Added division to RFs' Spaces. Added conversion to polynomial and RFs' spaces. Added requirements for RFs' denominators' changes for case of non-integral domain. Added requirements for non-zero divisor to RFs' divisions.

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

@@ -273,9 +273,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     /**
      * Converts the integer [value] to polynomial.
      */
-    public override fun number(value: Int): LabeledPolynomial<C> =
+    public override fun number(value: Int): LabeledPolynomial<C> = number(constantNumber(value))
-        if (value == 0) zero
-        else LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to constantNumber(value)))
 
     public operator fun C.plus(other: Symbol): LabeledPolynomial<C> =
         if (isZero()) LabeledPolynomial<C>(mapOf(
@@ -425,6 +423,13 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                 }
         )
 
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public override fun number(value: C): LabeledPolynomial<C> =
+        if (value == 0) zero
+        else LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to value))
+
     public operator fun Symbol.plus(other: Symbol): LabeledPolynomial<C> =
         if (this == other) LabeledPolynomial<C>(mapOf(
             mapOf(this to 1U) to constantOne * 2

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

@@ -144,24 +144,6 @@ public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
 
     // TODO: Разобрать
 
-    public operator fun LabeledRationalFunction<C>.div(other: LabeledRationalFunction<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator * other.denominator,
-            denominator * other.numerator
-        )
-
-    public operator fun LabeledRationalFunction<C>.div(other: LabeledPolynomial<C>): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator,
-            denominator * other
-        )
-
-    public operator fun LabeledRationalFunction<C>.div(other: C): LabeledRationalFunction<C> =
-        LabeledRationalFunction(
-            numerator,
-            denominator * other
-        )
-
 //    operator fun invoke(arg: Map<Symbol, C>): LabeledRationalFunction<C> =
 //        LabeledRationalFunction(
 //            numerator(arg),

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

@@ -66,7 +66,7 @@ public fun <C> ListPolynomial(coefficients: List<C>, reverse: Boolean = false):
 public fun <C> ListPolynomial(vararg coefficients: C, reverse: Boolean = false): ListPolynomial<C> =
     ListPolynomial(with(coefficients) { if (reverse) reversed() else toList() })
 
-public fun <C> C.asPolynomial() : ListPolynomial<C> = ListPolynomial(listOf(this))
+public fun <C> C.asListPolynomial() : ListPolynomial<C> = ListPolynomial(listOf(this))
 
 /**
  * Space of univariate polynomials constructed over ring.
@@ -199,9 +199,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
     /**
      * Converts the integer [value] to polynomial.
      */
-    public override fun number(value: Int): ListPolynomial<C> =
+    public override fun number(value: Int): ListPolynomial<C> = number(constantNumber(value))
-        if (value == 0) zero
-        else ListPolynomial(constantNumber(value))
 
     /**
      * Returns sum of the constant represented as polynomial and the polynomial.
@@ -313,6 +311,13 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
                 }
         )
 
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public override fun number(value: C): ListPolynomial<C> =
+        if (value.isZero()) zero
+        else ListPolynomial(value)
+
     /**
      * Returns negation of the polynomial.
      */

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

@@ -70,30 +70,6 @@ public class ListRationalFunctionSpace<C, A : Ring<C>> (
 
     // TODO: Разобрать
 
-    public operator fun ListRationalFunction<C>.div(other: ListRationalFunction<C>): ListRationalFunction<C> =
-        ListRationalFunction(
-            numerator * other.denominator,
-            denominator * other.numerator
-        )
-
-    public operator fun ListRationalFunction<C>.div(other: ListPolynomial<C>): ListRationalFunction<C> =
-        ListRationalFunction(
-            numerator,
-            denominator * other
-        )
-
-    public operator fun ListRationalFunction<C>.div(other: C): ListRationalFunction<C> =
-        ListRationalFunction(
-            numerator,
-            denominator * other
-        )
-
-    public operator fun ListRationalFunction<C>.div(other: Int): ListRationalFunction<C> =
-        ListRationalFunction(
-            numerator,
-            denominator * other
-        )
-
 //    operator fun invoke(arg: UnivariatePolynomial<T>): RationalFunction<T> =
 //        RationalFunction(
 //            numerator(arg),

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

@@ -225,9 +225,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
     /**
      * Converts the integer [value] to polynomial.
      */
-    public override fun number(value: Int): NumberedPolynomial<C> =
+    public override fun number(value: Int): NumberedPolynomial<C> = number(constantNumber(value))
-        if (value == 0) zero
-        else NumberedPolynomial(mapOf(emptyList<UInt>() to constantNumber(value)))
 
     /**
      * Returns sum of the constant represented as polynomial and the polynomial.
@@ -331,6 +329,13 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                 }
         )
 
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public override fun number(value: C): NumberedPolynomial<C> =
+        if (value == 0) zero
+        else NumberedPolynomial(mapOf(emptyList<UInt>() to value))
+
     /**
      * Returns negation of the polynomial.
      */

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

@@ -65,6 +65,10 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
      * Converts the integer [value] to constant.
      */
     public fun constantNumber(value: Int): C = constantOne * value
+    /**
+     * Converts the integer to constant.
+     */
+    public fun Int.asConstant(): C = constantNumber(this)
 
     /**
      * Returns sum of the polynomial and the integer represented as polynomial.
@@ -108,6 +112,10 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
      * Converts the integer [value] to polynomial.
      */
     public fun number(value: Int): P = one * value
+    /**
+     * Converts the integer to polynomial.
+     */
+    public fun Int.asPolynomial(): P = number(this)
 
     /**
      * Returns the same constant.
@@ -206,6 +214,15 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
      */
     public operator fun P.times(other: C): P
 
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public fun number(value: C): P = one * value
+    /**
+     * Converts the constant to polynomial.
+     */
+    public fun C.asPolynomial(): P = number(this)
+
     /**
      * Returns the same polynomial.
      */

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

@@ -72,6 +72,10 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * Converts the integer [value] to constant.
      */
     public fun constantNumber(value: Int): C = constantOne * value
+    /**
+     * Converts the integer to constant.
+     */
+    public fun Int.asConstant(): C = constantNumber(this)
 
     /**
      * Returns sum of the constant and the integer represented as polynomial.
@@ -115,6 +119,10 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * Converts the integer [value] to polynomial.
      */
     public fun polynomialNumber(value: Int): P = polynomialOne * value
+    /**
+     * Converts the integer to polynomial.
+     */
+    public fun Int.asPolynomial(): P = polynomialNumber(this)
 
     /**
      * Returns sum of the rational function and the integer represented as rational function.
@@ -134,6 +142,13 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public operator fun R.times(other: Int): R = multiplyBySquaring(this, other)
+    /**
+     * Returns quotient of the rational function and the integer represented as rational function.
+     *
+     * The operation is equivalent to creating a new rational function by preserving numerator of [this] and
+     * multiplication denominator of [this] to [other].
+     */
+    public operator fun R.div(other: Int): R = this / multiplyBySquaring(one, other)
 
     /**
      * Returns sum of the integer represented as rational function and the rational function.
@@ -153,11 +168,22 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * The operation is equivalent to sum of [this] copies of [other].
      */
     public operator fun Int.times(other: R): R = multiplyBySquaring(other, this)
+    /**
+     * Returns quotient of the integer represented as rational function and the rational function.
+     *
+     * The operation is equivalent to creating a new rational function which numerator is [this] times denominator of
+     * [other] and which denominator is [other]'s numerator.
+     */
+    public operator fun Int.div(other: R): R = multiplyBySquaring(one / other, this)
 
     /**
      * Converts the integer [value] to rational function.
      */
     public fun number(value: Int): R = one * value
+    /**
+     * Converts the integer to rational function.
+     */
+    public fun Int.asRationalFunction(): R = number(this)
 
     /**
      * Returns the same constant.
@@ -256,6 +282,15 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      */
     public operator fun P.times(other: C): P
 
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public fun polynomialNumber(value: C): P = polynomialOne * value
+    /**
+     * Converts the constant to polynomial.
+     */
+    public fun C.asPolynomial(): P = polynomialNumber(this)
+
     /**
      * Returns the same polynomial.
      */
@@ -276,6 +311,10 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * Returns product of the polynomials.
      */
     public operator fun P.times(other: P): P
+    /**
+     * Returns quotient of the polynomials as rational function.
+     */
+    public operator fun P.div(other: P): R
     /**
      * Raises [arg] to the integer power [exponent].
      */
@@ -336,19 +375,36 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * Returns product of the constant represented as polynomial and the rational function.
      */
     public operator fun C.times(other: R): R
+    /**
+     * Returns quotient of the constant represented as polynomial and the rational function.
+     */
+    public operator fun C.div(other: R): R
 
     /**
-     * Returns sum of the constant represented as rational function and the rational function.
+     * Returns sum of the rational function and the constant represented as rational function.
      */
     public operator fun R.plus(other: C): R
     /**
-     * Returns difference between the constant represented as rational function and the rational function.
+     * Returns difference between the rational function and the constant represented as rational function.
      */
     public operator fun R.minus(other: C): R
     /**
-     * Returns product of the constant represented as rational function and the rational function.
+     * Returns product of the rational function and the constant represented as rational function.
      */
     public operator fun R.times(other: C): R
+    /**
+     * Returns quotient of the rational function and the constant represented as rational function.
+     */
+    public operator fun R.div(other: C): R
+
+    /**
+     * Converts the constant [value] to rational function.
+     */
+    public fun number(value: C): R = one * value
+    /**
+     * Converts the constant to rational function.
+     */
+    public fun C.asRationalFunction(): R = number(this)
 
     /**
      * Returns sum of the polynomial represented as rational function and the rational function.
@@ -362,19 +418,36 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * Returns product of the polynomial represented as polynomial and the rational function.
      */
     public operator fun P.times(other: R): R
+    /**
+     * Returns quotient of the polynomial represented as polynomial and the rational function.
+     */
+    public operator fun P.div(other: R): R
 
     /**
-     * Returns sum of the polynomial represented as rational function and the rational function.
+     * Returns sum of the rational function and the polynomial represented as rational function.
      */
     public operator fun R.plus(other: P): R
     /**
-     * Returns difference between the polynomial represented as rational function and the rational function.
+     * Returns difference between the rational function and the polynomial represented as rational function.
      */
     public operator fun R.minus(other: P): R
     /**
-     * Returns product of the polynomial represented as rational function and the rational function.
+     * Returns product of the rational function and the polynomial represented as rational function.
      */
     public operator fun R.times(other: P): R
+    /**
+     * Returns quotient of the rational function and the polynomial represented as rational function.
+     */
+    public operator fun R.div(other: P): R
+
+    /**
+     * Converts the polynomial [value] to rational function.
+     */
+    public fun number(value: P): R = one * value
+    /**
+     * Converts the polynomial to rational function.
+     */
+    public fun P.asRationalFunction(): R = number(this)
 
     /**
      * Returns the same rational function.
@@ -396,6 +469,10 @@ public interface RationalFunctionalSpace<C, P: Polynomial<C>, R: RationalFunctio
      * Returns product of the rational functions.
      */
     public override operator fun R.times(other: R): R
+    /**
+     * Returns quotient of the rational functions.
+     */
+    public operator fun R.div(other: R): R
     /**
      * Raises [arg] to the integer power [exponent].
      */
@@ -649,6 +726,15 @@ public interface RationalFunctionalSpaceOverPolynomialSpace<
      */
     public override operator fun Int.times(other: C): C = polynomialRing { this@times * other }
 
+    /**
+     * Converts the integer [value] to constant.
+     */
+    public override fun constantNumber(value: Int): C = polynomialRing { constantNumber(value) }
+    /**
+     * Converts the integer to constant.
+     */
+    override fun Int.asConstant(): C = polynomialRing { asConstant() }
+
     /**
      * Returns sum of the constant and the integer represented as polynomial.
      *
@@ -691,6 +777,10 @@ public interface RationalFunctionalSpaceOverPolynomialSpace<
      * Converts the integer [value] to polynomial.
      */
     public override fun polynomialNumber(value: Int): P = polynomialRing { number(value) }
+    /**
+     * Converts the integer to polynomial.
+     */
+    public override fun Int.asPolynomial(): P = polynomialRing { asPolynomial() }
 
     /**
      * Returns the same constant.
@@ -783,6 +873,15 @@ public interface RationalFunctionalSpaceOverPolynomialSpace<
      */
     public override operator fun P.times(other: C): P = polynomialRing { this@times * other }
 
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public override fun polynomialNumber(value: C): P = polynomialRing { number(value) }
+    /**
+     * Converts the constant to polynomial.
+     */
+    public override fun C.asPolynomial(): P = polynomialRing { asPolynomial() }
+
     /**
      * Returns the same polynomial.
      */
@@ -933,6 +1032,19 @@ public abstract class PolynomialSpaceOfFractions<
             denominator
         )
 
+    public override operator fun R.div(other: Int): R {
+        val otherAsConstant = constantNumber(other)
+        require(otherAsConstant.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            numerator,
+            (denominator * other).also {
+                check(it.isNotZero()) {
+                    "Got zero denominator during division of rational functions to constant. It means underlying ring of polynomials is not integral domain."
+                }
+            }
+        )
+    }
+
     /**
      * Returns sum of the integer represented as rational function and the rational function.
      *
@@ -964,11 +1076,24 @@ public abstract class PolynomialSpaceOfFractions<
             other.denominator
         )
 
+    public override operator fun Int.div(other: R): R {
+        require(other.numerator.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            this * other.denominator,
+            other.numerator
+        )
+    }
+
     /**
      * Converts the integer [value] to rational function.
      */
     public override fun number(value: Int): R = constructRationalFunction(polynomialNumber(value))
 
+    /**
+     * Returns quotient of the polynomials as rational function.
+     */
+    public override operator fun P.div(other: P): R = constructRationalFunction(this, other)
+
     /**
      * Returns sum of the constant represented as rational function and the rational function.
      */
@@ -994,6 +1119,14 @@ public abstract class PolynomialSpaceOfFractions<
             other.denominator
         )
 
+    public override operator fun C.div(other: R): R {
+        require(other.numerator.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            this * other.denominator,
+            other.numerator
+        )
+    }
+
     /**
      * Returns sum of the constant represented as rational function and the rational function.
      */
@@ -1019,6 +1152,23 @@ public abstract class PolynomialSpaceOfFractions<
             denominator
         )
 
+    public override operator fun R.div(other: C): R {
+        require(other.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            numerator,
+            (denominator * other).also {
+                check(it.isNotZero()) {
+                    "Got zero denominator during division of rational functions to constant. It means underlying ring of polynomials is not integral domain."
+                }
+            }
+        )
+    }
+
+    /**
+     * Converts the constant [value] to rational function.
+     */
+    public override fun number(value: C): R = constructRationalFunction(polynomialNumber(value))
+
     /**
      * Returns sum of the polynomial represented as rational function and the rational function.
      */
@@ -1044,6 +1194,14 @@ public abstract class PolynomialSpaceOfFractions<
             other.denominator
         )
 
+    public override operator fun P.div(other: R): R {
+        require(other.numerator.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            this * other.denominator,
+            other.numerator
+        )
+    }
+
     /**
      * Returns sum of the polynomial represented as rational function and the rational function.
      */
@@ -1069,6 +1227,23 @@ public abstract class PolynomialSpaceOfFractions<
             denominator
         )
 
+    public override operator fun R.div(other: P): R {
+        require(other.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            numerator,
+            (denominator * other).also {
+                require(it.isNotZero()) {
+                    "Got zero denominator during division of rational functions to polynomial. It means underlying ring of polynomials is not integral domain."
+                }
+            }
+        )
+    }
+
+    /**
+     * Converts the polynomial [value] to rational function.
+     */
+    public override fun number(value: P): R = constructRationalFunction(value)
+
     /**
      * Returns negation of the rational function.
      */
@@ -1079,7 +1254,11 @@ public abstract class PolynomialSpaceOfFractions<
     public override operator fun R.plus(other: R): R =
         constructRationalFunction(
             numerator * other.denominator + denominator * other.numerator,
-            denominator * other.denominator
+            (denominator * other.denominator).also {
+                check(it.isNotZero()) {
+                    "Got zero denominator during addition of rational functions. It means underlying ring of polynomials is not integral domain."
+                }
+            }
         )
     /**
      * Returns difference of the rational functions.
@@ -1087,7 +1266,11 @@ public abstract class PolynomialSpaceOfFractions<
     public override operator fun R.minus(other: R): R =
         constructRationalFunction(
             numerator * other.denominator - denominator * other.numerator,
-            denominator * other.denominator
+            (denominator * other.denominator).also {
+                check(it.isNotZero()) {
+                    "Got zero denominator during subtraction of rational functions. It means underlying ring of polynomials is not integral domain."
+                }
+            }
         )
     /**
      * Returns product of the rational functions.
@@ -1095,9 +1278,25 @@ public abstract class PolynomialSpaceOfFractions<
     public override operator fun R.times(other: R): R =
         constructRationalFunction(
             numerator * other.numerator,
-            denominator * other.denominator
+            (denominator * other.denominator).also {
+                check(it.isNotZero()) {
+                    "Got zero denominator during multiplication of rational functions. It means underlying ring of polynomials is not integral domain."
+                }
+            }
         )
 
+    public override operator fun R.div(other: R): R {
+        require(other.isNotZero()) { "/ by zero." }
+        return constructRationalFunction(
+            numerator * other.denominator,
+            (denominator * other.numerator).also {
+                check(it.isNotZero()) {
+                    "Got zero denominator during division of rational functions. It means underlying ring of polynomials is not integral domain."
+                }
+            }
+        )
+    }
+
     /**
      * Instance of zero rational function (zero of the rational functions ring).
      */