Added abstract rational functions

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractPolynomial.kt

@@ -70,19 +70,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
 
     // region Polynomial-integer relation
     /**
-     * Returns sum of the constant and the integer represented as polynomial.
+     * Returns sum of the polynomial and the integer represented as polynomial.
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
     public operator fun P.plus(other: Int): P = optimizedAddMultiplied(this, one, other)
     /**
-     * Returns difference between the constant and the integer represented as polynomial.
+     * Returns difference between the polynomial and the integer represented as polynomial.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
     public operator fun P.minus(other: Int): P = optimizedAddMultiplied(this, one, -other)
     /**
-     * Returns product of the constant and the integer represented as polynomial.
+     * Returns product of the polynomial and the integer represented as polynomial.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
@@ -91,19 +91,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
 
     // region Integer-polynomial relation
     /**
-     * Returns sum of the integer represented as polynomial and the constant.
+     * Returns sum of the integer represented as polynomial and the polynomial.
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
     public operator fun Int.plus(other: P): P = optimizedAddMultiplied(other, one, this)
     /**
-     * Returns difference between the integer represented as polynomial and the constant.
+     * Returns difference between the integer represented as polynomial and the polynomial.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public operator fun Int.minus(other: P): P = optimizedAddMultiplied(-other, one, this)
     /**
-     * Returns product of the integer represented as polynomial and the constant.
+     * Returns product of the integer represented as polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
@@ -254,11 +254,11 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
     /**
      * Instance of zero polynomial (zero of the polynomial ring).
      */
-    override val zero: P
+    public override val zero: P
     /**
      * Instance of unit polynomial (unit of the polynomial ring).
      */
-    override val one: P
+    public override val one: P
 
     /**
      * Checks equality of the polynomials.

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractRationalFunction.kt

@@ -0,0 +1,507 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.functions.AbstractPolynomialSpace.Companion.optimizedAddMultiplied
+import space.kscience.kmath.functions.AbstractPolynomialSpace.Companion.optimizedMultiply
+import space.kscience.kmath.operations.*
+import kotlin.js.JsName
+import kotlin.jvm.JvmName
+
+
+/**
+ * Abstraction of rational function.
+ */
+public interface AbstractRationalFunction<C, P: AbstractPolynomial<C>>
+
+@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE")
+public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R: AbstractRationalFunction<C, P>> : Ring<R> {
+    // region Constant-integer relation
+    /**
+     * Returns sum of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
+     */
+    @JvmName("constantIntPlus")
+    public operator fun C.plus(other: Int): C
+    /**
+     * Returns difference between the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
+     */
+    @JvmName("constantIntMinus")
+    public operator fun C.minus(other: Int): C
+    /**
+     * Returns product of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    @JvmName("constantIntTimes")
+    public operator fun C.times(other: Int): C
+    // endregion
+
+    // region Integer-constant relation
+    /**
+     * Returns sum of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
+     */
+    @JvmName("intConstantPlus")
+    public operator fun Int.plus(other: C): C
+    /**
+     * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
+     */
+    @JvmName("intConstantMinus")
+    public operator fun Int.minus(other: C): C
+    /**
+     * Returns product of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    @JvmName("intConstantTimes")
+    public operator fun Int.times(other: C): C
+    // endregion
+
+    // region Polynomial-integer relation
+    /**
+     * Returns sum of the constant and the integer represented as polynomial.
+     *
+     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+     */
+    public operator fun P.plus(other: Int): P
+    /**
+     * Returns difference between the constant and the integer represented as polynomial.
+     *
+     * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
+     */
+    public operator fun P.minus(other: Int): P
+    /**
+     * Returns product of the constant and the integer represented as polynomial.
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public operator fun P.times(other: Int): P
+    // endregion
+
+    // region Integer-polynomial relation
+    /**
+     * Returns sum of the integer represented as polynomial and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit polynomial to [other].
+     */
+    public operator fun Int.plus(other: P): P
+    /**
+     * Returns difference between the integer represented as polynomial and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
+     */
+    public operator fun Int.minus(other: P): P
+    /**
+     * Returns product of the integer represented as polynomial and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public operator fun Int.times(other: P): P
+    // endregion
+
+    // region Rational-integer relation
+    /**
+     * Returns sum of the rational function and the integer represented as rational function.
+     *
+     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+     */
+    public operator fun R.plus(other: Int): R = optimizedAddMultiplied(this, one, other)
+    /**
+     * Returns difference between the rational function and the integer represented as rational function.
+     *
+     * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
+     */
+    public operator fun R.minus(other: Int): R = optimizedAddMultiplied(this, one, -other)
+    /**
+     * Returns product of the rational function and the integer represented as rational function.
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public operator fun R.times(other: Int): R = optimizedMultiply(this, other)
+    // endregion
+
+    // region Integer-Rational relation
+    /**
+     * Returns sum of the integer represented as rational function and the rational function.
+     *
+     * The operation is equivalent to adding [this] copies of unit polynomial to [other].
+     */
+    public operator fun Int.plus(other: R): R = optimizedAddMultiplied(other, one, this)
+    /**
+     * Returns difference between the integer represented as rational function and the rational function.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
+     */
+    public operator fun Int.minus(other: R): R = optimizedAddMultiplied(-other, one, this)
+    /**
+     * Returns product of the integer represented as rational function and the rational function.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public operator fun Int.times(other: R): R = optimizedMultiply(other, this)
+    // endregion
+
+    // region Constant-constant relation
+    /**
+     * Returns the same constant.
+     */
+    @JvmName("constantUnaryPlus")
+    @JsName("constantUnaryPlus")
+    public operator fun C.unaryPlus(): C = this
+    /**
+     * Returns negation of the constant.
+     */
+    @JvmName("constantUnaryMinus")
+    @JsName("constantUnaryMinus")
+    public operator fun C.unaryMinus(): C
+    /**
+     * Returns sum of the constants.
+     */
+    @JvmName("constantPlus")
+    @JsName("constantPlus")
+    public operator fun C.plus(other: C): C
+    /**
+     * Returns difference of the constants.
+     */
+    @JvmName("constantMinus")
+    @JsName("constantMinus")
+    public operator fun C.minus(other: C): C
+    /**
+     * Returns product of the constants.
+     */
+    @JvmName("constantTimes")
+    @JsName("constantTimes")
+    public operator fun C.times(other: C): C
+
+    /**
+     * Check if the instant is zero constant.
+     */
+    @JvmName("constantIsZero")
+    public fun C.isZero(): Boolean
+    /**
+     * Check if the instant is NOT zero constant.
+     */
+    @JvmName("constantIsNotZero")
+    public fun C.isNotZero(): Boolean
+    /**
+     * Check if the instant is unit constant.
+     */
+    @JvmName("constantIsOne")
+    public fun C.isOne(): Boolean
+    /**
+     * Check if the instant is NOT unit constant.
+     */
+    @JvmName("constantIsNotOne")
+    public fun C.isNotOne(): Boolean
+    /**
+     * Check if the instant is minus unit constant.
+     */
+    @JvmName("constantIsMinusOne")
+    public fun C.isMinusOne(): Boolean
+    /**
+     * Check if the instant is NOT minus unit constant.
+     */
+    @JvmName("constantIsNotMinusOne")
+    public fun C.isNotMinusOne(): Boolean
+    // endregion
+
+    // region Constant-polynomial relation
+    /**
+     * Returns sum of the constant represented as polynomial and the polynomial.
+     */
+    public operator fun C.plus(other: P): P
+    /**
+     * Returns difference between the constant represented as polynomial and the polynomial.
+     */
+    public operator fun C.minus(other: P): P
+    /**
+     * Returns product of the constant represented as polynomial and the polynomial.
+     */
+    public operator fun C.times(other: P): P
+    // endregion
+
+    // region Polynomial-constant relation
+    /**
+     * Returns sum of the constant represented as polynomial and the polynomial.
+     */
+    public operator fun P.plus(other: C): P
+    /**
+     * Returns difference between the constant represented as polynomial and the polynomial.
+     */
+    public operator fun P.minus(other: C): P
+    /**
+     * Returns product of the constant represented as polynomial and the polynomial.
+     */
+    public operator fun P.times(other: C): P
+    // endregion
+
+    // region Polynomial-polynomial relation
+    /**
+     * Returns the same polynomial.
+     */
+    public operator fun P.unaryPlus(): P = this
+    /**
+     * Returns negation of the polynomial.
+     */
+    public operator fun P.unaryMinus(): P
+    /**
+     * Returns sum of the polynomials.
+     */
+    public operator fun P.plus(other: P): P
+    /**
+     * Returns difference of the polynomials.
+     */
+    public operator fun P.minus(other: P): P
+    /**
+     * Returns product of the polynomials.
+     */
+    public operator fun P.times(other: P): P
+
+    /**
+     * Check if the instant is zero polynomial.
+     */
+    public fun P.isZero(): Boolean = this == zeroPolynomial
+    /**
+     * Check if the instant is NOT zero polynomial.
+     */
+    public fun P.isNotZero(): Boolean = this != zeroPolynomial
+    /**
+     * Check if the instant is unit polynomial.
+     */
+    public fun P.isOne(): Boolean = this == onePolynomial
+    /**
+     * Check if the instant is NOT unit polynomial.
+     */
+    public fun P.isNotOne(): Boolean = this != onePolynomial
+    /**
+     * Check if the instant is minus unit polynomial.
+     */
+    public fun P.isMinusOne(): Boolean = this == -onePolynomial
+    /**
+     * Check if the instant is NOT minus unit polynomial.
+     */
+    public fun P.isNotMinusOne(): Boolean = this != -onePolynomial
+
+    /**
+     * Instance of zero polynomial (zero of the polynomial ring).
+     */
+    public val zeroPolynomial: P
+    /**
+     * Instance of unit polynomial (unit of the polynomial ring).
+     */
+    public val onePolynomial: P
+
+    /**
+     * Checks equality of the polynomials.
+     */
+    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
+    public fun P.equals(other: P): Boolean
+    // endregion
+
+    // region Constant-rational relation
+    /**
+     * Returns sum of the constant represented as rational function and the rational function.
+     */
+    public operator fun C.plus(other: R): R
+    /**
+     * Returns difference between the constant represented as polynomial and the rational function.
+     */
+    public operator fun C.minus(other: R): R
+    /**
+     * Returns product of the constant represented as polynomial and the rational function.
+     */
+    public operator fun C.times(other: R): R
+    // endregion
+
+    // region Rational-constant relation
+    /**
+     * Returns sum of the constant represented as rational function and the rational function.
+     */
+    public operator fun R.plus(other: C): R
+    /**
+     * Returns difference between the constant represented as rational function and the rational function.
+     */
+    public operator fun R.minus(other: C): R
+    /**
+     * Returns product of the constant represented as rational function and the rational function.
+     */
+    public operator fun R.times(other: C): R
+    // endregion
+
+    // region Polynomial-rational relation
+    /**
+     * Returns sum of the polynomial represented as rational function and the rational function.
+     */
+    public operator fun P.plus(other: R): R
+    /**
+     * Returns difference between the polynomial represented as polynomial and the rational function.
+     */
+    public operator fun P.minus(other: R): R
+    /**
+     * Returns product of the polynomial represented as polynomial and the rational function.
+     */
+    public operator fun P.times(other: R): R
+    // endregion
+
+    // region Rational-polynomial relation
+    /**
+     * Returns sum of the polynomial represented as rational function and the rational function.
+     */
+    public operator fun R.plus(other: P): R
+    /**
+     * Returns difference between the polynomial represented as rational function and the rational function.
+     */
+    public operator fun R.minus(other: P): R
+    /**
+     * Returns product of the polynomial represented as rational function and the rational function.
+     */
+    public operator fun R.times(other: P): R
+    // endregion
+
+    // region Rational-rational relation
+    /**
+     * Returns the same rational function.
+     */
+    public override operator fun R.unaryPlus(): R = this
+    /**
+     * Returns negation of the rational function.
+     */
+    public override operator fun R.unaryMinus(): R
+    /**
+     * Returns sum of the rational functions.
+     */
+    public override operator fun R.plus(other: R): R
+    /**
+     * Returns difference of the rational functions.
+     */
+    public override operator fun R.minus(other: R): R
+    /**
+     * Returns product of the rational functions.
+     */
+    public override operator fun R.times(other: R): R
+
+    /**
+     * Check if the instant is zero rational function.
+     */
+    public fun R.isZero(): Boolean = this == zero
+    /**
+     * Check if the instant is NOT zero rational function.
+     */
+    public fun R.isNotZero(): Boolean = this != zero
+    /**
+     * Check if the instant is unit rational function.
+     */
+    public fun R.isOne(): Boolean = this == one
+    /**
+     * Check if the instant is NOT unit rational function.
+     */
+    public fun R.isNotOne(): Boolean = this != one
+    /**
+     * Check if the instant is minus unit rational function.
+     */
+    public fun R.isMinusOne(): Boolean = this == -one
+    /**
+     * Check if the instant is NOT minus unit rational function.
+     */
+    public fun R.isNotMinusOne(): Boolean = this != -one
+
+    /**
+     * Instance of zero rational function (zero of the rational functions ring).
+     */
+    public override val zero: R
+    /**
+     * Instance of unit polynomial (unit of the rational functions ring).
+     */
+    public override val one: R
+
+    /**
+     * Checks equality of the rational functions.
+     */
+    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
+    public fun R.equals(other: R): Boolean
+    // endregion
+
+    // Not sure is it necessary...
+    // 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.
+     */
+    public val P.degree: Int
+
+    /**
+     * Checks if the instant is constant polynomial (of degree no more than 0) over considered ring.
+     */
+    public fun P.isConstant(): Boolean = degree <= 0
+    /**
+     * 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
+}