Feature: Polynomials and rational functions #469
@ -1,142 +0,0 @@
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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.test.misc
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import space.kscience.kmath.functions.ListPolynomial
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import space.kscience.kmath.functions.ListPolynomialSpace
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.Ring
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class IntModulo {
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val residue: Int
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val modulus: Int
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@PublishedApi
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internal constructor(residue: Int, modulus: Int, toCheckInput: Boolean = true) {
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if (toCheckInput) {
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require(modulus != 0) { "modulus can not be zero" }
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this.modulus = if (modulus < 0) -modulus else modulus
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this.residue = residue.mod(modulus)
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} else {
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this.residue = residue
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this.modulus = modulus
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}
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}
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constructor(residue: Int, modulus: Int) : this(residue, modulus, true)
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operator fun unaryPlus(): IntModulo = this
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operator fun unaryMinus(): IntModulo =
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IntModulo(
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if (residue == 0) 0 else modulus - residue,
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modulus,
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toCheckInput = false
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)
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operator fun plus(other: IntModulo): IntModulo {
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require(modulus == other.modulus) { "can not add two residue different modulo" }
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return IntModulo(
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(residue + other.residue) % modulus,
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modulus,
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toCheckInput = false
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)
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}
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operator fun plus(other: Int): IntModulo =
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IntModulo(
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(residue + other) % modulus,
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modulus,
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toCheckInput = false
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)
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operator fun minus(other: IntModulo): IntModulo {
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require(modulus == other.modulus) { "can not subtract two residue different modulo" }
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return IntModulo(
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(residue - other.residue) % modulus,
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modulus,
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toCheckInput = false
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)
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}
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operator fun minus(other: Int): IntModulo =
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IntModulo(
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(residue - other) % modulus,
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modulus,
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toCheckInput = false
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)
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operator fun times(other: IntModulo): IntModulo {
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require(modulus == other.modulus) { "can not multiply two residue different modulo" }
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return IntModulo(
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(residue * other.residue) % modulus,
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modulus,
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toCheckInput = false
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)
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}
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operator fun times(other: Int): IntModulo =
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IntModulo(
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(residue * other) % modulus,
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modulus,
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toCheckInput = false
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)
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operator fun div(other: IntModulo): IntModulo {
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require(modulus == other.modulus) { "can not divide two residue different modulo" }
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val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other.residue, modulus)
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require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
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return IntModulo(
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(residue * reciprocalCandidate) % modulus,
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modulus,
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toCheckInput = false
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)
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}
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operator fun div(other: Int): IntModulo {
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val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other, modulus)
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require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
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return IntModulo(
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(residue * reciprocalCandidate) % modulus,
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modulus,
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toCheckInput = false
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)
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}
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override fun equals(other: Any?): Boolean =
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when (other) {
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is IntModulo -> residue == other.residue && modulus == other.modulus
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else -> false
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}
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override fun hashCode(): Int = residue.hashCode()
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override fun toString(): String = "$residue mod $modulus"
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}
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@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
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@OptIn(UnstableKMathAPI::class)
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class IntModuloRing : Ring<IntModulo> {
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val modulus: Int
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constructor(modulus: Int) {
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require(modulus != 0) { "modulus can not be zero" }
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this.modulus = if (modulus < 0) -modulus else modulus
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}
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override inline val zero: IntModulo get() = IntModulo(0, modulus, toCheckInput = false)
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override inline val one: IntModulo get() = IntModulo(1, modulus, toCheckInput = false)
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fun number(arg: Int) = IntModulo(arg, modulus, toCheckInput = false)
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override inline fun add(left: IntModulo, right: IntModulo): IntModulo = left + right
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override inline fun multiply(left: IntModulo, right: IntModulo): IntModulo = left * right
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override inline fun IntModulo.unaryMinus(): IntModulo = -this
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override inline fun IntModulo.plus(arg: IntModulo): IntModulo = this + arg
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override inline fun IntModulo.minus(arg: IntModulo): IntModulo = this - arg
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override inline fun IntModulo.times(arg: IntModulo): IntModulo = this * arg
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inline fun IntModulo.div(arg: IntModulo): IntModulo = this / arg
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}
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fun ListPolynomialSpace<IntModulo, IntModuloRing>.number(arg: Int) = IntModulo(arg, ring.modulus, toCheckInput = false)
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fun ListPolynomialSpace<IntModulo, IntModuloRing>.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
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ListPolynomial(coefs.map { IntModulo(it, ring.modulus) })
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fun IntModuloRing.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
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ListPolynomial(coefs.map { IntModulo(it, modulus) })
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@ -1,135 +0,0 @@
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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.test.misc
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.Field
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import space.kscience.kmath.operations.NumbersAddOps
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class Rational {
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companion object {
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val ZERO: Rational = Rational(0L)
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val ONE: Rational = Rational(1L)
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}
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val numerator: Long
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val denominator: Long
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internal constructor(numerator: Long, denominator: Long, toCheckInput: Boolean = true) {
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if (toCheckInput) {
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if (denominator == 0L) throw ArithmeticException("/ by zero")
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val greatestCommonDivider = gcd(numerator, denominator).let { if (denominator < 0L) -it else it }
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this.numerator = numerator / greatestCommonDivider
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this.denominator = denominator / greatestCommonDivider
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} else {
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this.numerator = numerator
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this.denominator = denominator
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}
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}
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constructor(numerator: Int, denominator: Int) : this(numerator.toLong(), denominator.toLong(), true)
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constructor(numerator: Int, denominator: Long) : this(numerator.toLong(), denominator, true)
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constructor(numerator: Long, denominator: Int) : this(numerator, denominator.toLong(), true)
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constructor(numerator: Long, denominator: Long) : this(numerator, denominator, true)
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constructor(numerator: Int) : this(numerator.toLong(), 1L, false)
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constructor(numerator: Long) : this(numerator, 1L, false)
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operator fun unaryPlus(): Rational = this
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operator fun unaryMinus(): Rational = Rational(-this.numerator, this.denominator)
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operator fun plus(other: Rational): Rational =
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Rational(
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numerator * other.denominator + denominator * other.numerator,
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denominator * other.denominator
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)
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operator fun plus(other: Int): Rational =
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Rational(
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numerator + denominator * other.toLong(),
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denominator
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)
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operator fun plus(other: Long): Rational =
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Rational(
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numerator + denominator * other,
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denominator
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)
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operator fun minus(other: Rational): Rational =
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Rational(
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numerator * other.denominator - denominator * other.numerator,
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denominator * other.denominator
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)
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operator fun minus(other: Int): Rational =
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Rational(
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numerator - denominator * other.toLong(),
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denominator
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)
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operator fun minus(other: Long): Rational =
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Rational(
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numerator - denominator * other,
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denominator
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)
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operator fun times(other: Rational): Rational =
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Rational(
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numerator * other.numerator,
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denominator * other.denominator
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)
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operator fun times(other: Int): Rational =
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Rational(
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numerator * other.toLong(),
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denominator
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)
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operator fun times(other: Long): Rational =
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Rational(
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numerator * other,
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denominator
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)
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operator fun div(other: Rational): Rational =
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Rational(
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numerator * other.denominator,
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denominator * other.numerator
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)
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operator fun div(other: Int): Rational =
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Rational(
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numerator,
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denominator * other.toLong()
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)
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operator fun div(other: Long): Rational =
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Rational(
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numerator,
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denominator * other
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)
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override fun equals(other: Any?): Boolean =
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when (other) {
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is Rational -> numerator == other.numerator && denominator == other.denominator
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is Int -> numerator == other && denominator == 1L
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is Long -> numerator == other && denominator == 1L
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else -> false
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}
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override fun hashCode(): Int = 31 * numerator.hashCode() + denominator.hashCode()
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override fun toString(): String = if (denominator == 1L) "$numerator" else "$numerator/$denominator"
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}
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@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
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@OptIn(UnstableKMathAPI::class)
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object RationalField : Field<Rational>, NumbersAddOps<Rational> {
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override inline val zero: Rational get() = Rational.ZERO
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override inline val one: Rational get() = Rational.ONE
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override inline fun number(value: Number): Rational = Rational(value.toLong())
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override inline fun add(left: Rational, right: Rational): Rational = left + right
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override inline fun multiply(left: Rational, right: Rational): Rational = left * right
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override inline fun divide(left: Rational, right: Rational): Rational = left / right
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override inline fun scale(a: Rational, value: Double): Rational = a * number(value)
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override inline fun Rational.unaryMinus(): Rational = -this
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override inline fun Rational.plus(arg: Rational): Rational = this + arg
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override inline fun Rational.minus(arg: Rational): Rational = this - arg
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override inline fun Rational.times(arg: Rational): Rational = this * arg
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override inline fun Rational.div(arg: Rational): Rational = this / arg
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}
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@ -1,107 +0,0 @@
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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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package space.kscience.kmath.test.misc
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.*
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class RationalWithMemorization private constructor(
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val value: Rational,
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override val memory : OperationsMemory
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): WithMemorization {
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companion object {
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/**
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* Constant containing the zero (the additive identity) of the [Rational] field.
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*/
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public val ZERO: RationalWithMemorization = RationalWithMemorization(Rational.ZERO, object : Endpoint {})
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/**
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* Constant containing the one (the multiplicative identity) of the [Rational] field.
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*/
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public val ONE: RationalWithMemorization = RationalWithMemorization(Rational.ONE, object : Endpoint {})
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}
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constructor(numerator: Int, denominator: Int) : this(Rational(numerator, denominator), object : Endpoint {})
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constructor(numerator: Int, denominator: Long) : this(Rational(numerator, denominator), object : Endpoint {})
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constructor(numerator: Long, denominator: Int) : this(Rational(numerator, denominator), object : Endpoint {})
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constructor(numerator: Long, denominator: Long) : this(Rational(numerator, denominator), object : Endpoint {})
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constructor(numerator: Int) : this(Rational(numerator), object : Endpoint {})
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constructor(numerator: Long) : this(Rational(numerator), object : Endpoint {})
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operator fun unaryPlus(): RationalWithMemorization = this
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operator fun unaryMinus(): RationalWithMemorization = RationalWithMemorization(
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-value,
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object : Negation {
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override val negated: OperationsMemory = memory
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}
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)
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operator fun plus(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
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value + other.value,
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object : Sum {
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override val augend: OperationsMemory = memory
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override val addend: OperationsMemory = other.memory
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}
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)
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operator fun minus(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
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value - other.value,
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object : Difference {
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override val minuend: OperationsMemory = memory
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override val subtrahend: OperationsMemory = other.memory
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}
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)
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operator fun times(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
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value * other.value,
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object : Product {
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override val multiplicand: OperationsMemory = memory
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override val multiplier: OperationsMemory = other.memory
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}
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)
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operator fun div(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
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value / other.value,
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object : Quotient {
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override val dividend: OperationsMemory = memory
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override val divisor: OperationsMemory = other.memory
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}
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)
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override fun equals(other: Any?): Boolean =
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other is RationalWithMemorization && value == other.value
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override fun hashCode(): Int = value.hashCode()
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override fun toString(): String = value.toString()
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}
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|
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@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
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object RationalWithMemorizationRing : Ring<RationalWithMemorization> {
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override inline val zero: RationalWithMemorization get() = RationalWithMemorization.ZERO
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override inline val one: RationalWithMemorization get() = RationalWithMemorization.ONE
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override inline fun add(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left + right
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override inline fun multiply(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left * right
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override inline fun RationalWithMemorization.unaryMinus(): RationalWithMemorization = -this
|
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override inline fun RationalWithMemorization.plus(arg: RationalWithMemorization): RationalWithMemorization = this + arg
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override inline fun RationalWithMemorization.minus(arg: RationalWithMemorization): RationalWithMemorization = this - arg
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||||
override inline fun RationalWithMemorization.times(arg: RationalWithMemorization): RationalWithMemorization = this * arg
|
||||
}
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||||
|
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@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
|
||||
object RationalWithMemorizationField : Field<RationalWithMemorization> {
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override inline val zero: RationalWithMemorization get() = RationalWithMemorization.ZERO
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||||
override inline val one: RationalWithMemorization get() = RationalWithMemorization.ONE
|
||||
|
||||
override inline fun number(value: Number): RationalWithMemorization = RationalWithMemorization(value.toLong())
|
||||
|
||||
override inline fun add(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left + right
|
||||
override inline fun multiply(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left * right
|
||||
override inline fun divide(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left / right
|
||||
override inline fun scale(a: RationalWithMemorization, value: Double): RationalWithMemorization = a * number(value)
|
||||
|
||||
override inline fun RationalWithMemorization.unaryMinus(): RationalWithMemorization = -this
|
||||
override inline fun RationalWithMemorization.plus(arg: RationalWithMemorization): RationalWithMemorization = this + arg
|
||||
override inline fun RationalWithMemorization.minus(arg: RationalWithMemorization): RationalWithMemorization = this - arg
|
||||
override inline fun RationalWithMemorization.times(arg: RationalWithMemorization): RationalWithMemorization = this * arg
|
||||
override inline fun RationalWithMemorization.div(arg: RationalWithMemorization): RationalWithMemorization = this / arg
|
||||
}
|
||||
@ -1,51 +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.test.misc
|
||||
|
||||
sealed interface OperationsMemory
|
||||
|
||||
interface Endpoint: OperationsMemory
|
||||
|
||||
interface Negation: OperationsMemory {
|
||||
val negated: OperationsMemory
|
||||
}
|
||||
|
||||
interface Sum: OperationsMemory {
|
||||
val augend: OperationsMemory
|
||||
val addend: OperationsMemory
|
||||
}
|
||||
|
||||
interface Difference: OperationsMemory {
|
||||
val minuend: OperationsMemory
|
||||
val subtrahend: OperationsMemory
|
||||
}
|
||||
|
||||
interface Product: OperationsMemory {
|
||||
val multiplicand: OperationsMemory
|
||||
val multiplier: OperationsMemory
|
||||
}
|
||||
|
||||
interface Quotient: OperationsMemory {
|
||||
val dividend: OperationsMemory
|
||||
val divisor: OperationsMemory
|
||||
}
|
||||
|
||||
|
||||
fun equalMemories(one: OperationsMemory, other: OperationsMemory) : Boolean =
|
||||
when(one) {
|
||||
is Negation -> other is Negation && equalMemories(one.negated, other.negated)
|
||||
is Sum -> other is Sum && equalMemories(one.augend, other.augend) && equalMemories(one.addend, other.addend)
|
||||
is Difference -> other is Difference && equalMemories(one.minuend, other.minuend) && equalMemories(one.subtrahend, other.subtrahend)
|
||||
is Product -> other is Product && equalMemories(one.multiplicand, other.multiplicand) && equalMemories(one.multiplier, other.multiplier)
|
||||
is Quotient -> other is Quotient && equalMemories(one.dividend, other.dividend) && equalMemories(one.divisor, other.divisor)
|
||||
is Endpoint -> one === other
|
||||
}
|
||||
|
||||
interface WithMemorization {
|
||||
val memory: OperationsMemory
|
||||
}
|
||||
|
||||
fun equalMemories(one: WithMemorization, other: WithMemorization) : Boolean = equalMemories(one.memory, other.memory)
|
||||
@ -1,31 +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.test.misc
|
||||
|
||||
// TODO: Move to corresponding module "kmath-number-theory"
|
||||
|
||||
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)
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user