Feature: Polynomials and rational functions #469
@ -70,19 +70,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
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// region Polynomial-integer relation
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/**
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* Returns sum of the constant and the integer represented as polynomial.
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* Returns sum of the polynomial and the integer represented as polynomial.
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*
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* The operation is equivalent to adding [other] copies of unit polynomial to [this].
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*/
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public operator fun P.plus(other: Int): P = optimizedAddMultiplied(this, one, other)
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/**
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* Returns difference between the constant and the integer represented as polynomial.
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* Returns difference between the polynomial and the integer represented as polynomial.
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*
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* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
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*/
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public operator fun P.minus(other: Int): P = optimizedAddMultiplied(this, one, -other)
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/**
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* Returns product of the constant and the integer represented as polynomial.
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* Returns product of the polynomial and the integer represented as polynomial.
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*
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* The operation is equivalent to sum of [other] copies of [this].
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*/
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@ -91,19 +91,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
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// region Integer-polynomial relation
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/**
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* Returns sum of the integer represented as polynomial and the constant.
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* Returns sum of the integer represented as polynomial and the polynomial.
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*
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* The operation is equivalent to adding [this] copies of unit polynomial to [other].
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*/
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public operator fun Int.plus(other: P): P = optimizedAddMultiplied(other, one, this)
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/**
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* Returns difference between the integer represented as polynomial and the constant.
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* Returns difference between the integer represented as polynomial and the polynomial.
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*
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* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
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*/
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public operator fun Int.minus(other: P): P = optimizedAddMultiplied(-other, one, this)
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/**
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* Returns product of the integer represented as polynomial and the constant.
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* Returns product of the integer represented as polynomial and the polynomial.
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*
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* The operation is equivalent to sum of [this] copies of [other].
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*/
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@ -254,11 +254,11 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
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/**
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* Instance of zero polynomial (zero of the polynomial ring).
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*/
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override val zero: P
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public override val zero: P
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/**
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* Instance of unit polynomial (unit of the polynomial ring).
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*/
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override val one: P
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public override val one: P
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/**
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* Checks equality of the polynomials.
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@ -0,0 +1,507 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.functions
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import space.kscience.kmath.functions.AbstractPolynomialSpace.Companion.optimizedAddMultiplied
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import space.kscience.kmath.functions.AbstractPolynomialSpace.Companion.optimizedMultiply
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import space.kscience.kmath.operations.*
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import kotlin.js.JsName
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import kotlin.jvm.JvmName
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/**
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* Abstraction of rational function.
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*/
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public interface AbstractRationalFunction<C, P: AbstractPolynomial<C>>
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@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE")
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public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R: AbstractRationalFunction<C, P>> : Ring<R> {
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// region Constant-integer relation
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/**
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* Returns sum of the constant and the integer represented as constant (member of underlying ring).
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*
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* The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
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*/
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@JvmName("constantIntPlus")
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public operator fun C.plus(other: Int): C
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/**
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* Returns difference between the constant and the integer represented as constant (member of underlying ring).
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*
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* The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
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*/
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@JvmName("constantIntMinus")
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public operator fun C.minus(other: Int): C
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/**
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* Returns product of the constant and the integer represented as constant (member of underlying ring).
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*
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* The operation is equivalent to sum of [other] copies of [this].
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*/
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@JvmName("constantIntTimes")
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public operator fun C.times(other: Int): C
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// endregion
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// region Integer-constant relation
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/**
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* Returns sum of the integer represented as constant (member of underlying ring) and the constant.
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*
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* The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
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*/
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@JvmName("intConstantPlus")
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public operator fun Int.plus(other: C): C
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/**
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* Returns difference between the integer represented as constant (member of underlying ring) and the constant.
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*
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* The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
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*/
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@JvmName("intConstantMinus")
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public operator fun Int.minus(other: C): C
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/**
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* Returns product of the integer represented as constant (member of underlying ring) and the constant.
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*
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* The operation is equivalent to sum of [this] copies of [other].
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*/
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@JvmName("intConstantTimes")
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public operator fun Int.times(other: C): C
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// endregion
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// region Polynomial-integer relation
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/**
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* Returns sum of the constant and the integer represented as polynomial.
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*
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* The operation is equivalent to adding [other] copies of unit polynomial to [this].
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*/
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public operator fun P.plus(other: Int): P
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/**
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* Returns difference between the constant and the integer represented as polynomial.
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*
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* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
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*/
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public operator fun P.minus(other: Int): P
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/**
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* Returns product of the constant and the integer represented as polynomial.
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*
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* The operation is equivalent to sum of [other] copies of [this].
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*/
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public operator fun P.times(other: Int): P
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// endregion
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// region Integer-polynomial relation
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/**
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* Returns sum of the integer represented as polynomial and the constant.
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*
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* The operation is equivalent to adding [this] copies of unit polynomial to [other].
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*/
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public operator fun Int.plus(other: P): P
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/**
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* Returns difference between the integer represented as polynomial and the constant.
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*
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* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
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*/
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public operator fun Int.minus(other: P): P
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/**
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* Returns product of the integer represented as polynomial and the constant.
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*
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* The operation is equivalent to sum of [this] copies of [other].
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*/
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public operator fun Int.times(other: P): P
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// endregion
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// region Rational-integer relation
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/**
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* Returns sum of the rational function and the integer represented as rational function.
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*
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* The operation is equivalent to adding [other] copies of unit polynomial to [this].
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*/
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public operator fun R.plus(other: Int): R = optimizedAddMultiplied(this, one, other)
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/**
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* Returns difference between the rational function and the integer represented as rational function.
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*
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* The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
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*/
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public operator fun R.minus(other: Int): R = optimizedAddMultiplied(this, one, -other)
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/**
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* Returns product of the rational function and the integer represented as rational function.
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*
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* The operation is equivalent to sum of [other] copies of [this].
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*/
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public operator fun R.times(other: Int): R = optimizedMultiply(this, other)
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// endregion
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// region Integer-Rational relation
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/**
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* Returns sum of the integer represented as rational function and the rational function.
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*
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* The operation is equivalent to adding [this] copies of unit polynomial to [other].
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*/
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public operator fun Int.plus(other: R): R = optimizedAddMultiplied(other, one, this)
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/**
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* Returns difference between the integer represented as rational function and the rational function.
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*
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* The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
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*/
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public operator fun Int.minus(other: R): R = optimizedAddMultiplied(-other, one, this)
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/**
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* Returns product of the integer represented as rational function and the rational function.
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*
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* The operation is equivalent to sum of [this] copies of [other].
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*/
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public operator fun Int.times(other: R): R = optimizedMultiply(other, this)
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// endregion
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// region Constant-constant relation
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/**
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* Returns the same constant.
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*/
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@JvmName("constantUnaryPlus")
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@JsName("constantUnaryPlus")
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public operator fun C.unaryPlus(): C = this
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/**
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* Returns negation of the constant.
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*/
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@JvmName("constantUnaryMinus")
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@JsName("constantUnaryMinus")
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public operator fun C.unaryMinus(): C
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/**
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* Returns sum of the constants.
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*/
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@JvmName("constantPlus")
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@JsName("constantPlus")
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public operator fun C.plus(other: C): C
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/**
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* Returns difference of the constants.
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*/
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@JvmName("constantMinus")
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@JsName("constantMinus")
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public operator fun C.minus(other: C): C
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/**
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* Returns product of the constants.
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*/
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@JvmName("constantTimes")
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@JsName("constantTimes")
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public operator fun C.times(other: C): C
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/**
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* Check if the instant is zero constant.
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*/
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@JvmName("constantIsZero")
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public fun C.isZero(): Boolean
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/**
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* Check if the instant is NOT zero constant.
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*/
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@JvmName("constantIsNotZero")
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public fun C.isNotZero(): Boolean
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/**
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* Check if the instant is unit constant.
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*/
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@JvmName("constantIsOne")
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public fun C.isOne(): Boolean
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/**
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* Check if the instant is NOT unit constant.
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*/
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@JvmName("constantIsNotOne")
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public fun C.isNotOne(): Boolean
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/**
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* Check if the instant is minus unit constant.
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*/
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@JvmName("constantIsMinusOne")
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public fun C.isMinusOne(): Boolean
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/**
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* Check if the instant is NOT minus unit constant.
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*/
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@JvmName("constantIsNotMinusOne")
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public fun C.isNotMinusOne(): Boolean
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// endregion
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// region Constant-polynomial relation
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/**
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* Returns sum of the constant represented as polynomial and the polynomial.
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*/
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public operator fun C.plus(other: P): P
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/**
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* Returns difference between the constant represented as polynomial and the polynomial.
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*/
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public operator fun C.minus(other: P): P
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/**
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* Returns product of the constant represented as polynomial and the polynomial.
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*/
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public operator fun C.times(other: P): P
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// endregion
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// region Polynomial-constant relation
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/**
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* Returns sum of the constant represented as polynomial and the polynomial.
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*/
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public operator fun P.plus(other: C): P
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/**
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* Returns difference between the constant represented as polynomial and the polynomial.
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*/
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public operator fun P.minus(other: C): P
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/**
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* Returns product of the constant represented as polynomial and the polynomial.
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*/
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public operator fun P.times(other: C): P
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// endregion
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// region Polynomial-polynomial relation
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/**
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* Returns the same polynomial.
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*/
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public operator fun P.unaryPlus(): P = this
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/**
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* Returns negation of the polynomial.
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*/
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public operator fun P.unaryMinus(): P
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/**
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* Returns sum of the polynomials.
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*/
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public operator fun P.plus(other: P): P
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/**
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* Returns difference of the polynomials.
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*/
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public operator fun P.minus(other: P): P
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/**
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* Returns product of the polynomials.
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*/
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public operator fun P.times(other: P): P
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/**
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* Check if the instant is zero polynomial.
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*/
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public fun P.isZero(): Boolean = this == zeroPolynomial
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/**
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* Check if the instant is NOT zero polynomial.
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*/
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public fun P.isNotZero(): Boolean = this != zeroPolynomial
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/**
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* Check if the instant is unit polynomial.
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*/
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public fun P.isOne(): Boolean = this == onePolynomial
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/**
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* Check if the instant is NOT unit polynomial.
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*/
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public fun P.isNotOne(): Boolean = this != onePolynomial
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/**
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* Check if the instant is minus unit polynomial.
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*/
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public fun P.isMinusOne(): Boolean = this == -onePolynomial
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/**
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* Check if the instant is NOT minus unit polynomial.
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*/
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public fun P.isNotMinusOne(): Boolean = this != -onePolynomial
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/**
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* Instance of zero polynomial (zero of the polynomial ring).
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*/
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public val zeroPolynomial: P
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/**
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* Instance of unit polynomial (unit of the polynomial ring).
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*/
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public val onePolynomial: P
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/**
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* Checks equality of the polynomials.
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*/
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@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
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public fun P.equals(other: P): Boolean
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// endregion
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// region Constant-rational relation
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/**
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* Returns sum of the constant represented as rational function and the rational function.
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*/
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public operator fun C.plus(other: R): R
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/**
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* Returns difference between the constant represented as polynomial and the rational function.
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*/
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public operator fun C.minus(other: R): R
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/**
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* Returns product of the constant represented as polynomial and the rational function.
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*/
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public operator fun C.times(other: R): R
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// endregion
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// region Rational-constant relation
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/**
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* Returns sum of the constant represented as rational function and the rational function.
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*/
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public operator fun R.plus(other: C): R
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/**
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* Returns difference between the constant represented as rational function and the rational function.
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*/
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public operator fun R.minus(other: C): R
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/**
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* Returns product of the constant represented as rational function and the rational function.
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*/
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public operator fun R.times(other: C): R
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// endregion
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// region Polynomial-rational relation
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/**
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* Returns sum of the polynomial represented as rational function and the rational function.
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*/
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public operator fun P.plus(other: R): R
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/**
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* Returns difference between the polynomial represented as polynomial and the rational function.
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*/
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public operator fun P.minus(other: R): R
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/**
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* Returns product of the polynomial represented as polynomial and the rational function.
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*/
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public operator fun P.times(other: R): R
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// endregion
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// region Rational-polynomial relation
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/**
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* Returns sum of the polynomial represented as rational function and the rational function.
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*/
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public operator fun R.plus(other: P): R
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/**
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* Returns difference between the polynomial represented as rational function and the rational function.
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*/
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public operator fun R.minus(other: P): R
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/**
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* Returns product of the polynomial represented as rational function and the rational function.
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*/
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public operator fun R.times(other: P): R
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// endregion
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// region Rational-rational relation
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/**
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* Returns the same rational function.
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*/
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public override operator fun R.unaryPlus(): R = this
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/**
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* Returns negation of the rational function.
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*/
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public override operator fun R.unaryMinus(): R
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/**
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* Returns sum of the rational functions.
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*/
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public override operator fun R.plus(other: R): R
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/**
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* Returns difference of the rational functions.
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*/
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public override operator fun R.minus(other: R): R
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/**
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* Returns product of the rational functions.
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*/
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public override operator fun R.times(other: R): R
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/**
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* Check if the instant is zero rational function.
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*/
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public fun R.isZero(): Boolean = this == zero
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/**
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* Check if the instant is NOT zero rational function.
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*/
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public fun R.isNotZero(): Boolean = this != zero
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/**
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* Check if the instant is unit rational function.
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*/
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public fun R.isOne(): Boolean = this == one
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/**
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* Check if the instant is NOT unit rational function.
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*/
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public fun R.isNotOne(): Boolean = this != one
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/**
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* Check if the instant is minus unit rational function.
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*/
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public fun R.isMinusOne(): Boolean = this == -one
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/**
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* Check if the instant is NOT minus unit rational function.
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*/
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public fun R.isNotMinusOne(): Boolean = this != -one
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/**
|
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* Instance of zero rational function (zero of the rational functions ring).
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*/
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public override val zero: R
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/**
|
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* Instance of unit polynomial (unit of the rational functions ring).
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*/
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public override val one: R
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|
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/**
|
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* Checks equality of the rational functions.
|
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*/
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@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
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public fun R.equals(other: R): Boolean
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// endregion
|
||||
|
||||
// Not sure is it necessary...
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// region Polynomial properties
|
||||
/**
|
||||
* Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
|
||||
* zero, degree is -1.
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||||
*/
|
||||
public val P.degree: Int
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|
||||
/**
|
||||
* Checks if the instant is constant polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun P.isConstant(): Boolean = degree <= 0
|
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/**
|
||||
* Checks if the instant is **not** constant polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun P.isNotConstant(): Boolean = !isConstant()
|
||||
/**
|
||||
* Checks if the instant is constant non-zero polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun P.isNonZeroConstant(): Boolean = degree == 0
|
||||
/**
|
||||
* Checks if the instant is **not** constant non-zero polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun P.isNotNonZeroConstant(): Boolean = !isNonZeroConstant()
|
||||
|
||||
public fun P.asConstantOrNull(): C?
|
||||
|
||||
public fun P.asConstant(): C = asConstantOrNull() ?: error("Can not represent non-constant polynomial as a constant")
|
||||
|
||||
// endregion
|
||||
|
||||
// Not sure is it necessary...
|
||||
// region Polynomial properties
|
||||
/**
|
||||
* Checks if the instant is constant polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun R.isConstant(): Boolean
|
||||
/**
|
||||
* Checks if the instant is **not** constant polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun R.isNotConstant(): Boolean = !isConstant()
|
||||
/**
|
||||
* Checks if the instant is constant non-zero polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun R.isNonZeroConstant(): Boolean
|
||||
/**
|
||||
* Checks if the instant is **not** constant non-zero polynomial (of degree no more than 0) over considered ring.
|
||||
*/
|
||||
public fun R.isNotNonZeroConstant(): Boolean = !isNonZeroConstant()
|
||||
|
||||
public fun R.asConstantOrNull(): C?
|
||||
|
||||
public fun R.asConstant(): C = asConstantOrNull() ?: error("Can not represent non-constant polynomial as a constant")
|
||||
|
||||
// TODO: Перенести в реализацию
|
||||
// fun R.substitute(argument: C): C
|
||||
// fun R.substitute(argument: P): R
|
||||
// fun R.substitute(argument: R): R
|
||||
//
|
||||
// fun R.asFunction(): (C) -> C = /*this::substitute*/ { this.substitute(it) }
|
||||
// fun R.asFunctionOnConstants(): (C) -> C = /*this::substitute*/ { this.substitute(it) }
|
||||
// fun P.asFunctionOnPolynomials(): (P) -> R = /*this::substitute*/ { this.substitute(it) }
|
||||
// fun R.asFunctionOnRationalFunctions(): (R) -> R = /*this::substitute*/ { this.substitute(it) }
|
||||
//
|
||||
// operator fun R.invoke(argument: C): C = this.substitute(argument)
|
||||
// operator fun R.invoke(argument: P): R = this.substitute(argument)
|
||||
// operator fun R.invoke(argument: R): R = this.substitute(argument)
|
||||
// endregion
|
||||
|
||||
// region Legacy
|
||||
override fun add(left: R, right: R): R = left + right
|
||||
override fun multiply(left: R, right: R): R = left * right
|
||||
// endregion
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user