Feature: Polynomials and rational functions #469
@ -54,7 +54,7 @@ import kotlin.contracts.*
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// else -> multiplyWithPowerInternalLogic(base, arg, pow)
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// else -> multiplyWithPowerInternalLogic(base, arg, pow)
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// }
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// }
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//
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//
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//// Trivial but slow as duck
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//// Trivial but very slow
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//context(LabeledPolynomialSpace<C, A>)
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//context(LabeledPolynomialSpace<C, A>)
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//internal tailrec fun <C, A: Ring<C>> multiplyWithPowerInternalLogic(base: LabeledPolynomial<C>, arg: LabeledPolynomial<C>, exponent: UInt): LabeledPolynomial<C> =
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//internal tailrec fun <C, A: Ring<C>> multiplyWithPowerInternalLogic(base: LabeledPolynomial<C>, arg: LabeledPolynomial<C>, exponent: UInt): LabeledPolynomial<C> =
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// when {
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// when {
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@ -71,7 +71,15 @@ import kotlin.contracts.*
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// region Utilities
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// region Utilities
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// TODO: Docs
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/**
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* Crates a [LabeledPolynomialSpace] over received ring.
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*/
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public fun <C, A : Ring<C>> A.labeledPolynomial(): LabeledPolynomialSpace<C, A> =
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LabeledPolynomialSpace(this)
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/**
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* Crates a [LabeledPolynomialSpace]'s scope over received ring.
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*/
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@OptIn(ExperimentalContracts::class)
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@OptIn(ExperimentalContracts::class)
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public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomialSpace<C, A>.() -> R): R {
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public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomialSpace<C, A>.() -> R): R {
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contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
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contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
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@ -254,64 +262,6 @@ public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomi
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//// region Field case
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//// region Field case
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//
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//
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//operator fun <T: Field<T>> Polynomial<T>.div(other: Polynomial<T>): Polynomial<T> {
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// if (isZero()) return this
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//
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// fun Map<List<Int>, T>.leadingTerm() =
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// this
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// .asSequence()
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// .map { Pair(it.key, it.value) }
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// .reduce { (accDegs, accC), (listDegs, listC) ->
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// for (i in 0..accDegs.lastIndex) {
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// if (accDegs[i] > listDegs.getOrElse(i) { 0 }) return@reduce accDegs to accC
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// if (accDegs[i] < listDegs.getOrElse(i) { 0 }) return@reduce listDegs to listC
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// }
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// if (accDegs.size < listDegs.size) listDegs to listC else accDegs to accC
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// }
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//
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// var thisCoefficients = coefficients.toMutableMap()
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// val otherCoefficients = other.coefficients
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// val quotientCoefficients = HashMap<List<Int>, T>()
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//
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// var (thisLeadingTermDegs, thisLeadingTermC) = thisCoefficients.leadingTerm()
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// val (otherLeadingTermDegs, otherLeadingTermC) = otherCoefficients.leadingTerm()
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//
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// while (
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// thisLeadingTermDegs.size >= otherLeadingTermDegs.size &&
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// (0..otherLeadingTermDegs.lastIndex).all { thisLeadingTermDegs[it] >= otherLeadingTermDegs[it] }
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// ) {
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// val multiplierDegs =
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// thisLeadingTermDegs
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// .mapIndexed { index, deg -> deg - otherLeadingTermDegs.getOrElse(index) { 0 } }
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// .cleanUp()
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// val multiplierC = thisLeadingTermC / otherLeadingTermC
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//
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// quotientCoefficients[multiplierDegs] = multiplierC
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//
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// for ((degs, t) in otherCoefficients) {
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// val productDegs =
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// (0..max(degs.lastIndex, multiplierDegs.lastIndex))
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// .map { degs.getOrElse(it) { 0 } + multiplierDegs.getOrElse(it) { 0 } }
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// .cleanUp()
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// val productC = t * multiplierC
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// thisCoefficients[productDegs] =
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// if (productDegs in thisCoefficients) thisCoefficients[productDegs]!! - productC else -productC
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// }
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//
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// thisCoefficients = thisCoefficients.filterValues { it.isNotZero() }.toMutableMap()
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//
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// if (thisCoefficients.isEmpty())
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// return Polynomial(quotientCoefficients, toCheckInput = false)
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//
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// val t = thisCoefficients.leadingTerm()
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// thisLeadingTermDegs = t.first
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// thisLeadingTermC = t.second
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// }
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//
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// return Polynomial(quotientCoefficients, toCheckInput = false)
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//}
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//
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//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
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//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// else
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// else
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@ -321,125 +271,6 @@ public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomi
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// toCheckInput = false
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// toCheckInput = false
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// )
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// )
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//
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//
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//operator fun <T: Field<T>> Polynomial<T>.rem(other: Polynomial<T>): Polynomial<T> {
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// if (isZero()) return this
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//
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// fun Map<List<Int>, T>.leadingTerm() =
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// this
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// .asSequence()
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// .map { Pair(it.key, it.value) }
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// .reduce { (accDegs, accC), (listDegs, listC) ->
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// for (i in 0..accDegs.lastIndex) {
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// if (accDegs[i] > listDegs.getOrElse(i) { 0 }) return@reduce accDegs to accC
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// if (accDegs[i] < listDegs.getOrElse(i) { 0 }) return@reduce listDegs to listC
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// }
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// if (accDegs.size < listDegs.size) listDegs to listC else accDegs to accC
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// }
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//
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// var thisCoefficients = coefficients.toMutableMap()
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// val otherCoefficients = other.coefficients
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//
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// var (thisLeadingTermDegs, thisLeadingTermC) = thisCoefficients.leadingTerm()
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// val (otherLeadingTermDegs, otherLeadingTermC) = otherCoefficients.leadingTerm()
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//
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// while (
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// thisLeadingTermDegs.size >= otherLeadingTermDegs.size &&
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// (0..otherLeadingTermDegs.lastIndex).all { thisLeadingTermDegs[it] >= otherLeadingTermDegs[it] }
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// ) {
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// val multiplierDegs =
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// thisLeadingTermDegs
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// .mapIndexed { index, deg -> deg - otherLeadingTermDegs.getOrElse(index) { 0 } }
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// .cleanUp()
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// val multiplierC = thisLeadingTermC / otherLeadingTermC
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//
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// for ((degs, t) in otherCoefficients) {
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// val productDegs =
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// (0..max(degs.lastIndex, multiplierDegs.lastIndex))
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// .map { degs.getOrElse(it) { 0 } + multiplierDegs.getOrElse(it) { 0 } }
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// .cleanUp()
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// val productC = t * multiplierC
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// thisCoefficients[productDegs] =
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// if (productDegs in thisCoefficients) thisCoefficients[productDegs]!! - productC else -productC
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// }
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//
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// thisCoefficients = thisCoefficients.filterValues { it.isNotZero() }.toMutableMap()
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//
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// if (thisCoefficients.isEmpty())
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// return Polynomial(thisCoefficients, toCheckInput = false)
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//
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// val t = thisCoefficients.leadingTerm()
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// thisLeadingTermDegs = t.first
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// thisLeadingTermC = t.second
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// }
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//
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// return Polynomial(thisCoefficients, toCheckInput = false)
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//}
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//
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//infix fun <T: Field<T>> Polynomial<T>.divrem(other: Polynomial<T>): Polynomial.Companion.DividingResult<T> {
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// if (isZero()) return Polynomial.Companion.DividingResult(this, this)
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//
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// fun Map<List<Int>, T>.leadingTerm() =
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// this
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// .asSequence()
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// .map { Pair(it.key, it.value) }
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// .reduce { (accDegs, accC), (listDegs, listC) ->
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// for (i in 0..accDegs.lastIndex) {
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// if (accDegs[i] > listDegs.getOrElse(i) { 0 }) return@reduce accDegs to accC
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// if (accDegs[i] < listDegs.getOrElse(i) { 0 }) return@reduce listDegs to listC
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// }
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// if (accDegs.size < listDegs.size) listDegs to listC else accDegs to accC
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// }
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//
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// var thisCoefficients = coefficients.toMutableMap()
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// val otherCoefficients = other.coefficients
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// val quotientCoefficients = HashMap<List<Int>, T>()
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//
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// var (thisLeadingTermDegs, thisLeadingTermC) = thisCoefficients.leadingTerm()
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// val (otherLeadingTermDegs, otherLeadingTermC) = otherCoefficients.leadingTerm()
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//
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// while (
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// thisLeadingTermDegs.size >= otherLeadingTermDegs.size &&
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// (0..otherLeadingTermDegs.lastIndex).all { thisLeadingTermDegs[it] >= otherLeadingTermDegs[it] }
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// ) {
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// val multiplierDegs =
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// thisLeadingTermDegs
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// .mapIndexed { index, deg -> deg - otherLeadingTermDegs.getOrElse(index) { 0 } }
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// .cleanUp()
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// val multiplierC = thisLeadingTermC / otherLeadingTermC
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//
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// quotientCoefficients[multiplierDegs] = multiplierC
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//
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// for ((degs, t) in otherCoefficients) {
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// val productDegs =
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// (0..max(degs.lastIndex, multiplierDegs.lastIndex))
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// .map { degs.getOrElse(it) { 0 } + multiplierDegs.getOrElse(it) { 0 } }
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// .cleanUp()
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// val productC = t * multiplierC
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// thisCoefficients[productDegs] =
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// if (productDegs in thisCoefficients) thisCoefficients[productDegs]!! - productC else -productC
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// }
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//
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// thisCoefficients = thisCoefficients.filterValues { it.isNotZero() }.toMutableMap()
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//
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// if (thisCoefficients.isEmpty())
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// return Polynomial.Companion.DividingResult(
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// Polynomial(quotientCoefficients, toCheckInput = false),
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// Polynomial(thisCoefficients, toCheckInput = false)
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// )
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//
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// val t = thisCoefficients.leadingTerm()
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// thisLeadingTermDegs = t.first
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// thisLeadingTermC = t.second
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// }
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//
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// return Polynomial.Companion.DividingResult(
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// Polynomial(quotientCoefficients, toCheckInput = false),
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// Polynomial(thisCoefficients, toCheckInput = false)
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// )
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//}
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//
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//// endregion
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//// endregion
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// endregion
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// endregion
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@ -38,7 +38,7 @@ import kotlin.jvm.JvmName
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// else -> multiplyWithPowerInternalLogic(base, arg, pow)
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// else -> multiplyWithPowerInternalLogic(base, arg, pow)
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// }
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// }
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//
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//
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//// Trivial but slow as duck
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//// Trivial but very slow
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//context(NumberedPolynomialSpace<C, A>)
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//context(NumberedPolynomialSpace<C, A>)
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//internal tailrec fun <C, A: Ring<C>> multiplyWithPowerInternalLogic(base: NumberedPolynomial<C>, arg: NumberedPolynomial<C>, exponent: UInt): NumberedPolynomial<C> =
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//internal tailrec fun <C, A: Ring<C>> multiplyWithPowerInternalLogic(base: NumberedPolynomial<C>, arg: NumberedPolynomial<C>, exponent: UInt): NumberedPolynomial<C> =
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// when {
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// when {
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@ -55,7 +55,15 @@ import kotlin.jvm.JvmName
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// region Utilities
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// region Utilities
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// TODO: Docs
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/**
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* Crates a [NumberedPolynomialSpace] over received ring.
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*/
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public fun <C, A : Ring<C>> A.numberedPolynomial(): NumberedPolynomialSpace<C, A> =
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NumberedPolynomialSpace(this)
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/**
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* Crates a [NumberedPolynomialSpace]'s scope over received ring.
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*/
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@OptIn(ExperimentalContracts::class)
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@OptIn(ExperimentalContracts::class)
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public inline fun <C, A : Ring<C>, R> A.numberedPolynomial(block: NumberedPolynomialSpace<C, A>.() -> R): R {
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public inline fun <C, A : Ring<C>, R> A.numberedPolynomial(block: NumberedPolynomialSpace<C, A>.() -> R): R {
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contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
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contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
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@ -282,64 +290,6 @@ public inline fun <C, A : Ring<C>, R> A.numberedPolynomial(block: NumberedPolyno
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//// region Field case
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//// region Field case
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//
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//
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//operator fun <T: Field<T>> Polynomial<T>.div(other: Polynomial<T>): Polynomial<T> {
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// if (isZero()) return this
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//
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// fun Map<List<Int>, T>.leadingTerm() =
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// this
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// .asSequence()
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// .map { Pair(it.key, it.value) }
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// .reduce { (accDegs, accC), (listDegs, listC) ->
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// for (i in 0..accDegs.lastIndex) {
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// if (accDegs[i] > listDegs.getOrElse(i) { 0 }) return@reduce accDegs to accC
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// if (accDegs[i] < listDegs.getOrElse(i) { 0 }) return@reduce listDegs to listC
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// }
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// if (accDegs.size < listDegs.size) listDegs to listC else accDegs to accC
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// }
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//
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// var thisCoefficients = coefficients.toMutableMap()
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// val otherCoefficients = other.coefficients
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// val quotientCoefficients = HashMap<List<Int>, T>()
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//
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// var (thisLeadingTermDegs, thisLeadingTermC) = thisCoefficients.leadingTerm()
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// val (otherLeadingTermDegs, otherLeadingTermC) = otherCoefficients.leadingTerm()
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//
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// while (
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// thisLeadingTermDegs.size >= otherLeadingTermDegs.size &&
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// (0..otherLeadingTermDegs.lastIndex).all { thisLeadingTermDegs[it] >= otherLeadingTermDegs[it] }
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// ) {
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// val multiplierDegs =
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// thisLeadingTermDegs
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// .mapIndexed { index, deg -> deg - otherLeadingTermDegs.getOrElse(index) { 0 } }
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// .cleanUp()
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// val multiplierC = thisLeadingTermC / otherLeadingTermC
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//
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// quotientCoefficients[multiplierDegs] = multiplierC
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//
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// for ((degs, t) in otherCoefficients) {
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// val productDegs =
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// (0..max(degs.lastIndex, multiplierDegs.lastIndex))
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// .map { degs.getOrElse(it) { 0 } + multiplierDegs.getOrElse(it) { 0 } }
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// .cleanUp()
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// val productC = t * multiplierC
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// thisCoefficients[productDegs] =
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// if (productDegs in thisCoefficients) thisCoefficients[productDegs]!! - productC else -productC
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// }
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//
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// thisCoefficients = thisCoefficients.filterValues { it.isNotZero() }.toMutableMap()
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//
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// if (thisCoefficients.isEmpty())
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// return Polynomial(quotientCoefficients, toCheckInput = false)
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//
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// val t = thisCoefficients.leadingTerm()
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// thisLeadingTermDegs = t.first
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// thisLeadingTermC = t.second
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// }
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//
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// return Polynomial(quotientCoefficients, toCheckInput = false)
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//}
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//
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//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
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//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// if (other.isZero()) throw ArithmeticException("/ by zero")
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// else
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// else
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@ -349,125 +299,6 @@ public inline fun <C, A : Ring<C>, R> A.numberedPolynomial(block: NumberedPolyno
|
|||||||
// toCheckInput = false
|
// toCheckInput = false
|
||||||
// )
|
// )
|
||||||
//
|
//
|
||||||
//operator fun <T: Field<T>> Polynomial<T>.rem(other: Polynomial<T>): Polynomial<T> {
|
|
||||||
// if (other.isZero()) throw ArithmeticException("/ by zero")
|
|
||||||
// if (isZero()) return this
|
|
||||||
//
|
|
||||||
// fun Map<List<Int>, T>.leadingTerm() =
|
|
||||||
// this
|
|
||||||
// .asSequence()
|
|
||||||
// .map { Pair(it.key, it.value) }
|
|
||||||
// .reduce { (accDegs, accC), (listDegs, listC) ->
|
|
||||||
// for (i in 0..accDegs.lastIndex) {
|
|
||||||
// if (accDegs[i] > listDegs.getOrElse(i) { 0 }) return@reduce accDegs to accC
|
|
||||||
// if (accDegs[i] < listDegs.getOrElse(i) { 0 }) return@reduce listDegs to listC
|
|
||||||
// }
|
|
||||||
// if (accDegs.size < listDegs.size) listDegs to listC else accDegs to accC
|
|
||||||
// }
|
|
||||||
//
|
|
||||||
// var thisCoefficients = coefficients.toMutableMap()
|
|
||||||
// val otherCoefficients = other.coefficients
|
|
||||||
//
|
|
||||||
// var (thisLeadingTermDegs, thisLeadingTermC) = thisCoefficients.leadingTerm()
|
|
||||||
// val (otherLeadingTermDegs, otherLeadingTermC) = otherCoefficients.leadingTerm()
|
|
||||||
//
|
|
||||||
// while (
|
|
||||||
// thisLeadingTermDegs.size >= otherLeadingTermDegs.size &&
|
|
||||||
// (0..otherLeadingTermDegs.lastIndex).all { thisLeadingTermDegs[it] >= otherLeadingTermDegs[it] }
|
|
||||||
// ) {
|
|
||||||
// val multiplierDegs =
|
|
||||||
// thisLeadingTermDegs
|
|
||||||
// .mapIndexed { index, deg -> deg - otherLeadingTermDegs.getOrElse(index) { 0 } }
|
|
||||||
// .cleanUp()
|
|
||||||
// val multiplierC = thisLeadingTermC / otherLeadingTermC
|
|
||||||
//
|
|
||||||
// for ((degs, t) in otherCoefficients) {
|
|
||||||
// val productDegs =
|
|
||||||
// (0..max(degs.lastIndex, multiplierDegs.lastIndex))
|
|
||||||
// .map { degs.getOrElse(it) { 0 } + multiplierDegs.getOrElse(it) { 0 } }
|
|
||||||
// .cleanUp()
|
|
||||||
// val productC = t * multiplierC
|
|
||||||
// thisCoefficients[productDegs] =
|
|
||||||
// if (productDegs in thisCoefficients) thisCoefficients[productDegs]!! - productC else -productC
|
|
||||||
// }
|
|
||||||
//
|
|
||||||
// thisCoefficients = thisCoefficients.filterValues { it.isNotZero() }.toMutableMap()
|
|
||||||
//
|
|
||||||
// if (thisCoefficients.isEmpty())
|
|
||||||
// return Polynomial(thisCoefficients, toCheckInput = false)
|
|
||||||
//
|
|
||||||
// val t = thisCoefficients.leadingTerm()
|
|
||||||
// thisLeadingTermDegs = t.first
|
|
||||||
// thisLeadingTermC = t.second
|
|
||||||
// }
|
|
||||||
//
|
|
||||||
// return Polynomial(thisCoefficients, toCheckInput = false)
|
|
||||||
//}
|
|
||||||
//
|
|
||||||
//infix fun <T: Field<T>> Polynomial<T>.divrem(other: Polynomial<T>): Polynomial.Companion.DividingResult<T> {
|
|
||||||
// if (other.isZero()) throw ArithmeticException("/ by zero")
|
|
||||||
// if (isZero()) return Polynomial.Companion.DividingResult(this, this)
|
|
||||||
//
|
|
||||||
// fun Map<List<Int>, T>.leadingTerm() =
|
|
||||||
// this
|
|
||||||
// .asSequence()
|
|
||||||
// .map { Pair(it.key, it.value) }
|
|
||||||
// .reduce { (accDegs, accC), (listDegs, listC) ->
|
|
||||||
// for (i in 0..accDegs.lastIndex) {
|
|
||||||
// if (accDegs[i] > listDegs.getOrElse(i) { 0 }) return@reduce accDegs to accC
|
|
||||||
// if (accDegs[i] < listDegs.getOrElse(i) { 0 }) return@reduce listDegs to listC
|
|
||||||
// }
|
|
||||||
// if (accDegs.size < listDegs.size) listDegs to listC else accDegs to accC
|
|
||||||
// }
|
|
||||||
//
|
|
||||||
// var thisCoefficients = coefficients.toMutableMap()
|
|
||||||
// val otherCoefficients = other.coefficients
|
|
||||||
// val quotientCoefficients = HashMap<List<Int>, T>()
|
|
||||||
//
|
|
||||||
// var (thisLeadingTermDegs, thisLeadingTermC) = thisCoefficients.leadingTerm()
|
|
||||||
// val (otherLeadingTermDegs, otherLeadingTermC) = otherCoefficients.leadingTerm()
|
|
||||||
//
|
|
||||||
// while (
|
|
||||||
// thisLeadingTermDegs.size >= otherLeadingTermDegs.size &&
|
|
||||||
// (0..otherLeadingTermDegs.lastIndex).all { thisLeadingTermDegs[it] >= otherLeadingTermDegs[it] }
|
|
||||||
// ) {
|
|
||||||
// val multiplierDegs =
|
|
||||||
// thisLeadingTermDegs
|
|
||||||
// .mapIndexed { index, deg -> deg - otherLeadingTermDegs.getOrElse(index) { 0 } }
|
|
||||||
// .cleanUp()
|
|
||||||
// val multiplierC = thisLeadingTermC / otherLeadingTermC
|
|
||||||
//
|
|
||||||
// quotientCoefficients[multiplierDegs] = multiplierC
|
|
||||||
//
|
|
||||||
// for ((degs, t) in otherCoefficients) {
|
|
||||||
// val productDegs =
|
|
||||||
// (0..max(degs.lastIndex, multiplierDegs.lastIndex))
|
|
||||||
// .map { degs.getOrElse(it) { 0 } + multiplierDegs.getOrElse(it) { 0 } }
|
|
||||||
// .cleanUp()
|
|
||||||
// val productC = t * multiplierC
|
|
||||||
// thisCoefficients[productDegs] =
|
|
||||||
// if (productDegs in thisCoefficients) thisCoefficients[productDegs]!! - productC else -productC
|
|
||||||
// }
|
|
||||||
//
|
|
||||||
// thisCoefficients = thisCoefficients.filterValues { it.isNotZero() }.toMutableMap()
|
|
||||||
//
|
|
||||||
// if (thisCoefficients.isEmpty())
|
|
||||||
// return Polynomial.Companion.DividingResult(
|
|
||||||
// Polynomial(quotientCoefficients, toCheckInput = false),
|
|
||||||
// Polynomial(thisCoefficients, toCheckInput = false)
|
|
||||||
// )
|
|
||||||
//
|
|
||||||
// val t = thisCoefficients.leadingTerm()
|
|
||||||
// thisLeadingTermDegs = t.first
|
|
||||||
// thisLeadingTermC = t.second
|
|
||||||
// }
|
|
||||||
//
|
|
||||||
// return Polynomial.Companion.DividingResult(
|
|
||||||
// Polynomial(quotientCoefficients, toCheckInput = false),
|
|
||||||
// Polynomial(thisCoefficients, toCheckInput = false)
|
|
||||||
// )
|
|
||||||
//}
|
|
||||||
//
|
|
||||||
//// endregion
|
//// endregion
|
||||||
|
|
||||||
// endregion
|
// endregion
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user