0u) this[index] = true
}
}
denominator.coefficients.entries.forEach { (degs, _) ->
degs.forEachIndexed { index, deg ->
if (deg != 0u) this[index] = true
}
}
}.count { it }
// TODO: Разобрать
// operator fun invoke(arg: Map<Int, C>): NumberedRationalFunction<C> =
// NumberedRationalFunction(
// numerator(arg),
// denominator(arg)
// )
//
// @JvmName("invokePolynomial")
// operator fun invoke(arg: Map<Int, Polynomial<C>>): NumberedRationalFunction<C> =
// NumberedRationalFunction(
// numerator(arg),
// denominator(arg)
// )
//
// @JvmName("invokeRationalFunction")
// operator fun invoke(arg: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> {
// var num = numerator invokeRFTakeNumerator arg
// var den = denominator invokeRFTakeNumerator arg
// for (variable in 0 until max(numerator.countOfVariables, denominator.countOfVariables)) if (variable in arg) {
// val degreeDif = numerator.degrees.getOrElse(variable) { 0 } - denominator.degrees.getOrElse(variable) { 0 }
// if (degreeDif > 0)
// den = multiplyByPower(den, arg[variable]!!.denominator, degreeDif)
// else
// num = multiplyByPower(num, arg[variable]!!.denominator, -degreeDif)
// }
// return NumberedRationalFunction(num, den)
// }
//
// override fun toString(): String = toString(Polynomial.variableName)
//
// fun toString(withVariableName: String = Polynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toString(withVariableName)
// else -> "${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)}"
// }
//
// fun toString(namer: (Int) -> String): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toString(namer)
// else -> "${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)}"
// }
//
// fun toStringWithBrackets(withVariableName: String = Polynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toStringWithBrackets(withVariableName)
// else -> "(${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)})"
// }
//
// fun toStringWithBrackets(namer: (Int) -> String): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toStringWithBrackets(namer)
// else -> "(${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)})"
// }
//
// fun toReversedString(withVariableName: String = Polynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedString(withVariableName)
// else -> "${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)}"
// }
//
// fun toReversedString(namer: (Int) -> String): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedString(namer)
// else -> "${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)}"
// }
//
// fun toReversedStringWithBrackets(withVariableName: String = Polynomial.variableName): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedStringWithBrackets(withVariableName)
// else -> "(${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)})"
// }
//
// fun toReversedStringWithBrackets(namer: (Int) -> String): String =
// when(true) {
// numerator.isZero() -> "0"
// denominator.isOne() -> numerator.toReversedStringWithBrackets(namer)
// else -> "(${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)})"
// }
}

152
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
View File

@ -25,38 +25,38 @@ public interface Polynomial<C>
@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE") // FIXME: Waiting for KT-31420
public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
/**
* Returns sum of the constant and the integer represented as constant (member of underlying ring).
* Returns sum of the constant and the integer represented as a constant (member of underlying ring).
*
* The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
*/
public operator fun C.plus(other: Int): C
/**
* Returns difference between the constant and the integer represented as constant (member of underlying ring).
* Returns difference between the constant and the integer represented as a constant (member of underlying ring).
*
* The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
*/
public operator fun C.minus(other: Int): C
/**
* Returns product of the constant and the integer represented as constant (member of underlying ring).
* Returns product of the constant and the integer represented as a constant (member of underlying ring).
*
* The operation is equivalent to sum of [other] copies of [this].
*/
public operator fun C.times(other: Int): C
/**
* Returns sum of the integer represented as constant (member of underlying ring) and the constant.
* Returns sum of the integer represented as a constant (member of underlying ring) and the constant.
*
* The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
*/
public operator fun Int.plus(other: C): C
/**
* Returns difference between the integer represented as constant (member of underlying ring) and the constant.
* Returns difference between the integer represented as a constant (member of underlying ring) and the constant.
*
* The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
*/
public operator fun Int.minus(other: C): C
/**
* Returns product of the integer represented as constant (member of underlying ring) and the constant.
* Returns product of the integer represented as a constant (member of underlying ring) and the constant.
*
* The operation is equivalent to sum of [this] copies of [other].
*/
@ -72,38 +72,38 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
public fun Int.asConstant(): C = constantNumber(this)
/**
* Returns sum of the polynomial and the integer represented as polynomial.
* Returns sum of the polynomial and the integer represented as a polynomial.
*
* The operation is equivalent to adding [other] copies of unit polynomial to [this].
*/
public operator fun P.plus(other: Int): P = addMultipliedByDoubling(this, one, other)
/**
* Returns difference between the polynomial and the integer represented as polynomial.
* Returns difference between the polynomial and the integer represented as a polynomial.
*
* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
*/
public operator fun P.minus(other: Int): P = addMultipliedByDoubling(this, one, -other)
/**
* Returns product of the polynomial and the integer represented as polynomial.
* Returns product of the polynomial and the integer represented as a polynomial.
*
* The operation is equivalent to sum of [other] copies of [this].
*/
public operator fun P.times(other: Int): P = multiplyByDoubling(this, other)
/**
* Returns sum of the integer represented as polynomial and the polynomial.
* Returns sum of the integer represented as a polynomial and the polynomial.
*
* The operation is equivalent to adding [this] copies of unit polynomial to [other].
*/
public operator fun Int.plus(other: P): P = addMultipliedByDoubling(other, one, this)
/**
* Returns difference between the integer represented as polynomial and the polynomial.
* Returns difference between the integer represented as a polynomial and the polynomial.
*
* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
*/
public operator fun Int.minus(other: P): P = addMultipliedByDoubling(-other, one, this)
/**
* Returns product of the integer represented as polynomial and the polynomial.
* Returns product of the integer represented as a polynomial and the polynomial.
*
* The operation is equivalent to sum of [this] copies of [other].
*/
@ -165,28 +165,28 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
public val constantOne: C
/**
* Returns sum of the constant represented as polynomial and the polynomial.
* Returns sum of the constant represented as a polynomial and the polynomial.
*/
public operator fun C.plus(other: P): P
/**
* Returns difference between the constant represented as polynomial and the polynomial.
* Returns difference between the constant represented as a polynomial and the polynomial.
*/
public operator fun C.minus(other: P): P
/**
* Returns product of the constant represented as polynomial and the polynomial.
* Returns product of the constant represented as a polynomial and the polynomial.
*/
public operator fun C.times(other: P): P
/**
* Returns sum of the constant represented as polynomial and the polynomial.
* Returns sum of the constant represented as a polynomial and the polynomial.
*/
public operator fun P.plus(other: C): P
/**
* Returns difference between the constant represented as polynomial and the polynomial.
* Returns difference between the constant represented as a polynomial and the polynomial.
*/
public operator fun P.minus(other: C): P
/**
* Returns product of the constant represented as polynomial and the polynomial.
* Returns product of the constant represented as a polynomial and the polynomial.
*/
public operator fun P.times(other: C): P
@ -254,41 +254,44 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420
public interface PolynomialSpaceOverRing<C, P: Polynomial<C>, A: Ring<C>> : PolynomialSpace<C, P> {
/**
* Underlying ring of constants. Its operations on constants are inherited by local operations on constants.
*/
public val ring: A
/**
* Returns sum of the constant and the integer represented as constant (member of underlying ring).
* Returns sum of the constant and the integer represented as a constant (member of underlying ring).
*
* The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
*/
public override operator fun C.plus(other: Int): C = ring { addMultipliedByDoubling(this@plus, one, other) }
/**
* Returns difference between the constant and the integer represented as constant (member of underlying ring).
* Returns difference between the constant and the integer represented as a constant (member of underlying ring).
*
* The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
*/
public override operator fun C.minus(other: Int): C = ring { addMultipliedByDoubling(this@minus, one, -other) }
/**
* Returns product of the constant and the integer represented as constant (member of underlying ring).
* Returns product of the constant and the integer represented as a constant (member of underlying ring).
*
* The operation is equivalent to sum of [other] copies of [this].
*/
public override operator fun C.times(other: Int): C = ring { multiplyByDoubling(this@times, other) }
/**
* Returns sum of the integer represented as constant (member of underlying ring) and the constant.
* Returns sum of the integer represented as a constant (member of underlying ring) and the constant.
*
* The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
*/
public override operator fun Int.plus(other: C): C = ring { addMultipliedByDoubling(other, one, this@plus) }
/**
* Returns difference between the integer represented as constant (member of underlying ring) and the constant.
* Returns difference between the integer represented as a constant (member of underlying ring) and the constant.
*
* The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
*/
public override operator fun Int.minus(other: C): C = ring { addMultipliedByDoubling(-other, one, this@minus) }
/**
* Returns product of the integer represented as constant (member of underlying ring) and the constant.
* Returns product of the integer represented as a constant (member of underlying ring) and the constant.
*
* The operation is equivalent to sum of [this] copies of [other].
*/
@ -330,58 +333,145 @@ public interface PolynomialSpaceOverRing<C, P: Polynomial<C>, A: Ring<C>> : Poly
public override val constantOne: C get() = ring.one
}
/**
* Abstraction of ring of polynomials of type [P] of variables of type [V] and over ring of constants of type [C].
*
* @param C the type of constants. Polynomials have them as coefficients in their terms.
* @param V the type of variables. Polynomials have them in representations of terms.
* @param P the type of polynomials.
*/
@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420
public interface MultivariatePolynomialSpace<C, V, P: Polynomial<C>>: PolynomialSpace<C, P> {
/**
* Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial.
*/
@JvmName("plusVariableInt")
public operator fun V.plus(other: Int): P
/**
* Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial.
*/
@JvmName("minusVariableInt")
public operator fun V.minus(other: Int): P
/**
* Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial.
*/
@JvmName("timesVariableInt")
public operator fun V.times(other: Int): P
/**
* Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial.
*/
@JvmName("plusIntVariable")
public operator fun Int.plus(other: V): P
/**
* Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial.
*/
@JvmName("minusIntVariable")
public operator fun Int.minus(other: V): P
/**
* Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial.
*/
@JvmName("timesIntVariable")
public operator fun Int.times(other: V): P
@JvmName("plusConstantVariable")
public operator fun C.plus(other: V): P
@JvmName("minusConstantVariable")
public operator fun C.minus(other: V): P
@JvmName("timesConstantVariable")
public operator fun C.times(other: V): P
/**
* Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial.
*/
@JvmName("plusVariableConstant")
public operator fun V.plus(other: C): P
/**
* Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial.
*/
@JvmName("minusVariableConstant")
public operator fun V.minus(other: C): P
/**
* Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial.
*/
@JvmName("timesVariableConstant")
public operator fun V.times(other: C): P
/**
* Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial.
*/
@JvmName("plusConstantVariable")
public operator fun C.plus(other: V): P
/**
* Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial.
*/
@JvmName("minusConstantVariable")
public operator fun C.minus(other: V): P
/**
* Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial.
*/
@JvmName("timesConstantVariable")
public operator fun C.times(other: V): P
/**
* Represents the variable as a monic monomial.
*/
@JvmName("unaryPlusVariable")
public operator fun V.unaryPlus(): P
/**
* Returns negation of representation of the variable as a monic monomial.
*/
@JvmName("unaryMinusVariable")
public operator fun V.unaryMinus(): P
/**
* Returns sum of the variables represented as monic monomials.
*/
@JvmName("plusVariableVariable")
public operator fun V.plus(other: V): P
/**
* Returns difference between the variables represented as monic monomials.
*/
@JvmName("minusVariableVariable")
public operator fun V.minus(other: V): P
/**
* Returns product of the variables represented as monic monomials.
*/
@JvmName("timesVariableVariable")
public operator fun V.times(other: V): P
/**
* Represents the [variable] as a monic monomial.
*/
@JvmName("numberVariable")
public fun number(variable: V): P = +variable
/**
* Represents the variable as a monic monomial.
*/
@JvmName("asPolynomialVariable")
public fun V.asPolynomial(): P = number(this)
/**
* Returns sum of the variable represented as a monic monomial and the polynomial.
*/
@JvmName("plusVariablePolynomial")
public operator fun V.plus(other: P): P
/**
* Returns difference between the variable represented as a monic monomial and the polynomial.
*/
@JvmName("minusVariablePolynomial")
public operator fun V.minus(other: P): P
/**
* Returns product of the variable represented as a monic monomial and the polynomial.
*/
@JvmName("timesVariablePolynomial")
public operator fun V.times(other: P): P
/**
* Returns sum of the polynomial and the variable represented as a monic monomial.
*/
@JvmName("plusPolynomialVariable")
public operator fun P.plus(other: V): P
/**
* Returns difference between the polynomial and the variable represented as a monic monomial.
*/
@JvmName("minusPolynomialVariable")
public operator fun P.minus(other: V): P
/**
* Returns product of the polynomial and the variable represented as a monic monomial.
*/
@JvmName("timesPolynomialVariable")
public operator fun P.times(other: V): P

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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.Ring
/**
* Returns the same degrees' description of the monomial, but without zero degrees.
*/
internal fun Map<Symbol, UInt>.cleanUp() = filterValues { it > 0U }
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(coefs, toCheckInput)
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(coefs, toCheckInput)
@Suppress("FunctionName")
internal fun <C, A: Ring<C>> A.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> {
if (!toCheckInput) return LabeledPolynomial<C>(coefs)
val fixedCoefs = LinkedHashMap<Map<Symbol, UInt>, C>(coefs.size)
for (entry in coefs) {
val key = entry.key.cleanUp()
val value = entry.value
fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
}
return LabeledPolynomial<C>(fixedCoefs)
}
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs, toCheckInput)
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs, toCheckInput)
@Suppress("FunctionName")
internal fun <C, A: Ring<C>> A.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, toCheckInput: Boolean = true) : LabeledPolynomial<C> {
if (!toCheckInput) return LabeledPolynomial<C>(pairs.toMap())
val fixedCoefs = LinkedHashMap<Map<Symbol, UInt>, C>(pairs.size)
for (entry in pairs) {
val key = entry.first.cleanUp()
val value = entry.second
fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
}
return LabeledPolynomial<C>(fixedCoefs)
}
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs = pairs, toCheckInput = toCheckInput)
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs = pairs, toCheckInput = toCheckInput)
@Suppress("FunctionName")
internal fun <C, A: Ring<C>> A.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> {
if (!toCheckInput) return LabeledPolynomial<C>(pairs.toMap())
val fixedCoefs = LinkedHashMap<Map<Symbol, UInt>, C>(pairs.size)
for (entry in pairs) {
val key = entry.first.cleanUp()
val value = entry.second
fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
}
return LabeledPolynomial<C>(fixedCoefs)
}
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs, toCheckInput = true)
//context(A)
//public fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to one))
//context(LabeledPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to constantOne))
//context(LabeledRationalFunctionSpace<C, A>)
//public fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to constantOne))
public fun <C> C.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this))
@DslMarker
@UnstableKMathAPI
internal annotation class LabeledPolynomialConstructorDSL
@UnstableKMathAPI
@LabeledPolynomialConstructorDSL
public class LabeledPolynomialTermSignatureBuilder {
private val signature: MutableMap<Symbol, UInt> = LinkedHashMap()
public fun build(): Map<Symbol, UInt> = signature
public infix fun Symbol.inPowerOf(deg: UInt) {
signature[this] = deg
}
@Suppress("NOTHING_TO_INLINE")
public inline infix fun Symbol.pow(deg: UInt): Unit = this inPowerOf deg
@Suppress("NOTHING_TO_INLINE")
public inline infix fun Symbol.`in`(deg: UInt): Unit = this inPowerOf deg
@Suppress("NOTHING_TO_INLINE")
public inline infix fun Symbol.of(deg: UInt): Unit = this inPowerOf deg
}
@UnstableKMathAPI
public class LabeledPolynomialBuilder<C>(private val zero: C, private val add: (C, C) -> C, capacity: Int = 0) {
private val coefficients: MutableMap<Map<Symbol, UInt>, C> = LinkedHashMap(capacity)
public fun build(): LabeledPolynomial<C> = LabeledPolynomial<C>(coefficients)
public operator fun C.invoke(block: LabeledPolynomialTermSignatureBuilder.() -> Unit) {
val signature = LabeledPolynomialTermSignatureBuilder().apply(block).build()
coefficients[signature] = add(coefficients.getOrElse(signature) { zero }, this@invoke)
}
@Suppress("NOTHING_TO_INLINE")
public inline infix fun C.with(noinline block: LabeledPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block)
@Suppress("NOTHING_TO_INLINE")
public inline infix fun (LabeledPolynomialTermSignatureBuilder.() -> Unit).with(coef: C): Unit = coef.invoke(this)
@Suppress("NOTHING_TO_INLINE")
public infix fun sig(block: LabeledPolynomialTermSignatureBuilder.() -> Unit): LabeledPolynomialTermSignatureBuilder.() -> Unit = block
}
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
@UnstableKMathAPI
@LabeledPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> A.LabeledPolynomial(block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(zero, ::add).apply(block).build()
@UnstableKMathAPI
@LabeledPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> A.LabeledPolynomial(capacity: Int, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(zero, ::add, capacity).apply(block).build()
@UnstableKMathAPI
@LabeledPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(constantZero, { left: C, right: C -> left + right}).apply(block).build()
@UnstableKMathAPI
@LabeledPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(capacity: Int, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(constantZero, { left: C, right: C -> left + right}, capacity).apply(block).build()
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>, denominatorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(
LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
LabeledPolynomial(denominatorCoefficients, toCheckInput = true)
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>, denominatorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(
LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
LabeledPolynomial(denominatorCoefficients, toCheckInput = true)
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numerator: LabeledPolynomial<C>): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(numerator, polynomialOne)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.LabeledRationalFunction(numerator: LabeledPolynomial<C>): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(numerator, LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to one), toCheckInput = false))
@Suppress("FunctionName")
public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(
LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
polynomialOne
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
LabeledRationalFunction<C>(
LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to one), toCheckInput = false)
)
//context(A)
//public fun <C, A: Ring<C>> Symbol.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
//context(LabeledRationalFunctionSpace<C, A>)
//public fun <C, A: Ring<C>> Symbol.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
//context(A)
//public fun <C, A: Ring<C>> C.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
//context(LabeledRationalFunctionSpace<C, A>)
//public fun <C, A: Ring<C>> C.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())

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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.Field
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.invoke
import kotlin.contracts.ExperimentalContracts
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
// TODO: Docs
/**
* Creates a [LabeledPolynomialSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.labeledPolynomial(): LabeledPolynomialSpace<C, A> =
LabeledPolynomialSpace(this)
/**
* Creates a [LabeledPolynomialSpace]'s scope over a received ring.
*/
@OptIn(ExperimentalContracts::class)
public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomialSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return LabeledPolynomialSpace(this).block()
}
///**
// * Represents the polynomial as a [String] with names of variables substituted with names from [names].
// * Consider that monomials are sorted in lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.represent(names: Map<Symbol, String> = emptyMap()): String =
// coefficients.entries
// .sortedWith { o1, o2 -> LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .toSortedMap()
// .filter { it.value > 0U }
// .map { (variable, deg) ->
// val variableName = names.getOrDefault(variable, variable.toString())
// when (deg) {
// 1U -> variableName
// else -> "$variableName^$deg"
// }
// }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer].
// * Consider that monomials are sorted in lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.represent(namer: (Symbol) -> String): String =
// coefficients.entries
// .sortedWith { o1, o2 -> LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .toSortedMap()
// .filter { it.value > 0U }
// .map { (variable, deg) ->
// when (deg) {
// 1U -> namer(variable)
// else -> "${namer(variable)}^$deg"
// }
// }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] with names of variables substituted with names from [names] and with
// * brackets around the string if needed (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.representWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
// with(represent(names)) { if (coefficients.count() == 1) this else "($this)" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
// * (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.representWithBrackets(namer: (Symbol) -> String): String =
// with(represent(namer)) { if (coefficients.count() == 1) this else "($this)" }
//
///**
// * Represents the polynomial as a [String] with names of variables substituted with names from [names].
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversed(names: Map<Symbol, String> = emptyMap()): String =
// coefficients.entries
// .sortedWith { o1, o2 -> -LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .toSortedMap()
// .filter { it.value > 0U }
// .map { (variable, deg) ->
// val variableName = names.getOrDefault(variable, variable.toString())
// when (deg) {
// 1U -> variableName
// else -> "$variableName^$deg"
// }
// }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer].
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversed(namer: (Symbol) -> String): String =
// coefficients.entries
// .sortedWith { o1, o2 -> -LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .toSortedMap()
// .filter { it.value > 0U }
// .map { (variable, deg) ->
// when (deg) {
// 1U -> namer(variable)
// else -> "${namer(variable)}^$deg"
// }
// }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] with names of variables substituted with names from [names] and with
// * brackets around the string if needed (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversedWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
// with(representReversed(names)) { if (coefficients.count() == 1) this else "($this)" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
// * (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(LabeledPolynomialSpace<C, A>)
//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversedWithBrackets(namer: (Symbol) -> String): String =
// with(representReversed(namer)) { if (coefficients.count() == 1) this else "($this)" }
//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
// if (other.isZero()) throw ArithmeticException("/ by zero")
// else
// Polynomial(
// coefficients
// .mapValues { it.value / other },
// toCheckInput = false
// )
//public fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, args: Map<Symbol, C>): LabeledPolynomial<C> = ring {
// if (coefficients.isEmpty()) return this@substitute
// LabeledPolynomial<C>(
// buildMap {
// coefficients.forEach { (degs, c) ->
// val newDegs = degs.filterKeys { it !in args }
// val newC = degs.entries.asSequence().filter { it.key in args }.fold(c) { acc, (variable, deg) ->
// multiplyWithPower(acc, args[variable]!!, deg)
// }
// this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
// }
// }
// )
//}
//
//// TODO: Replace with optimisation: the [result] may be unboxed, and all operations may be performed as soon as
//// possible on it
//@JvmName("substitutePolynomial")
//fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, arg: Map<Symbol, LabeledPolynomial<C>>) : LabeledPolynomial<C> =
// ring.labeledPolynomial {
// if (coefficients.isEmpty()) return zero
// coefficients
// .asSequence()
// .map { (degs, c) ->
// degs.entries
// .asSequence()
// .filter { it.key in arg }
// .fold(LabeledPolynomial(mapOf(degs.filterKeys { it !in arg } to c))) { acc, (index, deg) ->
// multiplyWithPower(acc, arg[index]!!, deg)
// }
// }
// .reduce { acc, polynomial -> acc + polynomial } // TODO: Rewrite. Might be slow.
// }
//
//// TODO: Substitute rational function
//
//fun <C, A : Ring<C>> LabeledPolynomial<C>.asFunctionOver(ring: A): (Map<Symbol, C>) -> LabeledPolynomial<C> =
// { substitute(ring, it) }
//
//fun <C, A : Ring<C>> LabeledPolynomial<C>.asPolynomialFunctionOver(ring: A): (Map<Symbol, LabeledPolynomial<C>>) -> LabeledPolynomial<C> =
// { substitute(ring, it) }
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
algebra: A,
variable: Symbol,
): LabeledPolynomial<C> = algebra {
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (variable !in degs) return@forEach
put(
buildMap {
degs.forEach { (vari, deg) ->
when {
vari != variable -> put(vari, deg)
deg > 1u -> put(vari, deg - 1u)
}
}
},
multiplyByDoubling(c, degs[variable]!!)
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
algebra: A,
variables: Collection<Symbol>,
): LabeledPolynomial<C> = algebra {
val cleanedVariables = variables.toSet()
if (cleanedVariables.isEmpty()) return this@derivativeWithRespectTo
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (!degs.keys.containsAll(cleanedVariables)) return@forEach
put(
buildMap {
degs.forEach { (vari, deg) ->
when {
vari !in cleanedVariables -> put(vari, deg)
deg > 1u -> put(vari, deg - 1u)
}
}
},
cleanedVariables.fold(c) { acc, variable -> multiplyByDoubling(acc, degs[variable]!!) }
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
algebra: A,
variable: Symbol,
order: UInt
): LabeledPolynomial<C> = algebra {
if (order == 0u) return this@nthDerivativeWithRespectTo
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (degs.getOrElse(variable) { 0u } < order) return@forEach
put(
buildMap {
degs.forEach { (vari, deg) ->
when {
vari != variable -> put(vari, deg)
deg > order -> put(vari, deg - order)
}
}
},
degs[variable]!!.let { deg ->
(deg downTo deg - order + 1u)
.fold(c) { acc, ord -> multiplyByDoubling(acc, ord) }
}
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
algebra: A,
variablesAndOrders: Map<Symbol, UInt>,
): LabeledPolynomial<C> = algebra {
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (filteredVariablesAndOrders.any { (variable, order) -> degs.getOrElse(variable) { 0u } < order }) return@forEach
put(
buildMap {
degs.forEach { (vari, deg) ->
if (vari !in filteredVariablesAndOrders) put(vari, deg)
else {
val order = filteredVariablesAndOrders[vari]!!
if (deg > order) put(vari, deg - order)
}
}
},
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
degs[index]!!.let { deg ->
(deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) }
}
}
)
}
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
algebra: A,
variable: Symbol,
): LabeledPolynomial<C> = algebra {
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
put(variable, 1u)
for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
}
put(
newDegs,
c / multiplyByDoubling(one, newDegs[variable]!!)
)
}
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
algebra: A,
variables: Collection<Symbol>,
): LabeledPolynomial<C> = algebra {
val cleanedVariables = variables.toSet()
if (cleanedVariables.isEmpty()) return this@antiderivativeWithRespectTo
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
for (variable in cleanedVariables) put(variable, 1u)
for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
}
put(
newDegs,
cleanedVariables.fold(c) { acc, variable -> acc / multiplyByDoubling(one, newDegs[variable]!!) }
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
algebra: A,
variable: Symbol,
order: UInt
): LabeledPolynomial<C> = algebra {
if (order == 0u) return this@nthAntiderivativeWithRespectTo
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
put(variable, order)
for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
}
put(
newDegs,
newDegs[variable]!!.let { deg ->
(deg downTo deg - order + 1u)
.fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) }
}
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
algebra: A,
variablesAndOrders: Map<Symbol, UInt>,
): LabeledPolynomial<C> = algebra {
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
LabeledPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
for ((variable, order) in filteredVariablesAndOrders) put(variable, order)
for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
}
put(
newDegs,
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
newDegs[index]!!.let { deg ->
(deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) }
}
}
)
}
}
)
}

33
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@ -1,33 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.operations.Ring
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
/**
* Creates a [LabeledRationalFunctionSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.labeledRationalFunction(): LabeledRationalFunctionSpace<C, A> =
LabeledRationalFunctionSpace(this)
/**
* Creates a [LabeledRationalFunctionSpace]'s scope over a received ring.
*/
public inline fun <C, A : Ring<C>, R> A.labeledRationalFunction(block: LabeledRationalFunctionSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return LabeledRationalFunctionSpace(this).block()
}
//fun <T: Field<T>> LabeledRationalFunction<T>.reduced(): LabeledRationalFunction<T> {
// val greatestCommonDivider = polynomialGCD(numerator, denominator)
// return LabeledRationalFunction(
// numerator / greatestCommonDivider,
// denominator / greatestCommonDivider
// )
//}

61
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@ -3,58 +3,95 @@
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.operations.Ring
/**
* Returns a [ListPolynomial] instance with given [coefficients]. The collection of coefficients will be reversed if
* [reverse] parameter is true.
* Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed
* if [reverse] parameter is true.
*/
@Suppress("FunctionName")
public fun <C> ListPolynomial(coefficients: List<C>, reverse: Boolean = false): ListPolynomial<C> =
ListPolynomial(with(coefficients) { if (reverse) reversed() else this })
/**
* Returns a [ListPolynomial] instance with given [coefficients]. The collection of coefficients will be reversed if
* [reverse] parameter is true.
* Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed
* if [reverse] parameter is true.
*/
@Suppress("FunctionName")
public fun <C> ListPolynomial(vararg coefficients: C, reverse: Boolean = false): ListPolynomial<C> =
ListPolynomial(with(coefficients) { if (reverse) reversed() else toList() })
/**
* Represents [this] constant as a [ListPolynomial].
*/
public fun <C> C.asListPolynomial() : ListPolynomial<C> = ListPolynomial(listOf(this))
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
/**
* Constructs [ListRationalFunction] instance with numerator and denominator constructed with provided
* [numeratorCoefficients] and [denominatorCoefficients]. The both collections of coefficients will be reversed if
* [reverse] parameter is true.
*/
@Suppress("FunctionName")
public fun <C> ListRationalFunction(numeratorCoefficients: List<C>, denominatorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
ListRationalFunction<C>(
ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
ListPolynomial( with(denominatorCoefficients) { if (reverse) reversed() else this } )
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
ListRationalFunction<C>(numerator, polynomialOne)
/**
* Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator.
*/
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
ListRationalFunction<C>(numerator, ListPolynomial(listOf(one)))
/**
* Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator.
*/
@Suppress("FunctionName")
public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
ListRationalFunction<C>(
ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
polynomialOne
)
public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
ListRationalFunction<C>(numerator, polynomialOne)
/**
* Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit
* denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true.
*/
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
ListRationalFunction<C>(
ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
ListPolynomial(listOf(one))
)
/**
* Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit
* denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true.
*/
@Suppress("FunctionName")
public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
ListRationalFunction<C>(
ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
polynomialOne
)
/**
* Represents [this] constant as a rational function.
*/ // FIXME: When context receivers will be ready, delete this function and uncomment the following two
public fun <C, A: Ring<C>> C.asListRationalFunction(ring: A) : ListRationalFunction<C> = ring.ListRationalFunction(asListPolynomial())
///**
// * Represents [this] constant as a rational function.
// */
//context(A)
//public fun <C, A: Ring<C>> C.asListRationalFunction() : ListRationalFunction<C> = ListRationalFunction(asListPolynomial())
///**
// * Represents [this] constant as a rational function.
// */
//context(ListRationalFunctionSpace<C, A>)
//public fun <C, A: Ring<C>> C.asListRationalFunction() : ListRationalFunction<C> = ListRationalFunction(asListPolynomial())

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@ -1,233 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.*
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.math.max
import kotlin.math.min
import kotlin.math.pow
/**
* Removes zeros on the end of the coefficient list of polynomial.
*/
//context(PolynomialSpace<C, A>)
//fun <C, A: Ring<C>> Polynomial<C>.removeZeros() : Polynomial<C> =
// if (degree > -1) Polynomial(coefficients.subList(0, degree + 1)) else zero
/**
* Creates a [ListPolynomialSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.listPolynomial(): ListPolynomialSpace<C, A> =
ListPolynomialSpace(this)
/**
* Creates a [ListPolynomialSpace]'s scope over a received ring.
*/
public inline fun <C, A : Ring<C>, R> A.listPolynomial(block: ListPolynomialSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return ListPolynomialSpace(this).block()
}
/**
* Creates a [ScalableListPolynomialSpace] over a received scalable ring.
*/
public fun <C, A> A.scalableListPolynomial(): ScalableListPolynomialSpace<C, A> where A : Ring<C>, A : ScaleOperations<C> =
ScalableListPolynomialSpace(this)
/**
* Creates a [ScalableListPolynomialSpace]'s scope over a received scalable ring.
*/
public inline fun <C, A, R> A.scalableListPolynomial(block: ScalableListPolynomialSpace<C, A>.() -> R): R where A : Ring<C>, A : ScaleOperations<C> {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return ScalableListPolynomialSpace(this).block()
}
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> copyTo(
origin: List<C>,
originDegree: Int,
target: MutableList<C>,
) {
for (deg in 0 .. originDegree) target[deg] = origin[deg]
}
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingToUpdater(
ring: Ring<C>,
multiplicand: MutableList<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
updater: MutableList<C>,
zero: C,
) {
multiplyAddingTo(
ring = ring,
multiplicand = multiplicand,
multiplicandDegree = multiplicandDegree,
multiplier = multiplier,
multiplierDegree = multiplierDegree,
target = updater
)
for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
multiplicand[updateDeg] = updater[updateDeg]
updater[updateDeg] = zero
}
}
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingTo(
ring: Ring<C>,
multiplicand: List<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
target: MutableList<C>
) = ring {
for (d in 0 .. multiplicandDegree + multiplierDegree)
for (k in max(0, d - multiplierDegree)..min(multiplicandDegree, d))
target[d] += multiplicand[k] * multiplier[d - k]
}
/**
* Evaluates the value of the given double polynomial for given double argument.
*/
public fun ListPolynomial<Double>.substitute(arg: Double): Double =
coefficients.reduceIndexedOrNull { index, acc, c ->
acc + c * arg.pow(index)
} ?: .0
/**
* Evaluates the value of the given polynomial for given argument.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/
public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
if (coefficients.isEmpty()) return@ring zero
var result: C = coefficients.last()
for (j in coefficients.size - 2 downTo 0) {
result = (arg * result) + coefficients[j]
}
return result
}
public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> = ring {
if (coefficients.isEmpty()) return ListPolynomial(emptyList())
val thisDegree = coefficients.lastIndex
if (thisDegree == -1) return ListPolynomial(emptyList())
val argDegree = arg.coefficients.lastIndex
if (argDegree == -1) return coefficients[0].asListPolynomial()
val constantZero = zero
val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
resultCoefs[0] = coefficients[thisDegree]
val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
var resultDegree = 0
for (deg in thisDegree - 1 downTo 0) {
resultCoefsUpdate[0] = coefficients[deg]
multiplyAddingToUpdater(
ring = ring,
multiplicand = resultCoefs,
multiplicandDegree = resultDegree,
multiplier = arg.coefficients,
multiplierDegree = argDegree,
updater = resultCoefsUpdate,
zero = constantZero
)
resultDegree += argDegree
}
return ListPolynomial<C>(resultCoefs)
}
/**
* Represent the polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListPolynomial<C>.asFunction(ring: A): (C) -> C = { substitute(ring, it) }
/**
* Represent the polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListPolynomial<C>.asPolynomialFunctionOver(ring: A): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.derivative(
algebra: A,
): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = algebra {
ListPolynomial(
buildList(max(0, coefficients.size - 1)) {
for (deg in 1 .. coefficients.lastIndex) add(number(deg) * coefficients[deg])
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.nthDerivative(
algebra: A,
order: Int,
): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = algebra {
require(order >= 0) { "Order of derivative must be non-negative" }
ListPolynomial(
buildList(max(0, coefficients.size - order)) {
for (deg in order.. coefficients.lastIndex)
add((deg - order + 1 .. deg).fold(coefficients[deg]) { acc, d -> acc * number(d) })
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.antiderivative(
algebra: A,
): ListPolynomial<C> where A : Field<C>, A : NumericAlgebra<C> = algebra {
ListPolynomial(
buildList(coefficients.size + 1) {
add(zero)
coefficients.mapIndexedTo(this) { index, t -> t / number(index + 1) }
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.nthAntiderivative(
algebra: A,
order: Int,
): ListPolynomial<C> where A : Field<C>, A : NumericAlgebra<C> = algebra {
require(order >= 0) { "Order of antiderivative must be non-negative" }
ListPolynomial(
buildList(coefficients.size + order) {
repeat(order) { add(zero) }
coefficients.mapIndexedTo(this) { index, c -> (1..order).fold(c) { acc, i -> acc / number(index + i) } }
}
)
}
/**
* Compute a definite integral of a given polynomial in a [range]
*/
@UnstableKMathAPI
public fun <C : Comparable<C>> ListPolynomial<C>.integrate(
algebra: Field<C>,
range: ClosedRange<C>,
): C = algebra {
val integral = antiderivative(algebra)
integral.substitute(algebra, range.endInclusive) - integral.substitute(algebra, range.start)
}

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@ -0,0 +1,268 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.*
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.math.max
import kotlin.math.pow
/**
* Creates a [ListPolynomialSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.listPolynomialSpace(): ListPolynomialSpace<C, A> =
ListPolynomialSpace(this)
/**
* Creates a [ListPolynomialSpace]'s scope over a received ring.
*/ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block]
public inline fun <C, A : Ring<C>, R> A.listPolynomialSpace(block: ListPolynomialSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return ListPolynomialSpace(this).block()
}
/**
* Creates a [ScalableListPolynomialSpace] over a received scalable ring.
*/
public fun <C, A> A.scalableListPolynomialSpace(): ScalableListPolynomialSpace<C, A> where A : Ring<C>, A : ScaleOperations<C> =
ScalableListPolynomialSpace(this)
/**
* Creates a [ScalableListPolynomialSpace]'s scope over a received scalable ring.
*/ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block]
public inline fun <C, A, R> A.scalableListPolynomialSpace(block: ScalableListPolynomialSpace<C, A>.() -> R): R where A : Ring<C>, A : ScaleOperations<C> {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return ScalableListPolynomialSpace(this).block()
}
/**
* Creates a [ListRationalFunctionSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.listRationalFunctionSpace(): ListRationalFunctionSpace<C, A> =
ListRationalFunctionSpace(this)
/**
* Creates a [ListRationalFunctionSpace]'s scope over a received ring.
*/ // TODO: When context will be ready move [ListRationalFunctionSpace] and add [A] to context receivers of [block]
public inline fun <C, A : Ring<C>, R> A.listRationalFunctionSpace(block: ListRationalFunctionSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return ListRationalFunctionSpace(this).block()
}
/**
* Evaluates value of [this] Double polynomial on provided Double argument.
*/
public fun ListPolynomial<Double>.substitute(arg: Double): Double =
coefficients.reduceIndexedOrNull { index, acc, c ->
acc + c * arg.pow(index)
} ?: .0
/**
* Evaluates value of [this] polynomial on provided argument.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/
public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
if (coefficients.isEmpty()) return zero
var result: C = coefficients.last()
for (j in coefficients.size - 2 downTo 0) {
result = (arg * result) + coefficients[j]
}
return result
}
/**
* Substitutes provided polynomial [arg] into [this] polynomial.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/ // TODO: To optimize boxing
public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> =
ring.listPolynomialSpace {
if (coefficients.isEmpty()) return zero
var result: ListPolynomial<C> = coefficients.last().asPolynomial()
for (j in coefficients.size - 2 downTo 0) {
result = (arg * result) + coefficients[j]
}
return result
}
/**
* Substitutes provided rational function [arg] into [this] polynomial.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/ // TODO: To optimize boxing
public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListRationalFunction<C>) : ListRationalFunction<C> =
ring.listRationalFunctionSpace {
if (coefficients.isEmpty()) return zero
var result: ListRationalFunction<C> = coefficients.last().asRationalFunction()
for (j in coefficients.size - 2 downTo 0) {
result = (arg * result) + coefficients[j]
}
return result
}
/**
* Evaluates value of [this] Double rational function in provided Double argument.
*/
public fun ListRationalFunction<Double>.substitute(arg: Double): Double =
numerator.substitute(arg) / denominator.substitute(arg)
/**
* Evaluates value of [this] polynomial for provided argument.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/
public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
}
/**
* Substitutes provided polynomial [arg] into [this] rational function.
*/ // TODO: To optimize boxing
public fun <C> ListRationalFunction<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListRationalFunction<C> =
ring.listRationalFunctionSpace {
numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
}
/**
* Substitutes provided rational function [arg] into [this] rational function.
*/ // TODO: To optimize boxing
public fun <C> ListRationalFunction<C>.substitute(ring: Ring<C>, arg: ListRationalFunction<C>) : ListRationalFunction<C> =
ring.listRationalFunctionSpace {
numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
}
/**
* Represent [this] polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListPolynomial<C>.asPolynomialFunctionOver(ring: A): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
/**
* Represent [this] polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfRationalFunctionOver(ring: A): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
/**
* Represent [this] rational function as a regular context-less function.
*/
public fun <C, A : Field<C>> ListRationalFunction<C>.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) }
/**
* Represent [this] rational function as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListRationalFunction<C>.asPolynomialFunctionOver(ring: A): (ListPolynomial<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
/**
* Represent [this] rational function as a regular context-less function.
*/
public fun <C, A : Ring<C>> ListRationalFunction<C>.asFunctionOfRationalFunctionOver(ring: A): (ListPolynomial<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.derivative(
ring: A,
): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = ring {
ListPolynomial(
buildList(max(0, coefficients.size - 1)) {
for (deg in 1 .. coefficients.lastIndex) add(number(deg) * coefficients[deg])
}
)
}
/**
* Returns algebraic derivative of received polynomial of specified [order]. The [order] should be non-negative integer.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.nthDerivative(
ring: A,
order: Int,
): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = ring {
require(order >= 0) { "Order of derivative must be non-negative" }
ListPolynomial(
buildList(max(0, coefficients.size - order)) {
for (deg in order.. coefficients.lastIndex)
add((deg - order + 1 .. deg).fold(coefficients[deg]) { acc, d -> acc * number(d) })
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.antiderivative(
ring: A,
): ListPolynomial<C> where A : Field<C>, A : NumericAlgebra<C> = ring {
ListPolynomial(
buildList(coefficients.size + 1) {
add(zero)
coefficients.mapIndexedTo(this) { index, t -> t / number(index + 1) }
}
)
}
/**
* Returns algebraic antiderivative of received polynomial of specified [order]. The [order] should be non-negative integer.
*/
@UnstableKMathAPI
public fun <C, A> ListPolynomial<C>.nthAntiderivative(
ring: A,
order: Int,
): ListPolynomial<C> where A : Field<C>, A : NumericAlgebra<C> = ring {
require(order >= 0) { "Order of antiderivative must be non-negative" }
ListPolynomial(
buildList(coefficients.size + order) {
repeat(order) { add(zero) }
coefficients.mapIndexedTo(this) { index, c -> (1..order).fold(c) { acc, i -> acc / number(index + i) } }
}
)
}
/**
* Computes a definite integral of [this] polynomial in the specified [range].
*/
@UnstableKMathAPI
public fun <C : Comparable<C>> ListPolynomial<C>.integrate(
ring: Field<C>,
range: ClosedRange<C>,
): C = ring {
val antiderivative = antiderivative(ring)
antiderivative.substitute(ring, range.endInclusive) - antiderivative.substitute(ring, range.start)
}
/**
* Returns algebraic derivative of received rational function.
*/
@UnstableKMathAPI
public fun <C, A> ListRationalFunction<C>.derivative(
ring: A,
): ListRationalFunction<C> where A : Ring<C>, A : NumericAlgebra<C> = ring.listRationalFunctionSpace {
ListRationalFunction(
numerator.derivative(ring) * denominator - numerator * denominator.derivative(ring),
denominator * denominator
)
}
/**
* Returns algebraic derivative of received rational function of specified [order]. The [order] should be non-negative integer.
*/
@UnstableKMathAPI
public tailrec fun <C, A> ListRationalFunction<C>.nthDerivative(
ring: A,
order: Int,
): ListRationalFunction<C> where A : Ring<C>, A : NumericAlgebra<C> =
if (order == 0) this else derivative(ring).nthDerivative(ring, order - 1)

129
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listRationalFunctionUtil.kt → kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listUtilOptimized.kt
View File

@ -5,41 +5,91 @@
package space.kscience.kmath.functions
import space.kscience.kmath.operations.Field
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.invoke
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.math.max
import kotlin.math.min
/**
* Creates a [ListRationalFunctionSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.listRationalFunction(): ListRationalFunctionSpace<C, A> =
ListRationalFunctionSpace(this)
/**
* Creates a [ListRationalFunctionSpace]'s scope over a received ring.
*/
public inline fun <C, A : Ring<C>, R> A.listRationalFunction(block: ListRationalFunctionSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return ListRationalFunctionSpace(this).block()
// TODO: Optimized copies of substitution and invocation
@UnstablePolynomialBoxingOptimization
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> copyTo(
origin: List<C>,
originDegree: Int,
target: MutableList<C>,
) {
for (deg in 0 .. originDegree) target[deg] = origin[deg]
}
/**
* Evaluates the value of the given double polynomial for given double argument.
*/
public fun ListRationalFunction<Double>.substitute(arg: Double): Double =
numerator.substitute(arg) / denominator.substitute(arg)
@UnstablePolynomialBoxingOptimization
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingToUpdater(
ring: Ring<C>,
multiplicand: MutableList<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
updater: MutableList<C>,
zero: C,
) {
multiplyAddingTo(
ring = ring,
multiplicand = multiplicand,
multiplicandDegree = multiplicandDegree,
multiplier = multiplier,
multiplierDegree = multiplierDegree,
target = updater
)
for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
multiplicand[updateDeg] = updater[updateDeg]
updater[updateDeg] = zero
}
}
/**
* Evaluates the value of the given polynomial for given argument.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/
public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
@UnstablePolynomialBoxingOptimization
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingTo(
ring: Ring<C>,
multiplicand: List<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
target: MutableList<C>
) = ring {
for (d in 0 .. multiplicandDegree + multiplierDegree)
for (k in max(0, d - multiplierDegree)..min(multiplicandDegree, d))
target[d] += multiplicand[k] * multiplier[d - k]
}
@UnstablePolynomialBoxingOptimization
public fun <C> ListPolynomial<C>.substitute2(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> = ring {
if (coefficients.isEmpty()) return ListPolynomial(emptyList())
val thisDegree = coefficients.lastIndex
if (thisDegree == -1) return ListPolynomial(emptyList())
val argDegree = arg.coefficients.lastIndex
if (argDegree == -1) return coefficients[0].asListPolynomial()
val constantZero = zero
val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
resultCoefs[0] = coefficients[thisDegree]
val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
var resultDegree = 0
for (deg in thisDegree - 1 downTo 0) {
resultCoefsUpdate[0] = coefficients[deg]
multiplyAddingToUpdater(
ring = ring,
multiplicand = resultCoefs,
multiplicandDegree = resultDegree,
multiplier = arg.coefficients,
multiplierDegree = argDegree,
updater = resultCoefsUpdate,
zero = constantZero
)
resultDegree += argDegree
}
return ListPolynomial<C>(resultCoefs)
}
/**
@ -52,6 +102,7 @@ public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = r
*
* Used in [ListPolynomial.substitute] and [ListRationalFunction.substitute] for performance optimisation.
*/ // TODO: Дописать
@UnstablePolynomialBoxingOptimization
internal fun <C> ListPolynomial<C>.substituteRationalFunctionTakeNumerator(ring: Ring<C>, arg: ListRationalFunction<C>): ListPolynomial<C> = ring {
if (coefficients.isEmpty()) return ListPolynomial(emptyList())
@ -196,26 +247,4 @@ internal fun <C> ListPolynomial<C>.substituteRationalFunctionTakeNumerator(ring:
end = thisDegree + 1
)
)
}
//operator fun <T: Field<T>> RationalFunction<T>.invoke(arg: T): T = numerator(arg) / denominator(arg)
//
//fun <T: Field<T>> RationalFunction<T>.reduced(): RationalFunction<T> =
// polynomialGCD(numerator, denominator).let {
// RationalFunction(
// numerator / it,
// denominator / it
// )
// }
///**
// * Returns result of applying formal derivative to the polynomial.
// *
// * @param T Field where we are working now.
// * @return Result of the operator.
// */
//fun <T: Ring<T>> RationalFunction<T>.derivative() =
// RationalFunction(
// numerator.derivative() * denominator - denominator.derivative() * numerator,
// denominator * denominator
// )
}

13
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/misc.kt Normal file
View File

@ -0,0 +1,13 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
@RequiresOptIn(
message = "It's copy of operation with optimized boxing. It's currently unstable.",
level = RequiresOptIn.Level.ERROR
)
internal annotation class UnstablePolynomialBoxingOptimization

195
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedConstructors.kt
View File

@ -1,195 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.Ring
/**
* Returns the same degrees' description of the monomial, but without extra zero degrees on the end.
*/
internal fun List<UInt>.cleanUp() = subList(0, indexOfLast { it != 0U } + 1)
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(coefs, toCheckInput)
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(coefs, toCheckInput)
@Suppress("FunctionName")
internal fun <C, A: Ring<C>> A.NumberedPolynomial(coefs: Map<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> {
if (!toCheckInput) return NumberedPolynomial<C>(coefs)
val fixedCoefs = mutableMapOf<List<UInt>, C>()
for (entry in coefs) {
val key = entry.key.cleanUp()
val value = entry.value
fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
}
return NumberedPolynomial<C>(fixedCoefs)
}
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs, toCheckInput)
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs, toCheckInput)
@Suppress("FunctionName")
internal fun <C, A: Ring<C>> A.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, toCheckInput: Boolean = true) : NumberedPolynomial<C> {
if (!toCheckInput) return NumberedPolynomial<C>(pairs.toMap())
val fixedCoefs = mutableMapOf<List<UInt>, C>()
for (entry in pairs) {
val key = entry.first.cleanUp()
val value = entry.second
fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
}
return NumberedPolynomial<C>(fixedCoefs)
}
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs = pairs, toCheckInput = toCheckInput)
@Suppress("FunctionName", "NOTHING_TO_INLINE")
internal inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs = pairs, toCheckInput = toCheckInput)
@Suppress("FunctionName")
internal fun <C, A: Ring<C>> A.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> {
if (!toCheckInput) return NumberedPolynomial<C>(pairs.toMap())
val fixedCoefs = mutableMapOf<List<UInt>, C>()
for (entry in pairs) {
val key = entry.first.cleanUp()
val value = entry.second
fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
}
return NumberedPolynomial<C>(fixedCoefs)
}
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs, toCheckInput = true)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs, toCheckInput = true)
public fun <C> C.asNumberedPolynomial() : NumberedPolynomial<C> = NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this))
@DslMarker
@UnstableKMathAPI
internal annotation class NumberedPolynomialConstructorDSL
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL
public class NumberedPolynomialTermSignatureBuilder {
private val signature: MutableList<UInt> = ArrayList()
public fun build(): List<UInt> = signature
public infix fun Int.inPowerOf(deg: UInt) {
if (this > signature.lastIndex) {
signature.addAll(List(this - signature.lastIndex - 1) { 0u })
signature.add(deg)
} else {
signature[this] = deg
}
}
@Suppress("NOTHING_TO_INLINE")
public inline infix fun Int.pow(deg: UInt): Unit = this inPowerOf deg
@Suppress("NOTHING_TO_INLINE")
public inline infix fun Int.`in`(deg: UInt): Unit = this inPowerOf deg
@Suppress("NOTHING_TO_INLINE")
public inline infix fun Int.of(deg: UInt): Unit = this inPowerOf deg
}
@UnstableKMathAPI
public class NumberedPolynomialBuilder<C>(private val zero: C, private val add: (C, C) -> C, capacity: Int = 0) {
private val coefficients: MutableMap<List<UInt>, C> = LinkedHashMap(capacity)
public fun build(): NumberedPolynomial<C> = NumberedPolynomial<C>(coefficients)
public operator fun C.invoke(block: NumberedPolynomialTermSignatureBuilder.() -> Unit) {
val signature = NumberedPolynomialTermSignatureBuilder().apply(block).build()
coefficients[signature] = add(coefficients.getOrElse(signature) { zero }, this@invoke)
}
@Suppress("NOTHING_TO_INLINE")
public inline infix fun C.with(noinline block: NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block)
@Suppress("NOTHING_TO_INLINE")
public inline infix fun (NumberedPolynomialTermSignatureBuilder.() -> Unit).with(coef: C): Unit = coef.invoke(this)
@Suppress("NOTHING_TO_INLINE")
public infix fun sig(block: NumberedPolynomialTermSignatureBuilder.() -> Unit): NumberedPolynomialTermSignatureBuilder.() -> Unit = block
}
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> A.NumberedPolynomial(block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(zero, ::add).apply(block).build()
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> A.NumberedPolynomial(capacity: Int, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(zero, ::add, capacity).apply(block).build()
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(constantZero, { left: C, right: C -> left + right}).apply(block).build()
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL
@Suppress("FunctionName")
public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(capacity: Int, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(constantZero, { left: C, right: C -> left + right}, capacity).apply(block).build()
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
NumberedPolynomial(denominatorCoefficients, toCheckInput = true)
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
NumberedPolynomial(denominatorCoefficients, toCheckInput = true)
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(numerator, polynomialOne)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(numerator, NumberedPolynomial(mapOf(emptyList<UInt>() to one), toCheckInput = false))
@Suppress("FunctionName")
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
polynomialOne
)
@Suppress("FunctionName")
public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
NumberedPolynomial(mapOf(emptyList<UInt>() to one), toCheckInput = false)
)
//context(A)
//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> = NumberedRationalFunction(asLabeledPolynomial())
//context(NumberedRationalFunctionSpace<C, A>)
//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> = NumberedRationalFunction(asLabeledPolynomial())

528
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedPolynomialUtil.kt
View File

@ -1,528 +0,0 @@
package space.kscience.kmath.functions
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.*
import kotlin.contracts.*
import kotlin.jvm.JvmName
import kotlin.math.max
// TODO: Docs
/**
* Creates a [NumberedPolynomialSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.numberedPolynomial(): NumberedPolynomialSpace<C, A> =
NumberedPolynomialSpace(this)
/**
* Creates a [NumberedPolynomialSpace]'s scope over a received ring.
*/
@OptIn(ExperimentalContracts::class)
public inline fun <C, A : Ring<C>, R> A.numberedPolynomial(block: NumberedPolynomialSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return NumberedPolynomialSpace(this).block()
}
///**
// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`.
// * Consider that monomials are sorted in lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.represent(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
// coefficients.entries
// .sortedWith { o1, o2 -> NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .mapIndexed { index, deg ->
// when (deg) {
// 0U -> ""
// 1U -> "${withVariableName}_${index+1}"
// else -> "${withVariableName}_${index+1}^$deg"
// }
// }
// .filter { it.isNotEmpty() }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer].
// * Consider that monomials are sorted in lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.represent(namer: (Int) -> String): String =
// coefficients.entries
// .sortedWith { o1, o2 -> NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .mapIndexed { index, deg ->
// when (deg) {
// 0U -> ""
// 1U -> namer(index)
// else -> "${namer(index)}^$deg"
// }
// }
// .filter { it.isNotEmpty() }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`
// * and with brackets around the string if needed (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representWithBrackets(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
// with(represent(withVariableName)) { if (coefficients.count() == 1) this else "($this)" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
// * (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representWithBrackets(namer: (Int) -> String): String =
// with(represent(namer)) { if (coefficients.count() == 1) this else "($this)" }
//
///**
// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`.
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversed(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
// coefficients.entries
// .sortedWith { o1, o2 -> -NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .mapIndexed { index, deg ->
// when (deg) {
// 0U -> ""
// 1U -> "${withVariableName}_${index+1}"
// else -> "${withVariableName}_${index+1}^$deg"
// }
// }
// .filter { it.isNotEmpty() }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer].
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversed(namer: (Int) -> String): String =
// coefficients.entries
// .sortedWith { o1, o2 -> -NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
// .asSequence()
// .map { (degs, t) ->
// if (degs.isEmpty()) "$t"
// else {
// when {
// t.isOne() -> ""
// t.isMinusOne() -> "-"
// else -> "$t "
// } +
// degs
// .mapIndexed { index, deg ->
// when (deg) {
// 0U -> ""
// 1U -> namer(index)
// else -> "${namer(index)}^$deg"
// }
// }
// .filter { it.isNotEmpty() }
// .joinToString(separator = " ") { it }
// }
// }
// .joinToString(separator = " + ") { it }
// .ifEmpty { "0" }
//
///**
// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`
// * and with brackets around the string if needed (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversedWithBrackets(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
// with(representReversed(withVariableName)) { if (coefficients.count() == 1) this else "($this)" }
//
///**
// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
// * (i.e. when there are at least two addends in the representation).
// * Consider that monomials are sorted in **reversed** lexicographic order.
// */
//context(NumberedPolynomialSpace<C, A>)
//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversedWithBrackets(namer: (Int) -> String): String =
// with(representReversed(namer)) { if (coefficients.count() == 1) this else "($this)" }
//public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>): NumberedPolynomial<C> = ring {
// if (coefficients.isEmpty()) return this@substitute
// NumberedPolynomial<C>(
// buildMap {
// coefficients.forEach { (degs, c) ->
// val newDegs = degs.mapIndexed { index, deg -> if (index in args) 0U else deg }.cleanUp()
// val newC = degs.foldIndexed(c) { index, acc, deg ->
// if (index in args) multiplyWithPower(acc, args[index]!!, deg)
// else acc
// }
// this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
// }
// }
// )
//}
//
//// TODO: Replace with optimisation: the [result] may be unboxed, and all operations may be performed as soon as
//// possible on it
//@JvmName("substitutePolynomial")
//public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, arg: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> =
// ring.numberedPolynomialSpace {
// if (coefficients.isEmpty()) return zero
// coefficients
// .asSequence()
// .map { (degs, c) ->
// degs.foldIndexed(
// NumberedPolynomial(
// degs.mapIndexed { index, deg -> if (index in arg) 0U else deg } to c
// )
// ) { index, acc, deg -> if (index in arg) multiplyWithPower(acc, arg[index]!!, deg) else acc }
// }
// .reduce { acc, polynomial -> acc + polynomial } // TODO: Rewrite. Might be slow.
// }
//
//// TODO: Substitute rational function
//
//public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunctionOver(ring: A): (Map<Int, C>) -> NumberedPolynomial<C> =
// { substitute(ring, it) }
//
//public fun <C, A : Ring<C>> NumberedPolynomial<C>.asPolynomialFunctionOver(ring: A): (Map<Int, NumberedPolynomial<C>>) -> NumberedPolynomial<C> =
// { substitute(ring, it) }
//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
// if (other.isZero()) throw ArithmeticException("/ by zero")
// else
// Polynomial(
// coefficients
// .mapValues { it.value / other },
// toCheckInput = false
// )
/**
* Evaluates the value of the given double polynomial for given double argument.
*/
public fun NumberedPolynomial<Double>.substitute(args: Map<Int, Double>): NumberedPolynomial<Double> = Double.algebra {
val acc = LinkedHashMap<List<UInt>, Double>(coefficients.size)
for ((degs, c) in coefficients) {
val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
val newC = args.entries.fold(c) { product, (variable, substitution) ->
val deg = degs.getOrElse(variable) { 0u }
if (deg == 0u) product else product * substitution.pow(deg.toInt())
}
if (newDegs !in acc) acc[newDegs] = newC
else acc[newDegs] = acc[newDegs]!! + newC
}
return NumberedPolynomial<Double>(acc)
}
/**
* Evaluates the value of the given polynomial for given argument.
*
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
*/
public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>): NumberedPolynomial<C> = ring {
val acc = LinkedHashMap<List<UInt>, C>(coefficients.size)
for ((degs, c) in coefficients) {
val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
val newC = args.entries.fold(c) { product, (variable, substitution) ->
val deg = degs.getOrElse(variable) { 0u }
if (deg == 0u) product else product * power(substitution, deg)
}
if (newDegs !in acc) acc[newDegs] = newC
else acc[newDegs] = acc[newDegs]!! + newC
}
return NumberedPolynomial<C>(acc)
}
// TODO: (Waiting for hero) Replace with optimisation: the [result] may be unboxed, and all operations may be performed
// as soon as possible on it
@JvmName("substitutePolynomial")
public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> = TODO() /*ring.numberedPolynomial {
val acc = LinkedHashMap<List<UInt>, NumberedPolynomial<C>>(coefficients.size)
for ((degs, c) in coefficients) {
val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
val newC = args.entries.fold(c.asNumberedPolynomial()) { product, (variable, substitution) ->
val deg = degs.getOrElse(variable) { 0u }
if (deg == 0u) product else product * power(substitution, deg)
}
if (newDegs !in acc) acc[newDegs] = c.asNumberedPolynomial()
else acc[newDegs] = acc[newDegs]!! + c
}
}*/
/**
* Represent the polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunction(ring: A): (Map<Int, C>) -> NumberedPolynomial<C> = { substitute(ring, it) }
/**
* Represent the polynomial as a regular context-less function.
*/
public fun <C, A : Ring<C>> NumberedPolynomial<C>.asPolynomialFunctionOver(ring: A): (Map<Int, NumberedPolynomial<C>>) -> NumberedPolynomial<C> = { substitute(ring, it) }
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
algebra: A,
variable: Int,
): NumberedPolynomial<C> = algebra {
NumberedPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (degs.size > variable) return@forEach
put(
degs.mapIndexed { index, deg ->
when {
index != variable -> deg
deg > 0u -> deg - 1u
else -> return@forEach
}
}.cleanUp(),
multiplyByDoubling(c, degs[variable])
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
algebra: A,
variables: Collection<Int>,
): NumberedPolynomial<C> = algebra {
val cleanedVariables = variables.toSet()
if (cleanedVariables.isEmpty()) return this@derivativeWithRespectTo
val maxRespectedVariable = cleanedVariables.maxOrNull()!!
NumberedPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (degs.size > maxRespectedVariable) return@forEach
put(
degs.mapIndexed { index, deg ->
when {
index !in cleanedVariables -> deg
deg > 0u -> deg - 1u
else -> return@forEach
}
}.cleanUp(),
cleanedVariables.fold(c) { acc, variable -> multiplyByDoubling(acc, degs[variable]) }
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
algebra: A,
variable: Int,
order: UInt
): NumberedPolynomial<C> = algebra {
if (order == 0u) return this@nthDerivativeWithRespectTo
NumberedPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (degs.size > variable) return@forEach
put(
degs.mapIndexed { index, deg ->
when {
index != variable -> deg
deg >= order -> deg - order
else -> return@forEach
}
}.cleanUp(),
degs[variable].let { deg ->
(deg downTo deg - order + 1u)
.fold(c) { acc, ord -> multiplyByDoubling(acc, ord) }
}
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
algebra: A,
variablesAndOrders: Map<Int, UInt>,
): NumberedPolynomial<C> = algebra {
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
NumberedPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
if (degs.size > maxRespectedVariable) return@forEach
put(
degs.mapIndexed { index, deg ->
if (index !in filteredVariablesAndOrders) return@mapIndexed deg
val order = filteredVariablesAndOrders[index]!!
if (deg >= order) deg - order else return@forEach
}.cleanUp(),
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
degs[index].let { deg ->
(deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) }
}
}
)
}
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
algebra: A,
variable: Int,
): NumberedPolynomial<C> = algebra {
NumberedPolynomial<C>(
buildMap(coefficients.size) {
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])
)
}
}
)
}
/**
* Returns algebraic antiderivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
algebra: A,
variables: Collection<Int>,
): NumberedPolynomial<C> = algebra {
val cleanedVariables = variables.toSet()
if (cleanedVariables.isEmpty()) return this@antiderivativeWithRespectTo
val maxRespectedVariable = cleanedVariables.maxOrNull()!!
NumberedPolynomial<C>(
buildMap(coefficients.size) {
coefficients
.forEach { (degs, c) ->
put(
List(max(maxRespectedVariable + 1, degs.size)) { if (it !in variables) degs[it] else degs[it] + 1u },
cleanedVariables.fold(c) { acc, variable -> acc / multiplyByDoubling(one, degs[variable]) }
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
algebra: A,
variable: Int,
order: UInt
): NumberedPolynomial<C> = algebra {
if (order == 0u) return this@nthAntiderivativeWithRespectTo
NumberedPolynomial<C>(
buildMap(coefficients.size) {
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)
.fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) }
}
)
}
}
)
}
/**
* Returns algebraic derivative of received polynomial.
*/
@UnstableKMathAPI
public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
algebra: A,
variablesAndOrders: Map<Int, UInt>,
): NumberedPolynomial<C> = algebra {
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
NumberedPolynomial<C>(
buildMap(coefficients.size) {
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) }
}
}
)
}
}
)
}

33
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedRationalFunctionUtil.kt
View File

@ -1,33 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.operations.Ring
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
/**
* Creates a [NumberedRationalFunctionSpace] over a received ring.
*/
public fun <C, A : Ring<C>> A.numberedRationalFunction(): NumberedRationalFunctionSpace<C, A> =
NumberedRationalFunctionSpace(this)
/**
* Creates a [NumberedRationalFunctionSpace]'s scope over a received ring.
*/
public inline fun <C, A : Ring<C>, R> A.numberedRationalFunction(block: NumberedRationalFunctionSpace<C, A>.() -> R): R {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return NumberedRationalFunctionSpace(this).block()
}
//fun <T: Field<T>> NumberedRationalFunction<T>.reduced(): NumberedRationalFunction<T> {
// val greatestCommonDivider = polynomialGCD(numerator, denominator)
// return NumberedRationalFunction(
// numerator / greatestCommonDivider,
// denominator / greatestCommonDivider
// )
//}

32
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialTest.kt
View File

@ -12,7 +12,7 @@ import kotlin.test.*
class ListPolynomialTest {
@Test
fun test_Polynomial_Int_plus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + -3,
@ -52,7 +52,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Int_minus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - -3,
@ -92,7 +92,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Int_times() {
IntModuloRing(35).listPolynomial {
IntModuloRing(35).listPolynomialSpace {
assertEquals(
ListPolynomial(34, 2, 1, 20, 2),
ListPolynomial(22, 26, 13, 15, 26) * 27,
@ -107,7 +107,7 @@ class ListPolynomialTest {
}
@Test
fun test_Int_Polynomial_plus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
-3 + ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
@ -147,7 +147,7 @@ class ListPolynomialTest {
}
@Test
fun test_Int_Polynomial_minus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
3 - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
@ -187,7 +187,7 @@ class ListPolynomialTest {
}
@Test
fun test_Int_Polynomial_times() {
IntModuloRing(35).listPolynomial {
IntModuloRing(35).listPolynomialSpace {
assertEquals(
ListPolynomial(34, 2, 1, 20, 2),
27 * ListPolynomial(22, 26, 13, 15, 26),
@ -202,7 +202,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Constant_plus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + Rational(-3),
@ -242,7 +242,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Constant_minus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - Rational(-3),
@ -282,7 +282,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Constant_times() {
IntModuloRing(35).listPolynomial {
IntModuloRing(35).listPolynomialSpace {
assertEquals(
ListPolynomial(34, 2, 1, 20, 2),
ListPolynomial(22, 26, 13, 15, 26) * 27.asConstant(),
@ -297,7 +297,7 @@ class ListPolynomialTest {
}
@Test
fun test_Constant_Polynomial_plus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
Rational(-3) + ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
@ -337,7 +337,7 @@ class ListPolynomialTest {
}
@Test
fun test_Constant_Polynomial_minus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
Rational(3) - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
@ -377,7 +377,7 @@ class ListPolynomialTest {
}
@Test
fun test_Constant_Polynomial_times() {
IntModuloRing(35).listPolynomial {
IntModuloRing(35).listPolynomialSpace {
assertEquals(
ListPolynomial(34, 2, 1, 20, 2),
27 * ListPolynomial(22, 26, 13, 15, 26),
@ -392,7 +392,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_unaryMinus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
assertEquals(
ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
-ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
@ -407,7 +407,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Polynomial_plus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
// (5/9 - 8/9 x - 8/7 x^2) + (-5/7 + 5/1 x + 5/8 x^2) ?= -10/63 + 37/9 x - 29/56 x^2
assertEquals(
ListPolynomial(Rational(-10, 63), Rational(37, 9), Rational(-29, 56)),
@ -440,7 +440,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Polynomial_minus() {
RationalField.listPolynomial {
RationalField.listPolynomialSpace {
// (5/9 - 8/9 x - 8/7 x^2) - (-5/7 + 5/1 x + 5/8 x^2) ?= 80/63 - 53/9 x - 99/56 x^2
assertEquals(
ListPolynomial(Rational(80, 63), Rational(-53, 9), Rational(-99, 56)),
@ -473,7 +473,7 @@ class ListPolynomialTest {
}
@Test
fun test_Polynomial_Polynomial_times() {
IntModuloRing(35).listPolynomial {
IntModuloRing(35).listPolynomialSpace {
// (1 + x + x^2) * (1 - x + x^2) ?= 1 + x^2 + x^4
assertEquals(
ListPolynomial(1, 0, 1, 0, 1),

2
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialUtilTest.kt
View File

@ -5,6 +5,7 @@
package space.kscience.kmath.functions
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.test.misc.Rational
import space.kscience.kmath.test.misc.RationalField
import kotlin.test.Test
@ -12,6 +13,7 @@ import kotlin.test.assertEquals
import kotlin.test.assertFailsWith
@OptIn(UnstableKMathAPI::class)
class ListPolynomialUtilTest {
@Test
fun test_substitute_Double() {

138
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/IntModulo.kt Normal file
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@ -0,0 +1,138 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.test.misc
import space.kscience.kmath.functions.ListPolynomial
import space.kscience.kmath.functions.ListPolynomialSpace
import space.kscience.kmath.operations.Ring
class IntModulo {
val residue: Int
val modulus: Int
@PublishedApi
internal constructor(residue: Int, modulus: Int, toCheckInput: Boolean = true) {
if (toCheckInput) {
require(modulus != 0) { "modulus can not be zero" }
this.modulus = if (modulus < 0) -modulus else modulus
this.residue = residue.mod(modulus)
} else {
this.residue = residue
this.modulus = modulus
}
}
constructor(residue: Int, modulus: Int) : this(residue, modulus, true)
operator fun unaryPlus(): IntModulo = this
operator fun unaryMinus(): IntModulo =
IntModulo(
if (residue == 0) 0 else modulus - residue,
modulus,
toCheckInput = false
)
operator fun plus(other: IntModulo): IntModulo {
require(modulus == other.modulus) { "can not add two residue different modulo" }
return IntModulo(
(residue + other.residue) % modulus,
modulus,
toCheckInput = false
)
}
operator fun plus(other: Int): IntModulo =
IntModulo(
(residue + other) % modulus,
modulus,
toCheckInput = false
)
operator fun minus(other: IntModulo): IntModulo {
require(modulus == other.modulus) { "can not subtract two residue different modulo" }
return IntModulo(
(residue - other.residue) % modulus,
modulus,
toCheckInput = false
)
}
operator fun minus(other: Int): IntModulo =
IntModulo(
(residue - other) % modulus,
modulus,
toCheckInput = false
)
operator fun times(other: IntModulo): IntModulo {
require(modulus == other.modulus) { "can not multiply two residue different modulo" }
return IntModulo(
(residue * other.residue) % modulus,
modulus,
toCheckInput = false
)
}
operator fun times(other: Int): IntModulo =
IntModulo(
(residue * other) % modulus,
modulus,
toCheckInput = false
)
operator fun div(other: IntModulo): IntModulo {
require(modulus == other.modulus) { "can not divide two residue different modulo" }
val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other.residue, modulus)
require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
return IntModulo(
(residue * reciprocalCandidate) % modulus,
modulus,
toCheckInput = false
)
}
operator fun div(other: Int): IntModulo {
val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other, modulus)
require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
return IntModulo(
(residue * reciprocalCandidate) % modulus,
modulus,
toCheckInput = false
)
}
override fun equals(other: Any?): Boolean =
when (other) {
is IntModulo -> residue == other.residue && modulus == other.modulus
else -> false
}
override fun hashCode(): Int = residue.hashCode()
override fun toString(): String = "$residue mod $modulus"
}
@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
class IntModuloRing : Ring<IntModulo> {
val modulus: Int
constructor(modulus: Int) {
require(modulus != 0) { "modulus can not be zero" }
this.modulus = if (modulus < 0) -modulus else modulus
}
override inline val zero: IntModulo get() = IntModulo(0, modulus, toCheckInput = false)
override inline val one: IntModulo get() = IntModulo(1, modulus, toCheckInput = false)
fun number(arg: Int) = IntModulo(arg, modulus, toCheckInput = false)
override inline fun add(left: IntModulo, right: IntModulo): IntModulo = left + right
override inline fun multiply(left: IntModulo, right: IntModulo): IntModulo = left * right
override inline fun IntModulo.unaryMinus(): IntModulo = -this
override inline fun IntModulo.plus(arg: IntModulo): IntModulo = this + arg
override inline fun IntModulo.minus(arg: IntModulo): IntModulo = this - arg
override inline fun IntModulo.times(arg: IntModulo): IntModulo = this * arg
inline fun IntModulo.div(arg: IntModulo): IntModulo = this / arg
}
fun ListPolynomialSpace<IntModulo, IntModuloRing>.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
ListPolynomial(coefs.map { IntModulo(it, ring.modulus) })
fun IntModuloRing.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
ListPolynomial(coefs.map { IntModulo(it, modulus) })

135
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/Rational.kt Normal file
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@ -0,0 +1,135 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.test.misc
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.Field
import space.kscience.kmath.operations.NumbersAddOps
class Rational {
companion object {
val ZERO: Rational = Rational(0L)
val ONE: Rational = Rational(1L)
}
val numerator: Long
val denominator: Long
internal constructor(numerator: Long, denominator: Long, toCheckInput: Boolean = true) {
if (toCheckInput) {
if (denominator == 0L) throw ArithmeticException("/ by zero")
val greatestCommonDivider = gcd(numerator, denominator).let { if (denominator < 0L) -it else it }
this.numerator = numerator / greatestCommonDivider
this.denominator = denominator / greatestCommonDivider
} else {
this.numerator = numerator
this.denominator = denominator
}
}
constructor(numerator: Int, denominator: Int) : this(numerator.toLong(), denominator.toLong(), true)
constructor(numerator: Int, denominator: Long) : this(numerator.toLong(), denominator, true)
constructor(numerator: Long, denominator: Int) : this(numerator, denominator.toLong(), true)
constructor(numerator: Long, denominator: Long) : this(numerator, denominator, true)
constructor(numerator: Int) : this(numerator.toLong(), 1L, false)
constructor(numerator: Long) : this(numerator, 1L, false)
operator fun unaryPlus(): Rational = this
operator fun unaryMinus(): Rational = Rational(-this.numerator, this.denominator)
operator fun plus(other: Rational): Rational =
Rational(
numerator * other.denominator + denominator * other.numerator,
denominator * other.denominator
)
operator fun plus(other: Int): Rational =
Rational(
numerator + denominator * other.toLong(),
denominator
)
operator fun plus(other: Long): Rational =
Rational(
numerator + denominator * other,
denominator
)
operator fun minus(other: Rational): Rational =
Rational(
numerator * other.denominator - denominator * other.numerator,
denominator * other.denominator
)
operator fun minus(other: Int): Rational =
Rational(
numerator - denominator * other.toLong(),
denominator
)
operator fun minus(other: Long): Rational =
Rational(
numerator - denominator * other,
denominator
)
operator fun times(other: Rational): Rational =
Rational(
numerator * other.numerator,
denominator * other.denominator
)
operator fun times(other: Int): Rational =
Rational(
numerator * other.toLong(),
denominator
)
operator fun times(other: Long): Rational =
Rational(
numerator * other,
denominator
)
operator fun div(other: Rational): Rational =
Rational(
numerator * other.denominator,
denominator * other.numerator
)
operator fun div(other: Int): Rational =
Rational(
numerator,
denominator * other.toLong()
)
operator fun div(other: Long): Rational =
Rational(
numerator,
denominator * other
)
override fun equals(other: Any?): Boolean =
when (other) {
is Rational -> numerator == other.numerator && denominator == other.denominator
is Int -> numerator == other && denominator == 1L
is Long -> numerator == other && denominator == 1L
else -> false
}
override fun hashCode(): Int = 31 * numerator.hashCode() + denominator.hashCode()
override fun toString(): String = if (denominator == 1L) "$numerator" else "$numerator/$denominator"
}
@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
@OptIn(UnstableKMathAPI::class)
object RationalField : Field<Rational>, NumbersAddOps<Rational> {
override inline val zero: Rational get() = Rational.ZERO
override inline val one: Rational get() = Rational.ONE
override inline fun number(value: Number): Rational = Rational(value.toLong())
override inline fun add(left: Rational, right: Rational): Rational = left + right
override inline fun multiply(left: Rational, right: Rational): Rational = left * right
override inline fun divide(left: Rational, right: Rational): Rational = left / right
override inline fun scale(a: Rational, value: Double): Rational = a * number(value)
override inline fun Rational.unaryMinus(): Rational = -this
override inline fun Rational.plus(arg: Rational): Rational = this + arg
override inline fun Rational.minus(arg: Rational): Rational = this - arg
override inline fun Rational.times(arg: Rational): Rational = this * arg
override inline fun Rational.div(arg: Rational): Rational = this / arg
}

29
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/misc.kt Normal file
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@ -0,0 +1,29 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.test.misc
import kotlin.math.abs
data class BezoutIdentityWithGCD<T>(val first: T, val second: T, val gcd: T)
tailrec fun gcd(a: Long, b: Long): Long = if (a == 0L) abs(b) else gcd(b % a, a)
fun bezoutIdentityWithGCD(a: Int, b: Int): BezoutIdentityWithGCD<Int> =
when {
a < 0 && b < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, -second, gcd) }
a < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, second, gcd) }
b < 0 -> with(bezoutIdentityWithGCDInternalLogic(a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(first, -second, gcd) }
else -> bezoutIdentityWithGCDInternalLogic(a, b, 1, 0, 0, 1)
}
internal tailrec fun bezoutIdentityWithGCDInternalLogic(a: Int, b: Int, m1: Int, m2: Int, m3: Int, m4: Int): BezoutIdentityWithGCD<Int> =
if (b == 0) BezoutIdentityWithGCD(m1, m3, a)
else {
val quotient = a / b
val reminder = a % b
bezoutIdentityWithGCDInternalLogic(b, reminder, m2, m1 - quotient * m2, m4, m3 - quotient * m4)
}