diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractPolynomial.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractPolynomial.kt
index b7b7116f0..69c45798a 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractPolynomial.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractPolynomial.kt
@@ -154,7 +154,7 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Check if the instant is NOT zero constant.
      */
     @JvmName("constantIsNotZero")
-    public fun C.isNotZero(): Boolean
+    public fun C.isNotZero(): Boolean = !isZero()
     /**
      * Check if the instant is unit constant.
      */
@@ -164,7 +164,7 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Check if the instant is NOT unit constant.
      */
     @JvmName("constantIsNotOne")
-    public fun C.isNotOne(): Boolean
+    public fun C.isNotOne(): Boolean = !isOne()
     /**
      * Check if the instant is minus unit constant.
      */
@@ -174,7 +174,7 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Check if the instant is NOT minus unit constant.
      */
     @JvmName("constantIsNotMinusOne")
-    public fun C.isNotMinusOne(): Boolean
+    public fun C.isNotMinusOne(): Boolean = !isMinusOne()
     // endregion
 
     // region Constant-polynomial relation
@@ -232,27 +232,27 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
     /**
      * Check if the instant is zero polynomial.
      */
-    public fun P.isZero(): Boolean = this == zero
+    public fun P.isZero(): Boolean = this equalsTo zero
     /**
      * Check if the instant is NOT zero polynomial.
      */
-    public fun P.isNotZero(): Boolean = this != zero
+    public fun P.isNotZero(): Boolean = !isZero()
     /**
      * Check if the instant is unit polynomial.
      */
-    public fun P.isOne(): Boolean = this == one
+    public fun P.isOne(): Boolean = this equalsTo one
     /**
      * Check if the instant is NOT unit polynomial.
      */
-    public fun P.isNotOne(): Boolean = this != one
+    public fun P.isNotOne(): Boolean = !isOne()
     /**
      * Check if the instant is minus unit polynomial.
      */
-    public fun P.isMinusOne(): Boolean = this == -one
+    public fun P.isMinusOne(): Boolean = this equalsTo -one
     /**
      * Check if the instant is NOT minus unit polynomial.
      */
-    public fun P.isNotMinusOne(): Boolean = this != -one
+    public fun P.isNotMinusOne(): Boolean = !isMinusOne()
 
     /**
      * Instance of zero polynomial (zero of the polynomial ring).
@@ -266,8 +266,11 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
     /**
      * Checks equality of the polynomials.
      */
-    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
-    public fun P.equals(other: P): Boolean
+    public infix fun P.equalsTo(other: P): Boolean
+    /**
+     * Checks NOT equality of the polynomials.
+     */
+    public infix fun P.notEqualsTo(other: P): Boolean = !(this equalsTo other)
     // endregion
 
     // Not sure is it necessary...
@@ -310,4 +313,107 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
     override fun add(left: P, right: P): P = left + right
     override fun multiply(left: P, right: P): P = left * right
     // endregion
+}
+
+/**
+ * Abstraction of ring of polynomials of type [P] over ring of constants of type [C].
+ *
+ * @param C the type of constants. Polynomials have them as a coefficients in their terms.
+ * @param P the type of polynomials.
+ */
+@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE")
+public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A: Ring<C>> : AbstractPolynomialSpace<C, P> {
+
+    public val ring: A
+
+    // region Constant-integer relation
+    /**
+     * Returns sum of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
+     */
+    @JvmName("constantIntPlus")
+    public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) }
+    /**
+     * Returns difference between the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
+     */
+    @JvmName("constantIntMinus")
+    public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) }
+    /**
+     * Returns product of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    @JvmName("constantIntTimes")
+    public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) }
+    // endregion
+
+    // region Integer-constant relation
+    /**
+     * Returns sum of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
+     */
+    @JvmName("intConstantPlus")
+    public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) }
+    /**
+     * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
+     */
+    @JvmName("intConstantMinus")
+    public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) }
+    /**
+     * Returns product of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    @JvmName("intConstantTimes")
+    public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) }
+    // endregion
+
+    // region Constant-constant relation
+    /**
+     * Returns negation of the constant.
+     */
+    @JvmName("constantUnaryMinus")
+    @JsName("constantUnaryMinus")
+    public override operator fun C.unaryMinus(): C = ring { -this@unaryMinus }
+    /**
+     * Returns sum of the constants.
+     */
+    @JvmName("constantPlus")
+    @JsName("constantPlus")
+    public override operator fun C.plus(other: C): C = ring { this@plus + other }
+    /**
+     * Returns difference of the constants.
+     */
+    @JvmName("constantMinus")
+    @JsName("constantMinus")
+    public override operator fun C.minus(other: C): C = ring { this@minus - other }
+    /**
+     * Returns product of the constants.
+     */
+    @JvmName("constantTimes")
+    @JsName("constantTimes")
+    public override operator fun C.times(other: C): C = ring { this@times * other }
+
+    /**
+     * Check if the instant is zero constant.
+     */
+    @JvmName("constantIsZero")
+    public override fun C.isZero(): Boolean = ring { this == zero }
+    /**
+     * Check if the instant is unit constant.
+     */
+    @JvmName("constantIsOne")
+    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
 }
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractRationalFunction.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractRationalFunction.kt
index 34050aa0f..9725ea078 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractRationalFunction.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractRationalFunction.kt
@@ -13,7 +13,12 @@ import kotlin.jvm.JvmName
 /**
  * Abstraction of rational function.
  */
-public interface AbstractRationalFunction<C, P: AbstractPolynomial<C>>
+public interface AbstractRationalFunction<C, P: AbstractPolynomial<C>> {
+    public val numerator: P
+    public val denominator: P
+    public operator fun component1(): P = numerator
+    public operator fun component2(): P = denominator
+}
 
 @Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE")
 public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R: AbstractRationalFunction<C, P>> : Ring<R> {
@@ -190,7 +195,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Check if the instant is NOT zero constant.
      */
     @JvmName("constantIsNotZero")
-    public fun C.isNotZero(): Boolean
+    public fun C.isNotZero(): Boolean = !isZero()
     /**
      * Check if the instant is unit constant.
      */
@@ -200,7 +205,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Check if the instant is NOT unit constant.
      */
     @JvmName("constantIsNotOne")
-    public fun C.isNotOne(): Boolean
+    public fun C.isNotOne(): Boolean = !isOne()
     /**
      * Check if the instant is minus unit constant.
      */
@@ -210,7 +215,7 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Check if the instant is NOT minus unit constant.
      */
     @JvmName("constantIsNotMinusOne")
-    public fun C.isNotMinusOne(): Boolean
+    public fun C.isNotMinusOne(): Boolean = !isMinusOne()
     // endregion
 
     // region Constant-polynomial relation
@@ -268,42 +273,45 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Check if the instant is zero polynomial.
      */
-    public fun P.isZero(): Boolean = this == zeroPolynomial
+    public fun P.isZero(): Boolean = this equalsTo polynomialZero
     /**
      * Check if the instant is NOT zero polynomial.
      */
-    public fun P.isNotZero(): Boolean = this != zeroPolynomial
+    public fun P.isNotZero(): Boolean = !isZero()
     /**
      * Check if the instant is unit polynomial.
      */
-    public fun P.isOne(): Boolean = this == onePolynomial
+    public fun P.isOne(): Boolean = this equalsTo polynomialOne
     /**
      * Check if the instant is NOT unit polynomial.
      */
-    public fun P.isNotOne(): Boolean = this != onePolynomial
+    public fun P.isNotOne(): Boolean = !isOne()
     /**
      * Check if the instant is minus unit polynomial.
      */
-    public fun P.isMinusOne(): Boolean = this == -onePolynomial
+    public fun P.isMinusOne(): Boolean = this equalsTo -polynomialOne
     /**
      * Check if the instant is NOT minus unit polynomial.
      */
-    public fun P.isNotMinusOne(): Boolean = this != -onePolynomial
+    public fun P.isNotMinusOne(): Boolean = !isMinusOne()
 
     /**
      * Instance of zero polynomial (zero of the polynomial ring).
      */
-    public val zeroPolynomial: P
+    public val polynomialZero: P
     /**
      * Instance of unit polynomial (unit of the polynomial ring).
      */
-    public val onePolynomial: P
+    public val polynomialOne: P
 
     /**
      * Checks equality of the polynomials.
      */
-    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
-    public fun P.equals(other: P): Boolean
+    public infix fun P.equalsTo(other: P): Boolean
+    /**
+     * Checks NOT equality of the polynomials.
+     */
+    public infix fun P.notEqualsTo(other: P): Boolean = !(this equalsTo other)
     // endregion
 
     // region Constant-rational relation
@@ -391,27 +399,27 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Check if the instant is zero rational function.
      */
-    public fun R.isZero(): Boolean = this == zero
+    public fun R.isZero(): Boolean = this equalsTo zero
     /**
      * Check if the instant is NOT zero rational function.
      */
-    public fun R.isNotZero(): Boolean = this != zero
+    public fun R.isNotZero(): Boolean = !isZero()
     /**
      * Check if the instant is unit rational function.
      */
-    public fun R.isOne(): Boolean = this == one
+    public fun R.isOne(): Boolean = this equalsTo one
     /**
      * Check if the instant is NOT unit rational function.
      */
-    public fun R.isNotOne(): Boolean = this != one
+    public fun R.isNotOne(): Boolean = !isOne()
     /**
      * Check if the instant is minus unit rational function.
      */
-    public fun R.isMinusOne(): Boolean = this == -one
+    public fun R.isMinusOne(): Boolean = this equalsTo -one
     /**
      * Check if the instant is NOT minus unit rational function.
      */
-    public fun R.isNotMinusOne(): Boolean = this != -one
+    public fun R.isNotMinusOne(): Boolean = !isMinusOne()
 
     /**
      * Instance of zero rational function (zero of the rational functions ring).
@@ -425,8 +433,11 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     /**
      * Checks equality of the rational functions.
      */
-    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
-    public fun R.equals(other: R): Boolean
+    public infix fun R.equalsTo(other: R): Boolean
+    /**
+     * Checks NOT equality of the polynomials.
+     */
+    public infix fun R.notEqualsTo(other: R): Boolean = !(this equalsTo other)
     // endregion
 
     // Not sure is it necessary...
@@ -453,35 +464,31 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Checks if the instant is **not** constant non-zero polynomial (of degree no more than 0) over considered ring.
      */
     public fun P.isNotNonZeroConstant(): Boolean = !isNonZeroConstant()
-
+    /**
+     * If polynomial is a constant polynomial represents and returns it as constant.
+     * Otherwise, (when the polynomial is not constant polynomial) returns `null`.
+     */
     public fun P.asConstantOrNull(): C?
-
+    /**
+     * If polynomial is a constant polynomial represents and returns it as constant.
+     * Otherwise, (when the polynomial is not constant polynomial) raises corresponding exception.
+     */
     public fun P.asConstant(): C = asConstantOrNull() ?: error("Can not represent non-constant polynomial as a constant")
 
     // endregion
 
     // Not sure is it necessary...
-    // region Polynomial properties
+    // region Rational properties
     /**
-     * Checks if the instant is constant polynomial (of degree no more than 0) over considered ring.
+     * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
+     * zero, degree is -1.
      */
-    public fun R.isConstant(): Boolean
+    public val R.numeratorDegree: Int get() = numerator.degree
     /**
-     * Checks if the instant is **not** constant polynomial (of degree no more than 0) over considered ring.
+     * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
+     * zero, degree is -1.
      */
-    public fun R.isNotConstant(): Boolean = !isConstant()
-    /**
-     * Checks if the instant is constant non-zero polynomial (of degree no more than 0) over considered ring.
-     */
-    public fun R.isNonZeroConstant(): Boolean
-    /**
-     * Checks if the instant is **not** constant non-zero polynomial (of degree no more than 0) over considered ring.
-     */
-    public fun R.isNotNonZeroConstant(): Boolean = !isNonZeroConstant()
-
-    public fun R.asConstantOrNull(): C?
-
-    public fun R.asConstant(): C = asConstantOrNull() ?: error("Can not represent non-constant polynomial as a constant")
+    public val R.denominatorDegree: Int get() = denominator.degree
 
     // TODO: Перенести в реализацию
 //    fun R.substitute(argument: C): C
@@ -501,5 +508,416 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     // region Legacy
     override fun add(left: R, right: R): R = left + right
     override fun multiply(left: R, right: R): R = left * right
+    // endregion
+}
+
+@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE")
+public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomial<C>, R: AbstractRationalFunction<C, P>, A: Ring<C>> : AbstractRationalFunctionalSpace<C, P, R> {
+
+    public val ring: A
+
+    // region Constant-integer relation
+    /**
+     * Returns sum of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
+     */
+    @JvmName("constantIntPlus")
+    public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) }
+    /**
+     * Returns difference between the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
+     */
+    @JvmName("constantIntMinus")
+    public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) }
+    /**
+     * Returns product of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    @JvmName("constantIntTimes")
+    public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) }
+    // endregion
+
+    // region Integer-constant relation
+    /**
+     * Returns sum of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
+     */
+    @JvmName("intConstantPlus")
+    public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) }
+    /**
+     * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
+     */
+    @JvmName("intConstantMinus")
+    public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) }
+    /**
+     * Returns product of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    @JvmName("intConstantTimes")
+    public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) }
+    // endregion
+
+    // region Constant-constant relation
+    /**
+     * Returns the same constant.
+     */
+    @JvmName("constantUnaryPlus")
+    @JsName("constantUnaryPlus")
+    public override operator fun C.unaryPlus(): C = ring { +this@unaryPlus }
+    /**
+     * Returns negation of the constant.
+     */
+    @JvmName("constantUnaryMinus")
+    @JsName("constantUnaryMinus")
+    public override operator fun C.unaryMinus(): C = ring { -this@unaryMinus }
+    /**
+     * Returns sum of the constants.
+     */
+    @JvmName("constantPlus")
+    @JsName("constantPlus")
+    public override operator fun C.plus(other: C): C = ring { this@plus + other }
+    /**
+     * Returns difference of the constants.
+     */
+    @JvmName("constantMinus")
+    @JsName("constantMinus")
+    public override operator fun C.minus(other: C): C = ring { this@minus - other }
+    /**
+     * Returns product of the constants.
+     */
+    @JvmName("constantTimes")
+    @JsName("constantTimes")
+    public override operator fun C.times(other: C): C = ring { this@times * other }
+
+    /**
+     * Check if the instant is zero constant.
+     */
+    @JvmName("constantIsZero")
+    public override fun C.isZero(): Boolean = ring { this@isZero.isZero() }
+    /**
+     * Check if the instant is NOT zero constant.
+     */
+    @JvmName("constantIsNotZero")
+    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
+}
+
+@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE")
+public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<C, P: AbstractPolynomial<C>, R: AbstractRationalFunction<C, P>, A: Ring<C>> : AbstractRationalFunctionalSpace<C, P, R> {
+
+    public val polynomialRing: AbstractPolynomialSpace<C, P>
+
+    // region Constant-integer relation
+    /**
+     * Returns sum of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
+     */
+    @JvmName("constantIntPlus")
+    public override operator fun C.plus(other: Int): C = polynomialRing { this@plus + other }
+    /**
+     * Returns difference between the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
+     */
+    @JvmName("constantIntMinus")
+    public override operator fun C.minus(other: Int): C = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the constant and the integer represented as constant (member of underlying ring).
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    @JvmName("constantIntTimes")
+    public override operator fun C.times(other: Int): C = polynomialRing { this@times * other }
+    // endregion
+
+    // region Integer-constant relation
+    /**
+     * Returns sum of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
+     */
+    @JvmName("intConstantPlus")
+    public override operator fun Int.plus(other: C): C = polynomialRing { this@plus + other }
+    /**
+     * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
+     */
+    @JvmName("intConstantMinus")
+    public override operator fun Int.minus(other: C): C = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the integer represented as constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    @JvmName("intConstantTimes")
+    public override operator fun Int.times(other: C): C = polynomialRing { this@times * other }
+    // endregion
+
+    // region Polynomial-integer relation
+    /**
+     * Returns sum of the constant and the integer represented as polynomial.
+     *
+     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+     */
+    public override operator fun P.plus(other: Int): P = polynomialRing { this@plus + other }
+    /**
+     * Returns difference between the constant and the integer represented as polynomial.
+     *
+     * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
+     */
+    public override operator fun P.minus(other: Int): P = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the constant and the integer represented as polynomial.
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public override operator fun P.times(other: Int): P = polynomialRing { this@times * other }
+    // endregion
+
+    // region Integer-polynomial relation
+    /**
+     * Returns sum of the integer represented as polynomial and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit polynomial to [other].
+     */
+    public override operator fun Int.plus(other: P): P = polynomialRing { this@plus + other }
+    /**
+     * Returns difference between the integer represented as polynomial and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
+     */
+    public override operator fun Int.minus(other: P): P = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the integer represented as polynomial and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public override operator fun Int.times(other: P): P = polynomialRing { this@times * other }
+    // endregion
+
+    // region Constant-constant relation
+    /**
+     * Returns the same constant.
+     */
+    @JvmName("constantUnaryPlus")
+    @JsName("constantUnaryPlus")
+    public override operator fun C.unaryPlus(): C = polynomialRing { +this@unaryPlus }
+    /**
+     * Returns negation of the constant.
+     */
+    @JvmName("constantUnaryMinus")
+    @JsName("constantUnaryMinus")
+    public override operator fun C.unaryMinus(): C = polynomialRing { -this@unaryMinus }
+    /**
+     * Returns sum of the constants.
+     */
+    @JvmName("constantPlus")
+    @JsName("constantPlus")
+    public override operator fun C.plus(other: C): C = polynomialRing { this@plus + other }
+    /**
+     * Returns difference of the constants.
+     */
+    @JvmName("constantMinus")
+    @JsName("constantMinus")
+    public override operator fun C.minus(other: C): C = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the constants.
+     */
+    @JvmName("constantTimes")
+    @JsName("constantTimes")
+    public override operator fun C.times(other: C): C = polynomialRing { this@times * other }
+
+    /**
+     * Check if the instant is zero constant.
+     */
+    @JvmName("constantIsZero")
+    public override fun C.isZero(): Boolean = polynomialRing { this@isZero.isZero() }
+    /**
+     * Check if the instant is NOT zero constant.
+     */
+    @JvmName("constantIsNotZero")
+    public override fun C.isNotZero(): Boolean = polynomialRing { this@isNotZero.isNotZero() }
+    /**
+     * Check if the instant is unit constant.
+     */
+    @JvmName("constantIsOne")
+    public override fun C.isOne(): Boolean = polynomialRing { this@isOne.isOne() }
+    /**
+     * Check if the instant is NOT unit constant.
+     */
+    @JvmName("constantIsNotOne")
+    public override fun C.isNotOne(): Boolean = polynomialRing { this@isNotOne.isNotOne() }
+    /**
+     * Check if the instant is minus unit constant.
+     */
+    @JvmName("constantIsMinusOne")
+    public override fun C.isMinusOne(): Boolean = polynomialRing { this@isMinusOne.isMinusOne() }
+    /**
+     * Check if the instant is NOT minus unit constant.
+     */
+    @JvmName("constantIsNotMinusOne")
+    public override fun C.isNotMinusOne(): Boolean = polynomialRing { this@isNotMinusOne.isNotMinusOne() }
+    // endregion
+
+    // region Constant-polynomial relation
+    /**
+     * Returns sum of the constant represented as polynomial and the polynomial.
+     */
+    public override operator fun C.plus(other: P): P = polynomialRing { this@plus + other }
+    /**
+     * Returns difference between the constant represented as polynomial and the polynomial.
+     */
+    public override operator fun C.minus(other: P): P = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the constant represented as polynomial and the polynomial.
+     */
+    public override operator fun C.times(other: P): P = polynomialRing { this@times * other }
+    // endregion
+
+    // region Polynomial-constant relation
+    /**
+     * Returns sum of the constant represented as polynomial and the polynomial.
+     */
+    public override operator fun P.plus(other: C): P = polynomialRing { this@plus + other }
+    /**
+     * Returns difference between the constant represented as polynomial and the polynomial.
+     */
+    public override operator fun P.minus(other: C): P = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the constant represented as polynomial and the polynomial.
+     */
+    public override operator fun P.times(other: C): P = polynomialRing { this@times * other }
+    // endregion
+
+    // region Polynomial-polynomial relation
+    /**
+     * Returns the same polynomial.
+     */
+    public override operator fun P.unaryPlus(): P = polynomialRing { +this@unaryPlus }
+    /**
+     * Returns negation of the polynomial.
+     */
+    public override operator fun P.unaryMinus(): P = polynomialRing { -this@unaryMinus }
+    /**
+     * Returns sum of the polynomials.
+     */
+    public override operator fun P.plus(other: P): P = polynomialRing { this@plus + other }
+    /**
+     * Returns difference of the polynomials.
+     */
+    public override operator fun P.minus(other: P): P = polynomialRing { this@minus - other }
+    /**
+     * Returns product of the polynomials.
+     */
+    public override operator fun P.times(other: P): P = polynomialRing { this@times * other }
+
+    /**
+     * Check if the instant is zero polynomial.
+     */
+    public override fun P.isZero(): Boolean = polynomialRing { this@isZero.isZero() }
+    /**
+     * Check if the instant is NOT zero polynomial.
+     */
+    public override fun P.isNotZero(): Boolean = polynomialRing { this@isNotZero.isNotZero() }
+    /**
+     * Check if the instant is unit polynomial.
+     */
+    public override fun P.isOne(): Boolean = polynomialRing { this@isOne.isOne() }
+    /**
+     * Check if the instant is NOT unit polynomial.
+     */
+    public override fun P.isNotOne(): Boolean = polynomialRing { this@isNotOne.isNotOne() }
+    /**
+     * Check if the instant is minus unit polynomial.
+     */
+    public override fun P.isMinusOne(): Boolean = polynomialRing { this@isMinusOne.isMinusOne() }
+    /**
+     * Check if the instant is NOT minus unit polynomial.
+     */
+    public override fun P.isNotMinusOne(): Boolean = polynomialRing { this@isNotMinusOne.isNotMinusOne() }
+
+    /**
+     * Instance of zero polynomial (zero of the polynomial ring).
+     */
+    public override val polynomialZero: P get() = polynomialRing.zero
+    /**
+     * Instance of unit polynomial (unit of the polynomial ring).
+     */
+    public override val polynomialOne: P get() = polynomialRing.one
+
+    /**
+     * Checks equality of the polynomials.
+     */
+    public override infix fun P.equalsTo(other: P): Boolean = polynomialRing { this@equalsTo equalsTo other }
+    /**
+     * Checks NOT equality of the polynomials.
+     */
+    public override infix fun P.notEqualsTo(other: P): Boolean = polynomialRing { this@notEqualsTo notEqualsTo other }
+    // endregion
+
+    // Not sure is it necessary...
+    // region Polynomial properties
+    /**
+     * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
+     * zero, degree is -1.
+     */
+    public override val P.degree: Int get() = polynomialRing { this@degree.degree }
+
+    /**
+     * Checks if the instant is constant polynomial (of degree no more than 0) over considered ring.
+     */
+    public override fun P.isConstant(): Boolean = polynomialRing { this@isConstant.isConstant() }
+    /**
+     * Checks if the instant is **not** constant polynomial (of degree no more than 0) over considered ring.
+     */
+    public override fun P.isNotConstant(): Boolean = polynomialRing { this@isNotConstant.isNotConstant() }
+    /**
+     * Checks if the instant is constant non-zero polynomial (of degree no more than 0) over considered ring.
+     */
+    public override fun P.isNonZeroConstant(): Boolean = polynomialRing { this@isNonZeroConstant.isNonZeroConstant() }
+    /**
+     * Checks if the instant is **not** constant non-zero polynomial (of degree no more than 0) over considered ring.
+     */
+    public override fun P.isNotNonZeroConstant(): Boolean = polynomialRing { this@isNotNonZeroConstant.isNotNonZeroConstant() }
+    /**
+     * If polynomial is a constant polynomial represents and returns it as constant.
+     * Otherwise, (when the polynomial is not constant polynomial) returns `null`.
+     */
+    public override fun P.asConstantOrNull(): C? = polynomialRing { this@asConstantOrNull.asConstantOrNull() }
+    /**
+     * If polynomial is a constant polynomial represents and returns it as constant.
+     * Otherwise, (when the polynomial is not constant polynomial) raises corresponding exception.
+     */
+    public override fun P.asConstant(): C = polynomialRing { this@asConstant.asConstant() }
+
     // endregion
 }
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt
index 48f6f57fa..cbd713d27 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt
@@ -13,7 +13,7 @@ import kotlin.math.max
  *
  * @param C Ring in which the polynomial is considered.
  */
-public class LabeledPolynomial<C>
+public data class LabeledPolynomial<C>
 internal constructor(
     /**
      * Map that collects coefficients of the polynomial. Every non-zero monomial
@@ -788,7 +788,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             isZero() -> zero
             other.isZero() -> zero
             else -> LabeledPolynomial<C>(
-                buildCoefficients {
+                buildCoefficients(coefficients.size * other.coefficients.size) {
                     for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
                         val degs = degs1.toMutableMap()
                         degs2.mapValuesTo(degs) { (variable, deg) -> degs.getOrElse(variable) { 0u } + deg }
@@ -804,7 +804,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
 
     // TODO: Docs
     @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
-    override fun LabeledPolynomial<C>.equals(other: LabeledPolynomial<C>): Boolean =
+    override infix fun LabeledPolynomial<C>.equalsTo(other: LabeledPolynomial<C>): Boolean =
         when {
             this === other -> true
             else -> coefficients.size == other.coefficients.size &&
@@ -896,15 +896,9 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
 //    public inline operator fun LabeledPolynomial<C>.invoke(argument: Map<Variable, LabeledPolynomial<C>>): LabeledPolynomial<C> = this.substitute(ring, argument)
     // endregion
 
-    // region Legacy
-    @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-    override inline fun add(left: LabeledPolynomial<C>, right: LabeledPolynomial<C>): LabeledPolynomial<C> = left + right
-    @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-    override inline fun multiply(left: LabeledPolynomial<C>, right: LabeledPolynomial<C>): LabeledPolynomial<C> = left * right
-    // endregion
-
     // region Utilities
     // TODO: Move to region internal utilities with context receiver
+    @JvmName("applyAndRemoveZerosInternal")
     internal fun MutableMap<Map<Variable, UInt>, C>.applyAndRemoveZeros(block: MutableMap<Map<Variable, UInt>, C>.() -> Unit) : MutableMap<Map<Variable, UInt>, C> {
         contract {
             callsInPlace(block, InvocationKind.EXACTLY_ONCE)
@@ -916,12 +910,20 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     internal fun Map<Map<Variable, UInt>, C>.applyAndRemoveZeros(block: MutableMap<Map<Variable, UInt>, C>.() -> Unit) : Map<Map<Variable, UInt>, C> =
         toMutableMap().applyAndRemoveZeros(block)
     @OptIn(ExperimentalTypeInference::class)
-    internal fun buildCoefficients(@BuilderInference builderAction: MutableMap<Map<Variable, UInt>, C>.() -> Unit): Map<Map<Variable, UInt>, C> {
+    internal inline fun buildCoefficients(@BuilderInference builderAction: MutableMap<Map<Variable, UInt>, C>.() -> Unit): Map<Map<Variable, UInt>, C> {
         contract { callsInPlace(builderAction, InvocationKind.EXACTLY_ONCE) }
         return buildMap {
             builderAction()
             for ((degs, c) in this) if (c.isZero()) this.remove(degs)
         }
     }
+    @OptIn(ExperimentalTypeInference::class)
+    internal inline fun buildCoefficients(capacity: Int, @BuilderInference builderAction: MutableMap<Map<Variable, UInt>, C>.() -> Unit): Map<Map<Variable, UInt>, C> {
+        contract { callsInPlace(builderAction, InvocationKind.EXACTLY_ONCE) }
+        return buildMap(capacity) {
+            builderAction()
+            for ((degs, c) in this) if (c.isZero()) this.remove(degs)
+        }
+    }
     // endregion
 }
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt
index f1ad9a74f..f11338161 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt
@@ -13,7 +13,7 @@ import kotlin.math.max
  *
  * @param C the type of constants.
  */
-public class NumberedPolynomial<C>
+public data class NumberedPolynomial<C>
 internal constructor(
     /**
      * Map that collects coefficients of the polynomial. Every monomial `a x_1^{d_1} ... x_n^{d_n}` is represented as
@@ -259,27 +259,9 @@ public fun <C, A: Ring<C>> C.asNumberedPolynomial() : NumberedPolynomial<C> = Nu
  * @param ring the [A] instance.
  */
 @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE", "INAPPLICABLE_JVM_NAME")
-public class NumberedPolynomialSpace<C, A : Ring<C>>(
-    public val ring: A,
-) : AbstractPolynomialSpace<C, NumberedPolynomial<C>> {
-    // 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
-
+public open class NumberedPolynomialSpace<C, A : Ring<C>>(
+    public final override val ring: A,
+) : AbstractPolynomialSpaceOverRing<C, NumberedPolynomial<C>, A> {
     // region Polynomial-integer relation
     public override operator fun NumberedPolynomial<C>.plus(other: Int): NumberedPolynomial<C> =
         if (other == 0) this
@@ -362,29 +344,6 @@ public class NumberedPolynomialSpace<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-polynomial relation
     override operator fun C.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         if (this.isZero()) other
@@ -521,7 +480,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
             other.isZero() -> zero
             else ->
                 NumberedPolynomial<C>(
-                    buildCoefficients {
+                    buildCoefficients(coefficients.size * other.coefficients.size) {
                         for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
                             val degs =
                                 (0..max(degs1.lastIndex, degs2.lastIndex))
@@ -534,7 +493,6 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         }
 
     public override fun NumberedPolynomial<C>.isZero(): Boolean = coefficients.values.all { it.isZero() }
-    public override fun NumberedPolynomial<C>.isNotZero(): Boolean = coefficients.values.any { it.isNotZero() }
     public override fun NumberedPolynomial<C>.isOne(): Boolean =
         with(coefficients) {
             var foundAbsoluteTermAndItIsOne = false
@@ -547,7 +505,6 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
             }
             foundAbsoluteTermAndItIsOne
         }
-    public override fun NumberedPolynomial<C>.isNotOne(): Boolean = !isOne()
     public override fun NumberedPolynomial<C>.isMinusOne(): Boolean =
         with(coefficients) {
             var foundAbsoluteTermAndItIsMinusOne = false
@@ -560,7 +517,6 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
             }
             foundAbsoluteTermAndItIsMinusOne
         }
-    public override fun NumberedPolynomial<C>.isNotMinusOne(): Boolean = !isMinusOne()
 
     override val zero: NumberedPolynomial<C> = NumberedPolynomial<C>(emptyMap())
     override val one: NumberedPolynomial<C> =
@@ -572,7 +528,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
 
     // TODO: Docs
     @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
-    override fun NumberedPolynomial<C>.equals(other: NumberedPolynomial<C>): Boolean =
+    override infix fun NumberedPolynomial<C>.equalsTo(other: NumberedPolynomial<C>): Boolean =
         when {
             this === other -> true
             else -> coefficients.size == other.coefficients.size &&
@@ -658,15 +614,9 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
     public inline operator fun NumberedPolynomial<C>.invoke(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = this.substitute(ring, argument)
     // endregion
 
-    // region Legacy
-    @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-    override inline fun add(left: NumberedPolynomial<C>, right: NumberedPolynomial<C>): NumberedPolynomial<C> = left + right
-    @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-    override inline fun multiply(left: NumberedPolynomial<C>, right: NumberedPolynomial<C>): NumberedPolynomial<C> = left * right
-    // endregion
-
     // region Utilities
     // TODO: Move to region internal utilities with context receiver
+    @JvmName("applyAndRemoveZerosInternal")
     internal fun MutableMap<List<UInt>, C>.applyAndRemoveZeros(block: MutableMap<List<UInt>, C>.() -> Unit) : MutableMap<List<UInt>, C> {
         contract {
             callsInPlace(block, InvocationKind.EXACTLY_ONCE)
@@ -678,12 +628,20 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
     internal fun Map<List<UInt>, C>.applyAndRemoveZeros(block: MutableMap<List<UInt>, C>.() -> Unit) : Map<List<UInt>, C> =
         toMutableMap().applyAndRemoveZeros(block)
     @OptIn(ExperimentalTypeInference::class)
-    internal fun buildCoefficients(@BuilderInference builderAction: MutableMap<List<UInt>, C>.() -> Unit): Map<List<UInt>, C> {
+    internal inline fun buildCoefficients(@BuilderInference builderAction: MutableMap<List<UInt>, C>.() -> Unit): Map<List<UInt>, C> {
         contract { callsInPlace(builderAction, InvocationKind.EXACTLY_ONCE) }
         return buildMap {
             builderAction()
             for ((degs, c) in this) if (c.isZero()) this.remove(degs)
         }
     }
+    @OptIn(ExperimentalTypeInference::class)
+    internal inline fun buildCoefficients(capacity: Int, @BuilderInference builderAction: MutableMap<List<UInt>, C>.() -> Unit): Map<List<UInt>, C> {
+        contract { callsInPlace(builderAction, InvocationKind.EXACTLY_ONCE) }
+        return buildMap(capacity) {
+            builderAction()
+            for ((degs, c) in this) if (c.isZero()) this.remove(degs)
+        }
+    }
     // endregion
 }
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
index 99d6b0659..2c764f4f5 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
@@ -15,7 +15,7 @@ import kotlin.math.min
  *
  * @param coefficients constant is the leftmost coefficient.
  */
-public class Polynomial<T>(public val coefficients: List<T>) : AbstractPolynomial<T> {
+public data class Polynomial<T>(public val coefficients: List<T>) : AbstractPolynomial<T> {
     override fun toString(): String = "Polynomial$coefficients"
 }
 
@@ -69,25 +69,8 @@ public fun <T> T.asPolynomial() : Polynomial<T> = Polynomial(listOf(this))
  */
 @Suppress("INAPPLICABLE_JVM_NAME") // TODO: KT-31420
 public open class PolynomialSpace<C, A : Ring<C>>(
-    public val ring: A,
-) : AbstractPolynomialSpace<C, Polynomial<C>> {
-    // 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
+    public final override val ring: A,
+) : AbstractPolynomialSpaceOverRing<C, Polynomial<C>, A> {
 
     // region Polynomial-integer relation
     public override operator fun Polynomial<C>.plus(other: Int): Polynomial<C> =
@@ -179,29 +162,6 @@ public open class PolynomialSpace<C, A : Ring<C>>(
         )
     // endregion
 
-    // region Constant-constant relation
-    @JvmName("constantUnaryMinus")
-    public override operator fun C.unaryMinus(): C = ring { -this@unaryMinus }
-    @JvmName("constantPlus")
-    public override operator fun C.plus(other: C): C = ring { this@plus + other }
-    @JvmName("constantMinus")
-    public override operator fun C.minus(other: C): C = ring { this@minus - other }
-    @JvmName("constantTimes")
-    public 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-polynomial relation
     public override operator fun C.plus(other: Polynomial<C>): Polynomial<C> =
         if (this.isZero()) other
@@ -355,19 +315,16 @@ public open class PolynomialSpace<C, A : Ring<C>>(
     }
 
     public override fun Polynomial<C>.isZero(): Boolean = coefficients.all { it.isZero() }
-    public override fun Polynomial<C>.isNotZero(): Boolean = coefficients.any { it.isNotZero() }
     public override fun Polynomial<C>.isOne(): Boolean =
         with(coefficients) { isNotEmpty() && asSequence().withIndex().any { (index, c) -> if (index == 0) c.isOne() else c.isZero() } } // TODO: It's better to write new methods like `anyIndexed`. But what's better way to do it?
-    public override fun Polynomial<C>.isNotOne(): Boolean = !isOne()
     public override fun Polynomial<C>.isMinusOne(): Boolean =
         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?
-    public override fun Polynomial<C>.isNotMinusOne(): Boolean = !isMinusOne()
 
     override val zero: Polynomial<C> = Polynomial(emptyList())
     override val one: Polynomial<C> = Polynomial(listOf(ring.one))
 
     @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
-    public override fun Polynomial<C>.equals(other: Polynomial<C>): Boolean =
+    public override infix fun Polynomial<C>.equalsTo(other: Polynomial<C>): Boolean =
         when {
             this === other -> true
             else -> {
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt
new file mode 100644
index 000000000..778ffb895
--- /dev/null
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt
@@ -0,0 +1,355 @@
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.operations.*
+import kotlin.jvm.JvmName
+import kotlin.math.max
+import kotlin.math.min
+
+
+public data class RationalFunction<C> internal constructor (
+    public override val numerator: Polynomial<C>,
+    public override val denominator: Polynomial<C>
+) : AbstractRationalFunction<C, Polynomial<C>> {
+    override fun toString(): String = "RationalFunction${numerator.coefficients}/${denominator.coefficients}"
+}
+
+// region Internal utilities
+
+/**
+ * Represents internal [RationalFunction] errors.
+ */
+internal class RationalFunctionError : Error {
+    constructor(): super()
+    constructor(message: String): super(message)
+    constructor(message: String?, cause: Throwable?): super(message, cause)
+    constructor(cause: Throwable?): super(cause)
+}
+
+/**
+ * Throws an [RationalFunction] with the given [message].
+ */
+internal fun rationalFunctionError(message: Any): Nothing = throw RationalFunctionError(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 } )
+//    )
+
+// endregion
+
+public class RationalFunctionSpace<C, A : Ring<C>> (
+    public val ring: A,
+) : AbstractRationalFunctionalSpaceOverPolynomialSpace<C, Polynomial<C>, RationalFunction<C>, A> {
+
+    override val polynomialRing : PolynomialSpace<C, A> = PolynomialSpace(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 RationalFunction<C>.plus(other: Int): RationalFunction<C> =
+        RationalFunction(
+            numerator + denominator * other,
+            denominator
+        )
+    /**
+     * Returns difference between the rational function and the integer represented as rational function.
+     *
+     * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
+     */
+    public override operator fun RationalFunction<C>.minus(other: Int): RationalFunction<C> =
+        RationalFunction(
+            numerator - denominator * other,
+            denominator
+        )
+    /**
+     * Returns product of the rational function and the integer represented as rational function.
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public override operator fun RationalFunction<C>.times(other: Int): RationalFunction<C> =
+        RationalFunction(
+            numerator * other,
+            denominator
+        )
+    // 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: RationalFunction<C>): RationalFunction<C> = TODO()
+    /**
+     * Returns difference between the integer represented as rational function and the rational function.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
+     */
+    public override operator fun Int.minus(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    /**
+     * Returns product of the integer represented as rational function and the rational function.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public override operator fun Int.times(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    // 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: RationalFunction<C>): RationalFunction<C> = TODO()
+    /**
+     * Returns difference between the constant represented as polynomial and the rational function.
+     */
+    public override operator fun C.minus(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    /**
+     * Returns product of the constant represented as polynomial and the rational function.
+     */
+    public override operator fun C.times(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    // endregion
+
+    // region Rational-constant relation
+    /**
+     * Returns sum of the constant represented as rational function and the rational function.
+     */
+    public override operator fun RationalFunction<C>.plus(other: C): RationalFunction<C> =
+        RationalFunction(
+            numerator + denominator * other,
+            denominator
+        )
+    /**
+     * Returns difference between the constant represented as rational function and the rational function.
+     */
+    public override operator fun RationalFunction<C>.minus(other: C): RationalFunction<C> =
+        RationalFunction(
+            numerator - denominator * other,
+            denominator
+        )
+    /**
+     * Returns product of the constant represented as rational function and the rational function.
+     */
+    public override operator fun RationalFunction<C>.times(other: C): RationalFunction<C> =
+        RationalFunction(
+            numerator * other,
+            denominator
+        )
+    // endregion
+
+    // region Polynomial-rational relation
+    /**
+     * Returns sum of the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun Polynomial<C>.plus(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    /**
+     * Returns difference between the polynomial represented as polynomial and the rational function.
+     */
+    public override operator fun Polynomial<C>.minus(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    /**
+     * Returns product of the polynomial represented as polynomial and the rational function.
+     */
+    public override operator fun Polynomial<C>.times(other: RationalFunction<C>): RationalFunction<C> = TODO()
+    // endregion
+
+    // region Rational-polynomial relation
+    /**
+     * Returns sum of the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun RationalFunction<C>.plus(other: Polynomial<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator + denominator * other,
+            denominator
+        )
+    /**
+     * Returns difference between the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun RationalFunction<C>.minus(other: Polynomial<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator - denominator * other,
+            denominator
+        )
+    /**
+     * Returns product of the polynomial represented as rational function and the rational function.
+     */
+    public override operator fun RationalFunction<C>.times(other: Polynomial<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator * other,
+            denominator
+        )
+    // endregion
+
+    // region Rational-rational relation
+    /**
+     * Returns negation of the rational function.
+     */
+    public override operator fun RationalFunction<C>.unaryMinus(): RationalFunction<C> = RationalFunction(-numerator, denominator)
+    /**
+     * Returns sum of the rational functions.
+     */
+    public override operator fun RationalFunction<C>.plus(other: RationalFunction<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator * other.denominator + denominator * other.numerator,
+            denominator * other.denominator
+        )
+    /**
+     * Returns difference of the rational functions.
+     */
+    public override operator fun RationalFunction<C>.minus(other: RationalFunction<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator * other.denominator - denominator * other.numerator,
+            denominator * other.denominator
+        )
+    /**
+     * Returns product of the rational functions.
+     */
+    public override operator fun RationalFunction<C>.times(other: RationalFunction<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator * other.numerator,
+            denominator * other.denominator
+        )
+
+    /**
+     * 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).
+     */
+    public override val zero: RationalFunction<C> = RationalFunction(polynomialZero, polynomialOne)
+    /**
+     * Instance of unit polynomial (unit of the rational functions ring).
+     */
+    public override val one: RationalFunction<C> = RationalFunction(polynomialOne, polynomialOne)
+
+    /**
+     * Checks equality of the rational functions.
+     */
+    @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "CovariantEquals")
+    public override infix fun RationalFunction<C>.equalsTo(other: RationalFunction<C>): Boolean =
+        when {
+            this === other -> true
+            numeratorDegree - denominatorDegree != with(other) { numeratorDegree - denominatorDegree } -> false
+            else -> numerator * other.denominator equalsTo other.numerator * denominator
+        }
+    // endregion
+
+    // region REST TODO: Разобрать
+
+    public operator fun RationalFunction<C>.div(other: RationalFunction<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator * other.denominator,
+            denominator * other.numerator
+        )
+
+    public operator fun RationalFunction<C>.div(other: Polynomial<C>): RationalFunction<C> =
+        RationalFunction(
+            numerator,
+            denominator * other
+        )
+
+    public operator fun RationalFunction<C>.div(other: C): RationalFunction<C> =
+        RationalFunction(
+            numerator,
+            denominator * other
+        )
+
+    public operator fun RationalFunction<C>.div(other: Int): RationalFunction<C> =
+        RationalFunction(
+            numerator,
+            denominator * other
+        )
+
+//    operator fun invoke(arg: UnivariatePolynomial<T>): RationalFunction<T> =
+//        RationalFunction(
+//            numerator(arg),
+//            denominator(arg)
+//        )
+//
+//    operator fun invoke(arg: RationalFunction<T>): RationalFunction<T> {
+//        val num = numerator invokeRFTakeNumerator arg
+//        val den = denominator invokeRFTakeNumerator arg
+//        val degreeDif = numeratorDegree - denominatorDegree
+//        return if (degreeDif > 0)
+//            RationalFunction(
+//                num,
+//                multiplyByPower(den, arg.denominator, degreeDif)
+//            )
+//        else
+//            RationalFunction(
+//                multiplyByPower(num, arg.denominator, -degreeDif),
+//                den
+//            )
+//    }
+//
+//    override fun toString(): String = toString(UnivariatePolynomial.variableName)
+//
+//    fun toString(withVariableName: String = UnivariatePolynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toString(withVariableName)
+//            else -> "${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)}"
+//        }
+//
+//    fun toStringWithBrackets(withVariableName: String = UnivariatePolynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toStringWithBrackets(withVariableName)
+//            else -> "(${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)})"
+//        }
+//
+//    fun toReversedString(withVariableName: String = UnivariatePolynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedString(withVariableName)
+//            else -> "${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)}"
+//        }
+//
+//    fun toReversedStringWithBrackets(withVariableName: String = UnivariatePolynomial.variableName): String =
+//        when(true) {
+//            numerator.isZero() -> "0"
+//            denominator.isOne() -> numerator.toReversedStringWithBrackets(withVariableName)
+//            else -> "(${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)})"
+//        }
+//
+//    fun removeZeros() =
+//        RationalFunction(
+//            numerator.removeZeros(),
+//            denominator.removeZeros()
+//        )
+    // endregion
+}
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/rationalFunctionUtil.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/rationalFunctionUtil.kt
new file mode 100644
index 000000000..9147bc023
--- /dev/null
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/rationalFunctionUtil.kt
@@ -0,0 +1,34 @@
+package space.kscience.kmath.functions
+
+
+// region Operator extensions
+
+// region Field case
+
+//operator fun <T: Field<T>> RationalFunction<T>.invoke(arg: T): T = numerator(arg) / denominator(arg)
+//
+//fun <T: Field<T>> RationalFunction<T>.reduced(): RationalFunction<T> =
+//    polynomialGCD(numerator, denominator).let {
+//        RationalFunction(
+//            numerator / it,
+//            denominator / it
+//        )
+//    }
+
+// endregion
+
+// endregion
+
+// region Derivatives
+///**
+// * Returns result of applying formal derivative to the polynomial.
+// *
+// * @param T Field where we are working now.
+// * @return Result of the operator.
+// */
+//fun <T: Ring<T>> RationalFunction<T>.derivative() =
+//    RationalFunction(
+//        numerator.derivative() * denominator - denominator.derivative() * numerator,
+//        denominator * denominator
+//    )
+// endregion
\ No newline at end of file