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

@@ -423,7 +423,13 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Checks equality of the rational functions.
      */
-    public infix fun R.equalsTo(other: R): Boolean
+    public infix fun R.equalsTo(other: R): Boolean =
+        when {
+            this === other -> true
+            numerator.isZero() != other.numerator.isZero() -> false
+            numeratorDegree - denominatorDegree != with(other) { numeratorDegree - denominatorDegree } -> false
+            else -> numerator * other.denominator equalsTo other.numerator * denominator
+        }
     /**
      * Checks NOT equality of the polynomials.
      */
@@ -858,3 +864,223 @@ public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<
      */
     public override fun P.asConstant(): C = polynomialRing { this@asConstant.asConstant() }
 }
+
+/**
+ * Abstraction of field of rational functions of type [R] with respect to polynomials of type [P] and constants of type
+ * [C]. It also assumes that there is provided [polynomialRing] (of type [AP]), that provides constant- and
+ * polynomial-wise operations.
+ *
+ * @param C the type of constants. Polynomials have them as coefficients in their terms.
+ * @param P the type of polynomials. Rational functions have them as numerators and denominators in them.
+ * @param R the type of rational functions.
+ * @param AP the type of algebraic structure (precisely, of ring) provided for polynomials.
+ */ // TODO: Add support of field
+@Suppress("INAPPLICABLE_JVM_NAME")
+public abstract class AbstractPolynomialFractionsSpace<
+        C,
+        P: AbstractPolynomial<C>,
+        R: AbstractRationalFunction<C, P>,
+        > : AbstractRationalFunctionalSpace<C, P, R> {
+    protected abstract fun constructRationalFunction(numerator: P, denominator: P) : R
+
+    /**
+     * 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 override operator fun R.plus(other: Int): R =
+        constructRationalFunction(
+            numerator + denominator * other,
+            denominator
+        )
+    /**
+     * 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 override operator fun R.minus(other: Int): R =
+        constructRationalFunction(
+            numerator - denominator * other,
+            denominator
+        )
+    /**
+     * 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 override operator fun R.times(other: Int): R =
+        constructRationalFunction(
+            numerator * other,
+            denominator
+        )
+
+    /**
+     * 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 override operator fun Int.plus(other: R): R =
+        constructRationalFunction(
+            other.denominator * this + other.numerator,
+            other.denominator
+        )
+    /**
+     * 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 override operator fun Int.minus(other: R): R =
+        constructRationalFunction(
+            other.denominator * this - other.numerator,
+            other.denominator
+        )
+    /**
+     * 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 override operator fun Int.times(other: R): R =
+        constructRationalFunction(
+            this * other.numerator,
+            other.denominator
+        )
+
+    /**
+     * Returns sum of the constant represented as rational function and the rational function.
+     */
+    public override operator fun C.plus(other: R): R =
+        constructRationalFunction(
+            other.denominator * this + other.numerator,
+            other.denominator
+        )
+    /**
+     * Returns difference between the constant represented as polynomial and the rational function.
+     */
+    public override operator fun C.minus(other: R): R =
+        constructRationalFunction(
+            other.denominator * this - other.numerator,
+            other.denominator
+        )
+    /**
+     * Returns product of the constant represented as polynomial and the rational function.
+     */
+    public override operator fun C.times(other: R): R =
+        constructRationalFunction(
+            this * other.numerator,
+            other.denominator
+        )
+
+    /**
+     * Returns sum of the constant represented as rational function and the rational function.
+     */
+    public override operator fun R.plus(other: C): R =
+        constructRationalFunction(
+            numerator + denominator * other,
+            denominator
+        )
+    /**
+     * Returns difference between the constant represented as rational function and the rational function.
+     */
+    public override operator fun R.minus(other: C): R =
+        constructRationalFunction(
+            numerator - denominator * other,
+            denominator
+        )
+    /**
+     * Returns product of the constant represented as rational function and the rational function.
+     */
+    public override operator fun R.times(other: C): R =
+        constructRationalFunction(
+            numerator * other,
+            denominator
+        )
+
+    /**
+     * Returns sum of the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun P.plus(other: R): R =
+        constructRationalFunction(
+            other.denominator * this + other.numerator,
+            other.denominator
+        )
+    /**
+     * Returns difference between the polynomial represented as polynomial and the rational function.
+     */
+    public override operator fun P.minus(other: R): R =
+        constructRationalFunction(
+            other.denominator * this - other.numerator,
+            other.denominator
+        )
+    /**
+     * Returns product of the polynomial represented as polynomial and the rational function.
+     */
+    public override operator fun P.times(other: R): R =
+        constructRationalFunction(
+            this * other.numerator,
+            other.denominator
+        )
+
+    /**
+     * Returns sum of the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun R.plus(other: P): R =
+        constructRationalFunction(
+            numerator + denominator * other,
+            denominator
+        )
+    /**
+     * Returns difference between the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun R.minus(other: P): R =
+        constructRationalFunction(
+            numerator - denominator * other,
+            denominator
+        )
+    /**
+     * Returns product of the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun R.times(other: P): R =
+        constructRationalFunction(
+            numerator * other,
+            denominator
+        )
+
+    /**
+     * Returns negation of the rational function.
+     */
+    public override operator fun R.unaryMinus(): R = constructRationalFunction(-numerator, denominator)
+    /**
+     * Returns sum of the rational functions.
+     */
+    public override operator fun R.plus(other: R): R =
+        constructRationalFunction(
+            numerator * other.denominator + denominator * other.numerator,
+            denominator * other.denominator
+        )
+    /**
+     * Returns difference of the rational functions.
+     */
+    public override operator fun R.minus(other: R): R =
+        constructRationalFunction(
+            numerator * other.denominator - denominator * other.numerator,
+            denominator * other.denominator
+        )
+    /**
+     * Returns product of the rational functions.
+     */
+    public override operator fun R.times(other: R): R =
+        constructRationalFunction(
+            numerator * other.numerator,
+            denominator * other.denominator
+        )
+
+    /**
+     * Instance of zero rational function (zero of the rational functions ring).
+     */
+    public override val zero: R get() = constructRationalFunction(polynomialZero, polynomialOne)
+
+    /**
+     * Instance of unit polynomial (unit of the rational functions ring).
+     */
+    public override val one: R get() = constructRationalFunction(polynomialOne, polynomialOne)
+}

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

@@ -64,205 +64,25 @@ public class LabeledRationalFunction<C>(
 
 public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
     public val ring: A,
-) : AbstractRationalFunctionalSpaceOverPolynomialSpace<
+) :
+    AbstractRationalFunctionalSpaceOverPolynomialSpace<
             C,
             LabeledPolynomial<C>,
             LabeledRationalFunction<C>,
             LabeledPolynomialSpace<C, A>,
-        > {
+            >,
+    AbstractPolynomialFractionsSpace<
+            C,
+            LabeledPolynomial<C>,
+            LabeledRationalFunction<C>,
+            >() {
 
     override val polynomialRing : LabeledPolynomialSpace<C, A> = LabeledPolynomialSpace(ring)
-
+    override fun constructRationalFunction(
-    /**
+        numerator: LabeledPolynomial<C>,
-     * Returns sum of the rational function and the integer represented as rational function.
+        denominator: LabeledPolynomial<C>
-     *
+    ): LabeledRationalFunction<C> =
-     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+        LabeledRationalFunction(numerator, denominator)
-     */
-    public override operator fun LabeledRationalFunction<C>.plus(other: Int): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * 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 override operator fun LabeledRationalFunction<C>.minus(other: Int): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * 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 override operator fun LabeledRationalFunction<C>.times(other: Int): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * 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 override operator fun Int.plus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * 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 override operator fun Int.minus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * 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 override operator fun Int.times(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the constant represented as rational function and the rational function.
-     */
-    public override operator fun C.plus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns difference between the constant represented as polynomial and the rational function.
-     */
-    public override operator fun C.minus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns product of the constant represented as polynomial and the rational function.
-     */
-    public override operator fun C.times(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the constant represented as rational function and the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.plus(other: C): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * Returns difference between the constant represented as rational function and the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.minus(other: C): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * Returns product of the constant represented as rational function and the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.times(other: C): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun LabeledPolynomial<C>.plus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns difference between the polynomial represented as polynomial and the rational function.
-     */
-    public override operator fun LabeledPolynomial<C>.minus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns product of the polynomial represented as polynomial and the rational function.
-     */
-    public override operator fun LabeledPolynomial<C>.times(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.plus(other: LabeledPolynomial<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * Returns difference between the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.minus(other: LabeledPolynomial<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * Returns product of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.times(other: LabeledPolynomial<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * Returns negation of the rational function.
-     */
-    public override operator fun LabeledRationalFunction<C>.unaryMinus(): LabeledRationalFunction<C> = LabeledRationalFunction(-numerator, denominator)
-    /**
-     * Returns sum of the rational functions.
-     */
-    public override operator fun LabeledRationalFunction<C>.plus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other.denominator + denominator * other.numerator,
-            denominator * other.denominator
-        )
-    /**
-     * Returns difference of the rational functions.
-     */
-    public override operator fun LabeledRationalFunction<C>.minus(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other.denominator - denominator * other.numerator,
-            denominator * other.denominator
-        )
-    /**
-     * Returns product of the rational functions.
-     */
-    public override operator fun LabeledRationalFunction<C>.times(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other.numerator,
-            denominator * other.denominator
-        )
 
     /**
      * Instance of zero rational function (zero of the rational functions ring).
@@ -279,7 +99,7 @@ public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
     public override infix fun LabeledRationalFunction<C>.equalsTo(other: LabeledRationalFunction<C>): Boolean {
         if (this === other) return true
 
-        if ( !(numerator.isZero() xor other.numerator.isZero()) ) return false
+        if (numerator.isZero() != other.numerator.isZero()) return false
 
         val variables = this.variables union other.variables
         val thisNumeratorDegrees = this.numerator.degrees

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

@@ -60,205 +60,25 @@ public class NumberedRationalFunction<C> internal constructor(
 
 public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
     public val ring: A,
-) : AbstractRationalFunctionalSpaceOverPolynomialSpace<
+) :
+    AbstractRationalFunctionalSpaceOverPolynomialSpace<
             C,
             NumberedPolynomial<C>,
             NumberedRationalFunction<C>,
             NumberedPolynomialSpace<C, A>,
-        > {
+            >,
+    AbstractPolynomialFractionsSpace<
+            C,
+            NumberedPolynomial<C>,
+            NumberedRationalFunction<C>,
+            >() {
 
     override val polynomialRing : NumberedPolynomialSpace<C, A> = NumberedPolynomialSpace(ring)
-
+    override fun constructRationalFunction(
-    /**
+        numerator: NumberedPolynomial<C>,
-     * Returns sum of the rational function and the integer represented as rational function.
+        denominator: NumberedPolynomial<C>
-     *
+    ): NumberedRationalFunction<C> =
-     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+        NumberedRationalFunction(numerator, denominator)
-     */
-    public override operator fun NumberedRationalFunction<C>.plus(other: Int): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * 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 override operator fun NumberedRationalFunction<C>.minus(other: Int): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * 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 override operator fun NumberedRationalFunction<C>.times(other: Int): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * 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 override operator fun Int.plus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * 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 override operator fun Int.minus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * 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 override operator fun Int.times(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the constant represented as rational function and the rational function.
-     */
-    public override operator fun C.plus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns difference between the constant represented as polynomial and the rational function.
-     */
-    public override operator fun C.minus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns product of the constant represented as polynomial and the rational function.
-     */
-    public override operator fun C.times(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the constant represented as rational function and the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.plus(other: C): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * Returns difference between the constant represented as rational function and the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.minus(other: C): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * Returns product of the constant represented as rational function and the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.times(other: C): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun NumberedPolynomial<C>.plus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns difference between the polynomial represented as polynomial and the rational function.
-     */
-    public override operator fun NumberedPolynomial<C>.minus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns product of the polynomial represented as polynomial and the rational function.
-     */
-    public override operator fun NumberedPolynomial<C>.times(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.plus(other: NumberedPolynomial<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * Returns difference between the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.minus(other: NumberedPolynomial<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * Returns product of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.times(other: NumberedPolynomial<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * Returns negation of the rational function.
-     */
-    public override operator fun NumberedRationalFunction<C>.unaryMinus(): NumberedRationalFunction<C> = NumberedRationalFunction(-numerator, denominator)
-    /**
-     * Returns sum of the rational functions.
-     */
-    public override operator fun NumberedRationalFunction<C>.plus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator * other.denominator + denominator * other.numerator,
-            denominator * other.denominator
-        )
-    /**
-     * Returns difference of the rational functions.
-     */
-    public override operator fun NumberedRationalFunction<C>.minus(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator * other.denominator - denominator * other.numerator,
-            denominator * other.denominator
-        )
-    /**
-     * Returns product of the rational functions.
-     */
-    public override operator fun NumberedRationalFunction<C>.times(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
-        NumberedRationalFunction(
-            numerator * other.numerator,
-            denominator * other.denominator
-        )
 
     /**
      * Instance of zero rational function (zero of the rational functions ring).
@@ -275,7 +95,7 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
     public override infix fun NumberedRationalFunction<C>.equalsTo(other: NumberedRationalFunction<C>): Boolean {
         if (this === other) return true
 
-        if ( !(numerator.isZero() xor other.numerator.isZero()) ) return false
+        if (numerator.isZero() != other.numerator.isZero()) return false
 
         val countOfVariables = max(this.lastVariable, other.lastVariable)
         val thisNumeratorDegrees = this.numerator.degrees

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

@@ -42,205 +42,22 @@ public data class RationalFunction<C> internal constructor (
 
 public class RationalFunctionSpace<C, A : Ring<C>> (
     public val ring: A,
-) : AbstractRationalFunctionalSpaceOverPolynomialSpace<
+) :
+    AbstractRationalFunctionalSpaceOverPolynomialSpace<
             C,
             Polynomial<C>,
             RationalFunction<C>,
             PolynomialSpace<C, A>,
-        > {
+            >,
+    AbstractPolynomialFractionsSpace<
+            C,
+            Polynomial<C>,
+            RationalFunction<C>,
+            >() {
 
     override val polynomialRing : PolynomialSpace<C, A> = PolynomialSpace(ring)
-
+    override fun constructRationalFunction(numerator: Polynomial<C>, denominator: Polynomial<C>): RationalFunction<C> =
-    /**
+        RationalFunction(numerator, denominator)
-     * 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 override operator fun RationalFunction<C>.plus(other: Int): RationalFunction<C> =
-        RationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * 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 override operator fun RationalFunction<C>.minus(other: Int): RationalFunction<C> =
-        RationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * 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 override operator fun RationalFunction<C>.times(other: Int): RationalFunction<C> =
-        RationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * 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 override operator fun Int.plus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * 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 override operator fun Int.minus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * 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 override operator fun Int.times(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the constant represented as rational function and the rational function.
-     */
-    public override operator fun C.plus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns difference between the constant represented as polynomial and the rational function.
-     */
-    public override operator fun C.minus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns product of the constant represented as polynomial and the rational function.
-     */
-    public override operator fun C.times(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the constant represented as rational function and the rational function.
-     */
-    public override operator fun RationalFunction<C>.plus(other: C): RationalFunction<C> =
-        RationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * Returns difference between the constant represented as rational function and the rational function.
-     */
-    public override operator fun RationalFunction<C>.minus(other: C): RationalFunction<C> =
-        RationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * Returns product of the constant represented as rational function and the rational function.
-     */
-    public override operator fun RationalFunction<C>.times(other: C): RationalFunction<C> =
-        RationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun Polynomial<C>.plus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            other.denominator * this + other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns difference between the polynomial represented as polynomial and the rational function.
-     */
-    public override operator fun Polynomial<C>.minus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            other.denominator * this - other.numerator,
-            other.denominator
-        )
-    /**
-     * Returns product of the polynomial represented as polynomial and the rational function.
-     */
-    public override operator fun Polynomial<C>.times(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            this * other.numerator,
-            other.denominator
-        )
-
-    /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun RationalFunction<C>.plus(other: Polynomial<C>): RationalFunction<C> =
-        RationalFunction(
-            numerator + denominator * other,
-            denominator
-        )
-    /**
-     * Returns difference between the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun RationalFunction<C>.minus(other: Polynomial<C>): RationalFunction<C> =
-        RationalFunction(
-            numerator - denominator * other,
-            denominator
-        )
-    /**
-     * Returns product of the polynomial represented as rational function and the rational function.
-     */
-    public override operator fun RationalFunction<C>.times(other: Polynomial<C>): RationalFunction<C> =
-        RationalFunction(
-            numerator * other,
-            denominator
-        )
-
-    /**
-     * Returns negation of the rational function.
-     */
-    public override operator fun RationalFunction<C>.unaryMinus(): RationalFunction<C> = RationalFunction(-numerator, denominator)
-    /**
-     * Returns sum of the rational functions.
-     */
-    public override operator fun RationalFunction<C>.plus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            numerator * other.denominator + denominator * other.numerator,
-            denominator * other.denominator
-        )
-    /**
-     * Returns difference of the rational functions.
-     */
-    public override operator fun RationalFunction<C>.minus(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            numerator * other.denominator - denominator * other.numerator,
-            denominator * other.denominator
-        )
-    /**
-     * Returns product of the rational functions.
-     */
-    public override operator fun RationalFunction<C>.times(other: RationalFunction<C>): RationalFunction<C> =
-        RationalFunction(
-            numerator * other.numerator,
-            denominator * other.denominator
-        )
 
     /**
      * Instance of zero rational function (zero of the rational functions ring).
@@ -251,16 +68,6 @@ public class RationalFunctionSpace<C, A : Ring<C>> (
      */
     public override val one: RationalFunction<C> = RationalFunction(polynomialOne, polynomialOne)
 
-    /**
-     * Checks equality of the rational functions.
-     */
-    public override infix fun RationalFunction<C>.equalsTo(other: RationalFunction<C>): Boolean =
-        when {
-            this === other -> true
-            numeratorDegree - denominatorDegree != with(other) { numeratorDegree - denominatorDegree } -> false
-            else -> numerator * other.denominator equalsTo other.numerator * denominator
-        }
-
     // TODO: Разобрать
 
     public operator fun RationalFunction<C>.div(other: RationalFunction<C>): RationalFunction<C> =