1. Prototyped rest 2 algebraic structures of rational functions

2. Added `constantZero` and `constantOne` to abstract spaces and applied them instead of `ring.zero` and `ring.one`
3. Moved logic of `R.isZero` and 5 others to `AbstractRationalFunctionalSpace`
4. Deleted forgotten overridden functions of constants
5. Added KMath contributors' copyright notes
6. Added TODO 😄 The `NumberedPolynomial`'s `countOfVariables` is a confusing

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

@@ -149,7 +149,7 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Check if the instant is zero constant.
      */
     @JvmName("constantIsZero")
-    public fun C.isZero(): Boolean
+    public fun C.isZero(): Boolean = this == constantZero
     /**
      * Check if the instant is NOT zero constant.
      */
@@ -159,7 +159,7 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Check if the instant is unit constant.
      */
     @JvmName("constantIsOne")
-    public fun C.isOne(): Boolean
+    public fun C.isOne(): Boolean = this == constantOne
     /**
      * Check if the instant is NOT unit constant.
      */
@@ -169,12 +169,21 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Check if the instant is minus unit constant.
      */
     @JvmName("constantIsMinusOne")
-    public fun C.isMinusOne(): Boolean
+    public fun C.isMinusOne(): Boolean = this == -constantOne
     /**
      * Check if the instant is NOT minus unit constant.
      */
     @JvmName("constantIsNotMinusOne")
     public fun C.isNotMinusOne(): Boolean = !isMinusOne()
+
+    /**
+     * Instance of zero constant (zero of the underlying ring).
+     */
+    public val constantZero: C
+    /**
+     * Instance of unit constant (unit of the underlying ring).
+     */
+    public val constantOne: C
     // endregion
 
     // region Constant-polynomial relation
@@ -401,19 +410,12 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
     public override operator fun C.times(other: C): C = ring { this@times * other }
 
     /**
-     * Check if the instant is zero constant.
+     * Instance of zero constant (zero of the underlying ring).
      */
-    @JvmName("constantIsZero")
+    public override val constantZero: C get() = ring.zero
-    public override fun C.isZero(): Boolean = ring { this == zero }
     /**
-     * Check if the instant is unit constant.
+     * Instance of unit constant (unit of the underlying ring).
      */
-    @JvmName("constantIsOne")
+    public override val constantOne: C get() = ring.one
-    public override fun C.isOne(): Boolean = ring { this == one }
-    /**
-     * Check if the instant is minus unit constant.
-     */
-    @JvmName("constantIsMinusOne")
-    public override fun C.isMinusOne(): Boolean = ring { this == -one }
     // endregion
 }

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

@@ -190,7 +190,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Check if the instant is zero constant.
      */
     @JvmName("constantIsZero")
-    public fun C.isZero(): Boolean
+    public fun C.isZero(): Boolean = this == constantZero
     /**
      * Check if the instant is NOT zero constant.
      */
@@ -200,7 +200,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Check if the instant is unit constant.
      */
     @JvmName("constantIsOne")
-    public fun C.isOne(): Boolean
+    public fun C.isOne(): Boolean =  this == constantOne
     /**
      * Check if the instant is NOT unit constant.
      */
@@ -210,12 +210,21 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Check if the instant is minus unit constant.
      */
     @JvmName("constantIsMinusOne")
-    public fun C.isMinusOne(): Boolean
+    public fun C.isMinusOne(): Boolean =  this == -constantOne
     /**
      * Check if the instant is NOT minus unit constant.
      */
     @JvmName("constantIsNotMinusOne")
     public fun C.isNotMinusOne(): Boolean = !isMinusOne()
+
+    /**
+     * Instance of zero constant (zero of the underlying ring).
+     */
+    public val constantZero: C
+    /**
+     * Instance of unit constant (unit of the underlying ring).
+     */
+    public val constantOne: C
     // endregion
 
     // region Constant-polynomial relation
@@ -399,7 +408,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Check if the instant is zero rational function.
      */
-    public fun R.isZero(): Boolean = this equalsTo zero
+    public fun R.isZero(): Boolean = numerator equalsTo polynomialZero
     /**
      * Check if the instant is NOT zero rational function.
      */
@@ -407,7 +416,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Check if the instant is unit rational function.
      */
-    public fun R.isOne(): Boolean = this equalsTo one
+    public fun R.isOne(): Boolean = numerator equalsTo denominator
     /**
      * Check if the instant is NOT unit rational function.
      */
@@ -415,7 +424,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Check if the instant is minus unit rational function.
      */
-    public fun R.isMinusOne(): Boolean = this equalsTo -one
+    public fun R.isMinusOne(): Boolean = (numerator + denominator).isZero()
     /**
      * Check if the instant is NOT minus unit rational function.
      */
@@ -597,35 +606,13 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
     public override operator fun C.times(other: C): C = ring { this@times * other }
 
     /**
-     * Check if the instant is zero constant.
+     * Instance of zero constant (zero of the underlying ring).
      */
-    @JvmName("constantIsZero")
+    public override val constantZero: C get() = ring.zero
-    public override fun C.isZero(): Boolean = ring { this@isZero.isZero() }
     /**
-     * Check if the instant is NOT zero constant.
+     * Instance of unit constant (unit of the underlying ring).
      */
-    @JvmName("constantIsNotZero")
+    public override val constantOne: C get() = ring.one
-    public override fun C.isNotZero(): Boolean = ring { this@isNotZero.isNotZero() }
-    /**
-     * Check if the instant is unit constant.
-     */
-    @JvmName("constantIsOne")
-    public override fun C.isOne(): Boolean = ring { this@isOne.isOne() }
-    /**
-     * Check if the instant is NOT unit constant.
-     */
-    @JvmName("constantIsNotOne")
-    public override fun C.isNotOne(): Boolean = ring { this@isNotOne.isNotOne() }
-    /**
-     * Check if the instant is minus unit constant.
-     */
-    @JvmName("constantIsMinusOne")
-    public override fun C.isMinusOne(): Boolean = ring { this@isMinusOne.isMinusOne() }
-    /**
-     * Check if the instant is NOT minus unit constant.
-     */
-    @JvmName("constantIsNotMinusOne")
-    public override fun C.isNotMinusOne(): Boolean = ring { this@isNotMinusOne.isNotMinusOne() }
     // endregion
 }
 
@@ -786,6 +773,15 @@ public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<C, P: Abstra
      */
     @JvmName("constantIsNotMinusOne")
     public override fun C.isNotMinusOne(): Boolean = polynomialRing { this@isNotMinusOne.isNotMinusOne() }
+
+    /**
+     * Instance of zero constant (zero of the underlying ring).
+     */
+    public override val constantZero: C get() = polynomialRing.constantZero
+    /**
+     * Instance of unit constant (unit of the underlying ring).
+     */
+    public override val constantOne: C get() = polynomialRing.constantOne
     // endregion
 
     // region Constant-polynomial relation

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

@@ -1,3 +1,8 @@
+/*
+ * 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.operations.*
@@ -305,7 +310,7 @@ internal fun Map<Variable, UInt>.cleanUp() = filterValues { it > 0U }
 //fun <C, A: Ring<C>> Variable.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf<Variable, UInt>(this to 1U) to one))
 //
 //context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> Variable.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf<Variable, UInt>(this to 1U) to ring.one))
+//fun <C, A: Ring<C>> Variable.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf<Variable, UInt>(this to 1U) to constantOne))
 //
 //context(A)
 //fun <C, A: Ring<C>> Variable.asLabeledPolynomial(c: C) : LabeledPolynomial<C> =
@@ -328,71 +333,54 @@ internal fun Map<Variable, UInt>.cleanUp() = filterValues { it > 0U }
  */
 @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE", "INAPPLICABLE_JVM_NAME")
 public class LabeledPolynomialSpace<C, A : Ring<C>>(
-    public val ring: A,
+    public override val ring: A,
-) : AbstractPolynomialSpace<C, LabeledPolynomial<C>> {
+) : AbstractPolynomialSpaceOverRing<C, LabeledPolynomial<C>, A> {
-    // region Constant-integer relation
-    @JvmName("constantIntPlus")
-    public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) }
-    @JvmName("constantIntMinus")
-    public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) }
-    @JvmName("constantIntTimes")
-    public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) }
-    // endregion
-
-    // region Integer-constant relation
-    @JvmName("intConstantPlus")
-    public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) }
-    @JvmName("intConstantMinus")
-    public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) }
-    @JvmName("intConstantTimes")
-    public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) }
-    // endregion
 
     // region Variable-integer relation
     public operator fun Variable.plus(other: Int): LabeledPolynomial<C> =
         if (other == 0) LabeledPolynomial<C>(mapOf(
-            mapOf(this@plus to 1U) to ring.one,
+            mapOf(this@plus to 1U) to constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this@plus to 1U) to ring.one,
+            mapOf(this@plus to 1U) to constantOne,
-            emptyMap<Variable, UInt>() to ring.one * other,
+            emptyMap<Variable, UInt>() to constantOne * other,
         ))
     public operator fun Variable.minus(other: Int): LabeledPolynomial<C> =
         if (other == 0) LabeledPolynomial<C>(mapOf(
-            mapOf(this@minus to 1U) to -ring.one,
+            mapOf(this@minus to 1U) to -constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this@minus to 1U) to -ring.one,
+            mapOf(this@minus to 1U) to -constantOne,
-            emptyMap<Variable, UInt>() to ring.one * other,
+            emptyMap<Variable, UInt>() to constantOne * other,
         ))
     public operator fun Variable.times(other: Int): LabeledPolynomial<C> =
         if (other == 0) zero
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this to 1U) to ring.one * other,
+            mapOf(this to 1U) to constantOne * other,
         ))
     // endregion
 
     // region Integer-variable relation
     public operator fun Int.plus(other: Variable): LabeledPolynomial<C> =
         if (this == 0) LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to ring.one,
+            mapOf(other to 1U) to constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to ring.one,
+            mapOf(other to 1U) to constantOne,
-            emptyMap<Variable, UInt>() to ring.one * this@plus,
+            emptyMap<Variable, UInt>() to constantOne * this@plus,
         ))
     public operator fun Int.minus(other: Variable): LabeledPolynomial<C> =
         if (this == 0) LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to -ring.one,
+            mapOf(other to 1U) to -constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to -ring.one,
+            mapOf(other to 1U) to -constantOne,
-            emptyMap<Variable, UInt>() to ring.one * this@minus,
+            emptyMap<Variable, UInt>() to constantOne * this@minus,
         ))
     public operator fun Int.times(other: Variable): LabeledPolynomial<C> =
         if (this == 0) zero
         else LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to ring.one * this@times,
+            mapOf(other to 1U) to constantOne * this@times,
         ))
     // endregion
 
@@ -406,7 +394,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } + other
+                        val result = getOrElse(degs) { constantZero } + other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -421,7 +409,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } - other
+                        val result = getOrElse(degs) { constantZero } - other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -447,7 +435,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = this@plus + getOrElse(degs) { ring.zero }
+                        val result = this@plus + getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -462,7 +450,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = this@minus - getOrElse(degs) { ring.zero }
+                        val result = this@minus - getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -478,44 +466,21 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         )
     // endregion
 
-    // region Constant-constant relation
-    @JvmName("constantUnaryMinus")
-    override operator fun C.unaryMinus(): C = ring { -this@unaryMinus }
-    @JvmName("constantPlus")
-    override operator fun C.plus(other: C): C = ring { this@plus + other }
-    @JvmName("constantMinus")
-    override operator fun C.minus(other: C): C = ring { this@minus - other }
-    @JvmName("constantTimes")
-    override operator fun C.times(other: C): C = ring { this@times * other }
-    @JvmName("constantIsZero")
-    public override fun C.isZero(): Boolean = ring { this == zero }
-    @JvmName("constantIsNotZero")
-    public override fun C.isNotZero(): Boolean = ring { this != zero }
-    @JvmName("constantIsOne")
-    public override fun C.isOne(): Boolean = ring { this == one }
-    @JvmName("constantIsNotOne")
-    public override fun C.isNotOne(): Boolean = ring { this != one }
-    @JvmName("constantIsMinusOne")
-    public override fun C.isMinusOne(): Boolean = ring { this == -one }
-    @JvmName("constantIsNotMinusOne")
-    public override fun C.isNotMinusOne(): Boolean = ring { this != -one }
-    // endregion
-
     // region Constant-variable relation
     public operator fun C.plus(other: Variable): LabeledPolynomial<C> =
         if (isZero()) LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to ring.one,
+            mapOf(other to 1U) to constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to ring.one,
+            mapOf(other to 1U) to constantOne,
             emptyMap<Variable, UInt>() to this@plus,
         ))
     public operator fun C.minus(other: Variable): LabeledPolynomial<C> =
         if (isZero()) LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to -ring.one,
+            mapOf(other to 1U) to -constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to -ring.one,
+            mapOf(other to 1U) to -constantOne,
             emptyMap<Variable, UInt>() to this@minus,
         ))
     public operator fun C.times(other: Variable): LabeledPolynomial<C> =
@@ -528,18 +493,18 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     // region Variable-constant relation
     public operator fun Variable.plus(other: C): LabeledPolynomial<C> =
         if (other.isZero()) LabeledPolynomial<C>(mapOf(
-            mapOf(this@plus to 1U) to ring.one,
+            mapOf(this@plus to 1U) to constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this@plus to 1U) to ring.one,
+            mapOf(this@plus to 1U) to constantOne,
             emptyMap<Variable, UInt>() to other,
         ))
     public operator fun Variable.minus(other: C): LabeledPolynomial<C> =
         if (other.isZero()) LabeledPolynomial<C>(mapOf(
-            mapOf(this@minus to 1U) to -ring.one,
+            mapOf(this@minus to 1U) to -constantOne,
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this@minus to 1U) to -ring.one,
+            mapOf(this@minus to 1U) to -constantOne,
             emptyMap<Variable, UInt>() to other,
         ))
     public operator fun Variable.times(other: C): LabeledPolynomial<C> =
@@ -559,7 +524,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = this@plus + getOrElse(degs) { ring.zero }
+                        val result = this@plus + getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -577,7 +542,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
 
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = this@minus - getOrElse(degs) { ring.zero }
+                        val result = this@minus - getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -607,7 +572,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } + other
+                        val result = getOrElse(degs) { constantZero } + other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -628,7 +593,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
 
                         val degs = emptyMap<Variable, UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } - other
+                        val result = getOrElse(degs) { constantZero } - other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -651,37 +616,37 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     // region Variable-variable relation
     public operator fun Variable.plus(other: Variable): LabeledPolynomial<C> =
         if (this == other) LabeledPolynomial<C>(mapOf(
-            mapOf(this to 1U) to ring.one * 2
+            mapOf(this to 1U) to constantOne * 2
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this to 1U) to ring.one,
+            mapOf(this to 1U) to constantOne,
-            mapOf(other to 1U) to ring.one,
+            mapOf(other to 1U) to constantOne,
         ))
     public operator fun Variable.minus(other: Variable): LabeledPolynomial<C> =
         if (this == other) zero
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this to 1U) to ring.one,
+            mapOf(this to 1U) to constantOne,
-            mapOf(other to 1U) to -ring.one,
+            mapOf(other to 1U) to -constantOne,
         ))
     public operator fun Variable.times(other: Variable): LabeledPolynomial<C> =
         if (this == other) LabeledPolynomial<C>(mapOf(
-            mapOf(this to 2U) to ring.one
+            mapOf(this to 2U) to constantOne
         ))
         else LabeledPolynomial<C>(mapOf(
-            mapOf(this to 1U, other to 1U) to ring.one,
+            mapOf(this to 1U, other to 1U) to constantOne,
         ))
     // endregion
 
     // region Variable-polynomial relation
     public operator fun Variable.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@plus to 1u) to ring.one))
+            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@plus to 1u) to constantOne))
             else LabeledPolynomial<C>(
                 toMutableMap()
                     .apply {
                         val degs = mapOf(this@plus to 1U)
 
-                        val result = ring.one + getOrElse(degs) { ring.zero }
+                        val result = constantOne + getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -690,7 +655,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         }
     public operator fun Variable.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@minus to 1u) to ring.one))
+            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@minus to 1u) to constantOne))
             else LabeledPolynomial<C>(
                 toMutableMap()
                     .apply {
@@ -698,7 +663,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
 
                         val degs = mapOf(this@minus to 1U)
 
-                        val result = ring.one - getOrElse(degs) { ring.zero }
+                        val result = constantOne - getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -715,13 +680,13 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     // region Polynomial-variable relation
     public operator fun LabeledPolynomial<C>.plus(other: Variable): LabeledPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to ring.one))
+            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to constantOne))
             else LabeledPolynomial<C>(
                 toMutableMap()
                     .apply {
                         val degs = mapOf(other to 1U)
 
-                        val result = ring.one + getOrElse(degs) { ring.zero }
+                        val result = constantOne + getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -730,13 +695,13 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         }
     public operator fun LabeledPolynomial<C>.minus(other: Variable): LabeledPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to ring.one))
+            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to constantOne))
             else LabeledPolynomial<C>(
                 toMutableMap()
                     .apply {
                         val degs = mapOf(other to 1U)
 
-                        val result = ring.one - getOrElse(degs) { ring.zero }
+                        val result = constantOne - getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -799,8 +764,8 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
 
-    override val zero: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Variable, UInt>() to ring.zero))
+    override val zero: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Variable, UInt>() to constantZero))
-    override val one: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Variable, UInt>() to ring.one))
+    override val one: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Variable, UInt>() to constantOne))
 
     // TODO: Docs
     @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
@@ -872,7 +837,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
 
     override fun LabeledPolynomial<C>.asConstantOrNull(): C? =
         with(coefficients) {
-            if(isConstant()) getOrElse(emptyMap()) { ring.zero }
+            if(isConstant()) getOrElse(emptyMap()) { constantZero }
             else null
         }
 

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

@@ -0,0 +1,464 @@
+/*
+ * 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.operations.Ring
+import space.kscience.kmath.operations.invoke
+
+
+public class LabeledRationalFunction<C>(
+    public override val numerator: LabeledPolynomial<C>,
+    public override val denominator: LabeledPolynomial<C>
+) : AbstractRationalFunction<C, LabeledPolynomial<C>> {
+    override fun toString(): String = "LabeledRationalFunction${numerator.coefficients}/${denominator.coefficients}"
+}
+
+// region Internal utilities
+
+/**
+ * Represents internal [LabeledRationalFunction] errors.
+ */
+internal class LabeledRationalFunctionError : Error {
+    constructor(): super()
+    constructor(message: String): super(message)
+    constructor(message: String?, cause: Throwable?): super(message, cause)
+    constructor(cause: Throwable?): super(cause)
+}
+
+/**
+ * Throws an [LabeledRationalFunctionError] with the given [message].
+ */
+internal fun labeledRationalFunctionError(message: Any): Nothing = throw LabeledRationalFunctionError(message.toString())
+
+// endregion
+
+// region Constructors and converters
+// Waiting for context receivers :( TODO: Replace with context receivers when they will be available
+
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//internal fun <C, A: Ring<C>> RationalFunction(numerator: Polynomial<C>, denominator: Polynomial<C>): RationalFunction<C> =
+//    if (denominator.isZero()) throw ArithmeticException("/ by zero")
+//    else RationalFunction<C>(numerator, denominator)
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//public fun <C, A: Ring<C>> RationalFunction(numeratorCoefficients: List<C>, denominatorCoefficients: List<C>, reverse: Boolean = false): RationalFunction<C> =
+//    RationalFunction<C>(
+//        Polynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
+//        Polynomial( with(denominatorCoefficients) { if (reverse) reversed() else this } ).also { if (it.isZero()) }
+//    )
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//public fun <C, A: Ring<C>> RationalFunction(numerator: Polynomial<C>): RationalFunction<C> =
+//    RationalFunction(numerator, onePolynomial)
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//public fun <C, A: Ring<C>> RationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): RationalFunction<C> =
+//    RationalFunction(
+//        Polynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } )
+//    )
+
+// TODO: Rewrite former constructors as fabrics
+//constructor(numeratorCoefficients: Map<Map<Variable, Int>, C>, denominatorCoefficients: Map<Map<Variable, Int>, C>) : this(
+//LabeledPolynomial(numeratorCoefficients),
+//LabeledPolynomial(denominatorCoefficients)
+//)
+//
+//constructor(numeratorCoefficients: Collection<Pair<Map<Variable, Int>, C>>, denominatorCoefficients: Collection<Pair<Map<Variable, Int>, C>>) : this(
+//LabeledPolynomial(numeratorCoefficients),
+//LabeledPolynomial(denominatorCoefficients)
+//)
+//
+//constructor(numerator: LabeledPolynomial<C>) : this(numerator, numerator.getOne())
+//constructor(numeratorCoefficients: Map<Map<Variable, Int>, C>) : this(
+//LabeledPolynomial(numeratorCoefficients)
+//)
+//
+//constructor(numeratorCoefficients: Collection<Pair<Map<Variable, Int>, C>>) : this(
+//LabeledPolynomial(numeratorCoefficients)
+//)
+
+// endregion
+
+public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
+    public val ring: A,
+) : AbstractRationalFunctionalSpaceOverPolynomialSpace<C, LabeledPolynomial<C>, LabeledRationalFunction<C>, A> {
+
+    override val polynomialRing : LabeledPolynomialSpace<C, A> = LabeledPolynomialSpace(ring)
+
+    // 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 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
+        )
+    // 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 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
+        )
+    // endregion
+
+    // region Constant-rational relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Rational-constant relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Polynomial-rational relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Rational-polynomial relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Rational-rational relation
+    /**
+     * 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).
+     */
+    public override val zero: LabeledRationalFunction<C> = LabeledRationalFunction(polynomialZero, polynomialOne)
+    /**
+     * Instance of unit polynomial (unit of the rational functions ring).
+     */
+    public override val one: LabeledRationalFunction<C> = LabeledRationalFunction(polynomialOne, polynomialOne)
+
+    /**
+     * Checks equality of the rational functions.
+     */
+    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
+    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
+
+        val variables = this.variables union other.variables
+        val thisNumeratorDegrees = this.numerator.degrees
+        val thisDenominatorDegrees = this.denominator.degrees
+        val otherNumeratorDegrees = other.numerator.degrees
+        val otherDenominatorDegrees = other.denominator.degrees
+        for (variable in variables)
+            if (
+                thisNumeratorDegrees.getOrElse(variable) { 0u } + otherDenominatorDegrees.getOrElse(variable) { 0u }
+                != thisDenominatorDegrees.getOrElse(variable) { 0u } + otherNumeratorDegrees.getOrElse(variable) { 0u }
+            ) return false
+
+        return numerator * other.denominator equalsTo other.numerator * denominator
+    }
+    // endregion
+
+    // region Polynomial properties
+    /**
+     * Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents
+     * in which they are appeared in the polynomial.
+     *
+     * As consequence all values in the map are positive integers. Also, if the polynomial is constant, the map is empty.
+     * And keys of the map is the same as in [variables].
+     */
+    public val LabeledPolynomial<C>.degrees: Map<Variable, UInt> get() = polynomialRing { degrees }
+    /**
+     * Set of all variables that appear in the polynomial in positive exponents.
+     */
+    public val LabeledPolynomial<C>.variables: Set<Variable> get() = polynomialRing { variables }
+    /**
+     * Count of all variables that appear in the polynomial in positive exponents.
+     */
+    public val LabeledPolynomial<C>.countOfVariables: Int get() = polynomialRing { countOfVariables }
+    // endregion
+
+    // region Rational properties
+    /**
+     * Count of all variables that appear in the polynomial in positive exponents.
+     */
+    public val LabeledRationalFunction<C>.variables: Set<Variable>
+        get() = numerator.variables union denominator.variables
+    /**
+     * Count of all variables that appear in the polynomial in positive exponents.
+     */
+    public val LabeledRationalFunction<C>.countOfVariables: Int get() = variables.size
+    // endregion
+
+    // region REST 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<Variable, C>): LabeledRationalFunction<C> =
+//        LabeledRationalFunction(
+//            numerator(arg),
+//            denominator(arg)
+//        )
+//
+//    @JvmName("invokeLabeledPolynomial")
+//    operator fun invoke(arg: Map<Variable, LabeledPolynomial<C>>): LabeledRationalFunction<C> =
+//        LabeledRationalFunction(
+//            numerator(arg),
+//            denominator(arg)
+//        )
+//
+//    @JvmName("invokeLabeledRationalFunction")
+//    operator fun invoke(arg: Map<Variable, LabeledRationalFunction<C>>): LabeledRationalFunction<C> {
+//        var num = numerator invokeRFTakeNumerator arg
+//        var den = denominator invokeRFTakeNumerator arg
+//        for (variable in variables) if (variable in arg) {
+//            val degreeDif = degrees[variable]!!
+//            if (degreeDif > 0)
+//                den = multiplyByPower(den, arg[variable]!!.denominator, degreeDif)
+//            else
+//                num = multiplyByPower(num, arg[variable]!!.denominator, -degreeDif)
+//        }
+//        return LabeledRationalFunction(num, den)
+//    }
+//
+//    override fun toString(): String = toString(emptyMap())
+//
+//    fun toString(names: Map<Variable, String> = emptyMap()): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toString(names)
+//            else -> "${numerator.toStringWithBrackets(names)}/${denominator.toStringWithBrackets(names)}"
+//        }
+//
+//    fun toString(namer: (Variable) -> String): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toString(namer)
+//            else -> "${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)}"
+//        }
+//
+//    fun toStringWithBrackets(names: Map<Variable, String> = emptyMap()): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toStringWithBrackets(names)
+//            else -> "(${numerator.toStringWithBrackets(names)}/${denominator.toStringWithBrackets(names)})"
+//        }
+//
+//    fun toStringWithBrackets(namer: (Variable) -> String): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toStringWithBrackets(namer)
+//            else -> "(${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)})"
+//        }
+//
+//    fun toReversedString(names: Map<Variable, String> = emptyMap()): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedString(names)
+//            else -> "${numerator.toReversedStringWithBrackets(names)}/${denominator.toReversedStringWithBrackets(names)}"
+//        }
+//
+//    fun toReversedString(namer: (Variable) -> String): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedString(namer)
+//            else -> "${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)}"
+//        }
+//
+//    fun toReversedStringWithBrackets(names: Map<Variable, String> = emptyMap()): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedStringWithBrackets(names)
+//            else -> "(${numerator.toReversedStringWithBrackets(names)}/${denominator.toReversedStringWithBrackets(names)})"
+//        }
+//
+//    fun toReversedStringWithBrackets(namer: (Variable) -> String): String =
+//        when (true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedStringWithBrackets(namer)
+//            else -> "(${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)})"
+//        }
+}

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

@@ -1,3 +1,8 @@
+/*
+ * 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.operations.*
@@ -272,7 +277,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } + other
+                        val result = getOrElse(degs) { constantZero } + other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -287,7 +292,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } - other
+                        val result = getOrElse(degs) { constantZero } - other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -313,7 +318,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = this@plus + getOrElse(degs) { ring.zero }
+                        val result = this@plus + getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -328,7 +333,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = this@minus - getOrElse(degs) { ring.zero }
+                        val result = this@minus - getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -354,7 +359,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = this@plus + getOrElse(degs) { ring.zero }
+                        val result = this@plus + getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -372,7 +377,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
 
                         val degs = emptyList<UInt>()
 
-                        val result = this@minus - getOrElse(degs) { ring.zero }
+                        val result = this@minus - getOrElse(degs) { constantZero }
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -402,7 +407,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } + other
+                        val result = getOrElse(degs) { constantZero } + other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -421,7 +426,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         val degs = emptyList<UInt>()
 
-                        val result = getOrElse(degs) { ring.zero } - other
+                        val result = getOrElse(degs) { constantZero } - other
 
                         if (result.isZero()) remove(degs)
                         else this[degs] = result
@@ -522,7 +527,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
     override val one: NumberedPolynomial<C> =
         NumberedPolynomial<C>(
             mapOf(
-                listOf<UInt>() to ring.one // 1 * x_1^0 * x_2^0 * ...
+                listOf<UInt>() to constantOne // 1 * x_1^0 * x_2^0 * ...
             )
         )
 
@@ -538,6 +543,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
 
     // Not sure is it necessary...
     // region Polynomial properties
+    // TODO: Replace `countOfVariables` with `lastVariable` and create new `countOfVariables`
     /**
      * Count of all variables that appear in the polynomial in positive exponents.
      */
@@ -590,7 +596,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
 
     override fun NumberedPolynomial<C>.asConstantOrNull(): C? =
         with(coefficients) {
-            if(isConstant()) getOrElse(emptyList()) { ring.zero }
+            if(isConstant()) getOrElse(emptyList()) { constantZero }
             else null
         }
 

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

@@ -0,0 +1,453 @@
+/*
+ * 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.operations.*
+import kotlin.math.max
+
+
+public class NumberedRationalFunction<C> internal constructor(
+    public override val numerator: NumberedPolynomial<C>,
+    public override val denominator: NumberedPolynomial<C>
+) : AbstractRationalFunction<C, NumberedPolynomial<C>> {
+    override fun toString(): String = "NumberedRationalFunction${numerator.coefficients}/${denominator.coefficients}"
+}
+
+// region Internal utilities
+
+/**
+ * Represents internal [NumberedRationalFunction] errors.
+ */
+internal class NumberedRationalFunctionError : Error {
+    constructor(): super()
+    constructor(message: String): super(message)
+    constructor(message: String?, cause: Throwable?): super(message, cause)
+    constructor(cause: Throwable?): super(cause)
+}
+
+/**
+ * Throws an [NumberedRationalFunctionError] with the given [message].
+ */
+internal fun numberedRationalFunctionError(message: Any): Nothing = throw NumberedRationalFunctionError(message.toString())
+
+// endregion
+
+// region Constructors and converters
+// Waiting for context receivers :( TODO: Replace with context receivers when they will be available
+
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//internal fun <C, A: Ring<C>> RationalFunction(numerator: Polynomial<C>, denominator: Polynomial<C>): RationalFunction<C> =
+//    if (denominator.isZero()) throw ArithmeticException("/ by zero")
+//    else RationalFunction<C>(numerator, denominator)
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//public fun <C, A: Ring<C>> RationalFunction(numeratorCoefficients: List<C>, denominatorCoefficients: List<C>, reverse: Boolean = false): RationalFunction<C> =
+//    RationalFunction<C>(
+//        Polynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
+//        Polynomial( with(denominatorCoefficients) { if (reverse) reversed() else this } ).also { if (it.isZero()) }
+//    )
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//public fun <C, A: Ring<C>> RationalFunction(numerator: Polynomial<C>): RationalFunction<C> =
+//    RationalFunction(numerator, onePolynomial)
+//context(RationalFunctionSpace<C, A>)
+//@Suppress("FunctionName")
+//public fun <C, A: Ring<C>> RationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): RationalFunction<C> =
+//    RationalFunction(
+//        Polynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } )
+//    )
+
+// TODO: Rewrite former constructors as fabrics
+//constructor(numeratorCoefficients: Map<List<Int>, C>, denominatorCoefficients: Map<List<Int>, C>) : this(
+//Polynomial(numeratorCoefficients),
+//Polynomial(denominatorCoefficients)
+//)
+//constructor(numeratorCoefficients: Collection<Pair<List<Int>, C>>, denominatorCoefficients: Collection<Pair<List<Int>, C>>) : this(
+//Polynomial(numeratorCoefficients),
+//Polynomial(denominatorCoefficients)
+//)
+//constructor(numerator: Polynomial<C>) : this(numerator, numerator.getOne())
+//constructor(numeratorCoefficients: Map<List<Int>, C>) : this(
+//Polynomial(numeratorCoefficients)
+//)
+//constructor(numeratorCoefficients: Collection<Pair<List<Int>, C>>) : this(
+//Polynomial(numeratorCoefficients)
+//)
+
+// endregion
+
+public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
+    public val ring: A,
+) : AbstractRationalFunctionalSpaceOverPolynomialSpace<C, NumberedPolynomial<C>, NumberedRationalFunction<C>, A> {
+
+    override val polynomialRing : NumberedPolynomialSpace<C, A> = NumberedPolynomialSpace(ring)
+
+    // 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 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
+        )
+    // 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 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
+        )
+    // endregion
+
+    // region Constant-rational relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Rational-constant relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Polynomial-rational relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Rational-polynomial relation
+    /**
+     * 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
+        )
+    // endregion
+
+    // region Rational-rational relation
+    /**
+     * 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).
+     */
+    public override val zero: NumberedRationalFunction<C> = NumberedRationalFunction(polynomialZero, polynomialOne)
+    /**
+     * Instance of unit polynomial (unit of the rational functions ring).
+     */
+    public override val one: NumberedRationalFunction<C> = NumberedRationalFunction(polynomialOne, polynomialOne)
+
+    /**
+     * Checks equality of the rational functions.
+     */
+    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
+    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
+
+        val countOfVariables = max(this.countOfVariables, other.countOfVariables)
+        val thisNumeratorDegrees = this.numerator.degrees
+        val thisDenominatorDegrees = this.denominator.degrees
+        val otherNumeratorDegrees = other.numerator.degrees
+        val otherDenominatorDegrees = other.denominator.degrees
+        for (variable in 0 until countOfVariables)
+            if (
+                thisNumeratorDegrees.getOrElse(variable) { 0u } + otherDenominatorDegrees.getOrElse(variable) { 0u }
+                != thisDenominatorDegrees.getOrElse(variable) { 0u } + otherNumeratorDegrees.getOrElse(variable) { 0u }
+            ) return false
+
+        return numerator * other.denominator equalsTo other.numerator * denominator
+    }
+    // endregion
+
+    // region Polynomial properties
+    /**
+     * Count of all variables that appear in the polynomial in positive exponents.
+     */
+    public val NumberedPolynomial<C>.countOfVariables: Int get() = polynomialRing { countOfVariables }
+    /**
+     * List that associates indices of variables (that appear in the polynomial in positive exponents) with their most
+     * exponents in which the variables are appeared in the polynomial.
+     *
+     * As consequence all values in the list are non-negative integers. Also, if the polynomial is constant, the list is empty.
+     * And size of the list is [countOfVariables].
+     */
+    public val NumberedPolynomial<C>.degrees: List<UInt> get() = polynomialRing { degrees }
+    // endregion
+
+    // region Rational properties
+    /**
+     * Count of all variables that appear in the polynomial in positive exponents.
+     */
+    public val NumberedRationalFunction<C>.countOfVariables: Int
+        get() = polynomialRing { max(numerator.countOfVariables, denominator.countOfVariables) }
+    // endregion
+
+    // region REST TODO: Разобрать
+
+    public operator fun NumberedRationalFunction<C>.div(other: NumberedRationalFunction<C>): NumberedRationalFunction<C> =
+        NumberedRationalFunction(
+            numerator * other.denominator,
+            denominator * other.numerator
+        )
+
+    public operator fun NumberedRationalFunction<C>.div(other: NumberedPolynomial<C>): NumberedRationalFunction<C> =
+        NumberedRationalFunction(
+            numerator,
+            denominator * other
+        )
+
+    public operator fun NumberedRationalFunction<C>.div(other: C): NumberedRationalFunction<C> =
+        NumberedRationalFunction(
+            numerator,
+            denominator * other
+        )
+
+//    operator fun invoke(arg: Map<Int, C>): NumberedRationalFunction<C> =
+//        NumberedRationalFunction(
+//            numerator(arg),
+//            denominator(arg)
+//        )
+//
+//    @JvmName("invokePolynomial")
+//    operator fun invoke(arg: Map<Int, Polynomial<C>>): NumberedRationalFunction<C> =
+//        NumberedRationalFunction(
+//            numerator(arg),
+//            denominator(arg)
+//        )
+//
+//    @JvmName("invokeRationalFunction")
+//    operator fun invoke(arg: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> {
+//        var num = numerator invokeRFTakeNumerator arg
+//        var den = denominator invokeRFTakeNumerator arg
+//        for (variable in 0 until max(numerator.countOfVariables, denominator.countOfVariables)) if (variable in arg) {
+//            val degreeDif = numerator.degrees.getOrElse(variable) { 0 } - denominator.degrees.getOrElse(variable) { 0 }
+//            if (degreeDif > 0)
+//                den = multiplyByPower(den, arg[variable]!!.denominator, degreeDif)
+//            else
+//                num = multiplyByPower(num, arg[variable]!!.denominator, -degreeDif)
+//        }
+//        return NumberedRationalFunction(num, den)
+//    }
+//
+//    override fun toString(): String = toString(Polynomial.variableName)
+//
+//    fun toString(withVariableName: String = Polynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toString(withVariableName)
+//            else -> "${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)}"
+//        }
+//
+//    fun toString(namer: (Int) -> String): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toString(namer)
+//            else -> "${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)}"
+//        }
+//
+//    fun toStringWithBrackets(withVariableName: String = Polynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toStringWithBrackets(withVariableName)
+//            else -> "(${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)})"
+//        }
+//
+//    fun toStringWithBrackets(namer: (Int) -> String): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toStringWithBrackets(namer)
+//            else -> "(${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)})"
+//        }
+//
+//    fun toReversedString(withVariableName: String = Polynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedString(withVariableName)
+//            else -> "${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)}"
+//        }
+//
+//    fun toReversedString(namer: (Int) -> String): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedString(namer)
+//            else -> "${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)}"
+//        }
+//
+//    fun toReversedStringWithBrackets(withVariableName: String = Polynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedStringWithBrackets(withVariableName)
+//            else -> "(${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)})"
+//        }
+//
+//    fun toReversedStringWithBrackets(namer: (Int) -> String): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedStringWithBrackets(namer)
+//            else -> "(${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)})"
+//        }
+}

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

@@ -80,7 +80,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
                 coefficients
                     .toMutableList()
                     .apply {
-                        val result = getOrElse(0) { ring.zero } + other
+                        val result = getOrElse(0) { constantZero } + other
                         val isResultZero = result.isZero()
 
                         when {
@@ -97,7 +97,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
                 coefficients
                     .toMutableList()
                     .apply {
-                        val result = getOrElse(0) { ring.zero } - other
+                        val result = getOrElse(0) { constantZero } - other
                         val isResultZero = result.isZero()
 
                         when {
@@ -124,7 +124,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
                 other.coefficients
                     .toMutableList()
                     .apply {
-                        val result = this@plus + getOrElse(0) { ring.zero }
+                        val result = this@plus + getOrElse(0) { constantZero }
                         val isResultZero = result.isZero()
 
                         when {
@@ -143,7 +143,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
                     .apply {
                         forEachIndexed { index, c -> if (index != 0) this[index] = -c }
 
-                        val result = this@minus - getOrElse(0) { ring.zero }
+                        val result = this@minus - getOrElse(0) { constantZero }
                         val isResultZero = result.isZero()
 
                         when {
@@ -281,7 +281,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
                         else -> coefficients[it] + other.coefficients[it]
                     }
                 }
-                .ifEmpty { listOf(ring.zero) }
+                .ifEmpty { listOf(constantZero) }
         )
     public override operator fun Polynomial<C>.minus(other: Polynomial<C>): Polynomial<C> =
         Polynomial(
@@ -293,7 +293,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
                         else -> coefficients[it] - other.coefficients[it]
                     }
                 }
-                .ifEmpty { listOf(ring.zero) }
+                .ifEmpty { listOf(constantZero) }
         )
     public override operator fun Polynomial<C>.times(other: Polynomial<C>): Polynomial<C> {
         val thisDegree = degree
@@ -321,7 +321,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
         with(coefficients) { isNotEmpty() && asSequence().withIndex().any { (index, c) -> if (index == 0) c.isMinusOne() else c.isZero() } } // TODO: It's better to write new methods like `anyIndexed`. But what's better way to do it?
 
     override val zero: Polynomial<C> = Polynomial(emptyList())
-    override val one: Polynomial<C> = Polynomial(listOf(ring.one))
+    override val one: Polynomial<C> = Polynomial(listOf(constantZero))
 
     @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
     public override infix fun Polynomial<C>.equalsTo(other: Polynomial<C>): Boolean =
@@ -337,12 +337,12 @@ public open class PolynomialSpace<C, A : Ring<C>>(
 
     // region Polynomial properties
 
-    public override val Polynomial<C>.degree: Int get() = coefficients.indexOfLast { it != ring.zero }
+    public override val Polynomial<C>.degree: Int get() = coefficients.indexOfLast { it != constantZero }
 
     public override fun Polynomial<C>.asConstantOrNull(): C? =
         with(coefficients) {
             when {
-                isEmpty() -> ring.zero
+                isEmpty() -> constantZero
                 degree > 0 -> null
                 else -> first()
             }

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

@@ -1,3 +1,8 @@
+/*
+ * 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.operations.*
@@ -270,19 +275,6 @@ public class RationalFunctionSpace<C, A : Ring<C>> (
             denominator * other.denominator
         )
 
-    /**
-     * Check if the instant is zero rational function.
-     */
-    public override fun RationalFunction<C>.isZero(): Boolean = numerator.isZero()
-    /**
-     * Check if the instant is unit rational function.
-     */
-    public override fun RationalFunction<C>.isOne(): Boolean = numerator.equalsTo(denominator)
-    /**
-     * Check if the instant is minus unit rational function.
-     */
-    public override fun RationalFunction<C>.isMinusOne(): Boolean = (numerator + denominator).isZero()
-
     /**
      * Instance of zero rational function (zero of the rational functions ring).
      */

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

@@ -1,3 +1,8 @@
+/*
+ * 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.operations.*
@@ -30,7 +35,7 @@ import kotlin.contracts.*
 //fun <C, A: Ring<C>> power(arg: Variable, pow: UInt): LabeledPolynomial<C> =
 //    if (pow == 0U) one
 //    else LabeledPolynomial<C>(mapOf(
-//        mapOf(arg to pow) to ring.one
+//        mapOf(arg to pow) to constantOne
 //    ))
 //
 //// endregion

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

@@ -0,0 +1,130 @@
+package math.polynomials
+
+import math.ringsAndFields.*
+import space.kscience.kmath.functions.LabeledRationalFunction
+
+
+fun <T: Ring<T>> T.toLabeledRationalFunction() = LabeledRationalFunction(this.toLabeledPolynomial())
+
+// region Operator extensions
+
+// region Field case
+
+fun <T: Field<T>> LabeledRationalFunction<T>.reduced(): LabeledRationalFunction<T> {
+    val greatestCommonDivider = polynomialGCD(numerator, denominator)
+    return LabeledRationalFunction(
+        numerator / greatestCommonDivider,
+        denominator / greatestCommonDivider
+    )
+}
+
+// endregion
+
+// region Constants
+
+operator fun <T: Ring<T>> T.plus(other: LabeledRationalFunction<T>) = other + this
+operator fun <T: Ring<T>> Integer.plus(other: LabeledRationalFunction<T>) = other + this
+operator fun <T: Ring<T>> Int.plus(other: LabeledRationalFunction<T>) = other + this
+operator fun <T: Ring<T>> Long.plus(other: LabeledRationalFunction<T>) = other + this
+
+operator fun <T: Ring<T>> T.minus(other: LabeledRationalFunction<T>) = -other + this
+operator fun <T: Ring<T>> Integer.minus(other: LabeledRationalFunction<T>) = -other + this
+operator fun <T: Ring<T>> Int.minus(other: LabeledRationalFunction<T>) = -other + this
+operator fun <T: Ring<T>> Long.minus(other: LabeledRationalFunction<T>) = -other + this
+
+operator fun <T: Ring<T>> T.times(other: LabeledRationalFunction<T>) = other * this
+operator fun <T: Ring<T>> Integer.times(other: LabeledRationalFunction<T>) = other * this
+operator fun <T: Ring<T>> Int.times(other: LabeledRationalFunction<T>) = other * this
+operator fun <T: Ring<T>> Long.times(other: LabeledRationalFunction<T>) = other * this
+
+// endregion
+
+// region Polynomials
+
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.plus(other: UnivariatePolynomial<T>) =
+    LabeledRationalFunction(
+        numerator + denominator * other.toLabeledPolynomial(),
+        denominator
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.plus(other: UnivariateRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.denominator.toLabeledPolynomial() + denominator * other.numerator.toLabeledPolynomial(),
+        denominator * other.denominator.toLabeledPolynomial()
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.plus(other: Polynomial<T>) =
+    LabeledRationalFunction(
+        numerator + denominator * other.toLabeledPolynomial(),
+        denominator
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.plus(other: NumberedRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.denominator.toLabeledPolynomial() + denominator * other.numerator.toLabeledPolynomial(),
+        denominator * other.denominator.toLabeledPolynomial()
+    )
+
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.minus(other: UnivariatePolynomial<T>) =
+    LabeledRationalFunction(
+        numerator - denominator * other.toLabeledPolynomial(),
+        denominator
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.minus(other: UnivariateRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.denominator.toLabeledPolynomial() - denominator * other.numerator.toLabeledPolynomial(),
+        denominator * other.denominator.toLabeledPolynomial()
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.minus(other: Polynomial<T>) =
+    LabeledRationalFunction(
+        numerator - denominator * other.toLabeledPolynomial(),
+        denominator
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.minus(other: NumberedRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.denominator.toLabeledPolynomial() - denominator * other.numerator.toLabeledPolynomial(),
+        denominator * other.denominator.toLabeledPolynomial()
+    )
+
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.times(other: UnivariatePolynomial<T>) =
+    LabeledRationalFunction(
+        numerator * other.toLabeledPolynomial(),
+        denominator
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.times(other: UnivariateRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.numerator.toLabeledPolynomial(),
+        denominator * other.denominator.toLabeledPolynomial()
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.times(other: Polynomial<T>) =
+    LabeledRationalFunction(
+        numerator * other.toLabeledPolynomial(),
+        denominator
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.times(other: NumberedRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.numerator.toLabeledPolynomial(),
+        denominator * other.denominator.toLabeledPolynomial()
+    )
+
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.div(other: UnivariatePolynomial<T>) =
+    LabeledRationalFunction(
+        numerator,
+        denominator * other.toLabeledPolynomial()
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.div(other: UnivariateRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.denominator.toLabeledPolynomial(),
+        denominator * other.numerator.toLabeledPolynomial()
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.div(other: Polynomial<T>) =
+    LabeledRationalFunction(
+        numerator,
+        denominator * other.toLabeledPolynomial()
+    )
+operator fun <T: Ring<T>> LabeledRationalFunction<T>.div(other: NumberedRationalFunction<T>) =
+    LabeledRationalFunction(
+        numerator * other.denominator.toLabeledPolynomial(),
+        denominator * other.numerator.toLabeledPolynomial()
+    )
+
+// endregion
+
+// endregion

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

@@ -0,0 +1,23 @@
+/*
+ * 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
+
+
+//// region Operator extensions
+//
+//// region Field case
+//
+//fun <T: Field<T>> NumberedRationalFunction<T>.reduced(): NumberedRationalFunction<T> {
+//    val greatestCommonDivider = polynomialGCD(numerator, denominator)
+//    return NumberedRationalFunction(
+//        numerator / greatestCommonDivider,
+//        denominator / greatestCommonDivider
+//    )
+//}
+//
+//// endregion
+//
+//// endregion

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

@@ -1,3 +1,8 @@
+/*
+ * 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