diff --git a/examples/build.gradle.kts b/examples/build.gradle.kts
index 67b28cd85..aa5c1f47a 100644
--- a/examples/build.gradle.kts
+++ b/examples/build.gradle.kts
@@ -16,7 +16,7 @@ dependencies {
     implementation(project(":kmath-commons"))
     implementation(project(":kmath-complex"))
     implementation(project(":kmath-functions"))
-    implementation(project(":kmath-polynomialX"))
+    implementation(project(":kmath-polynomial"))
     implementation(project(":kmath-optimization"))
     implementation(project(":kmath-stat"))
     implementation(project(":kmath-viktor"))
diff --git a/kmath-polynomialX/build.gradle.kts b/kmath-polynomial/build.gradle.kts
similarity index 81%
rename from kmath-polynomialX/build.gradle.kts
rename to kmath-polynomial/build.gradle.kts
index 51b3c0665..dcfcb1b46 100644
--- a/kmath-polynomialX/build.gradle.kts
+++ b/kmath-polynomial/build.gradle.kts
@@ -10,13 +10,11 @@ kotlin.sourceSets {
     commonMain {
         dependencies {
             api(projects.kmathCore)
-            api(projects.kmathFunctions)
         }
     }
     commonTest {
         dependencies {
-            api(projects.testUtilsFunctions)
-            api(projects.testUtilsPolynomialX)
+            api(projects.testUtilsPolynomial)
             api(kotlin("test"))
         }
     }
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledRationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledRationalFunction.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledRationalFunction.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledRationalFunction.kt
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt
new file mode 100644
index 000000000..76e1a6bb6
--- /dev/null
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt
@@ -0,0 +1,387 @@
+/*
+ * 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.
+ */
+
+@file:Suppress("NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress")
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.ScaleOperations
+import space.kscience.kmath.operations.invoke
+import kotlin.math.max
+import kotlin.math.min
+
+
+/**
+ * Represents univariate polynomial that stores its coefficients in a [List].
+ *
+ * @param C the type of constants.
+ */
+public data class ListPolynomial<C>(
+    /**
+     * List that contains coefficients of the polynomial. Every monomial `a x^d` is stored as a coefficient `a` placed
+     * into the list at index `d`. For example, coefficients of a polynomial `5 x^2 - 6` can be represented as
+     * ```
+     * listOf(
+     *     -6, // -6 +
+     *     0,  // 0 x +
+     *     5,  // 5 x^2
+     * )
+     * ```
+     * and also as
+     * ```
+     * listOf(
+     *     -6, // -6 +
+     *     0,  // 0 x +
+     *     5,  // 5 x^2
+     *     0,  // 0 x^3
+     *     0,  // 0 x^4
+     * )
+     * ```
+     * It is not prohibited to put extra zeros at end of the list (as for `0x^3` and `0x^4` in the example). But the
+     * longer the coefficients list the worse performance of arithmetical operations performed on it. Thus, it is
+     * recommended not to put (or even to remove) extra (or useless) coefficients at the end of the coefficients list.
+     */
+    public val coefficients: List<C>
+) : Polynomial<C> {
+    override fun toString(): String = "ListPolynomial$coefficients"
+}
+
+/**
+ * Arithmetic context for univariate polynomials with coefficients stored as a [List] constructed with the provided
+ * [ring] of constants.
+ *
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
+ */
+public open class ListPolynomialSpace<C, A : Ring<C>>(
+    public override val ring: A,
+) : PolynomialSpaceOverRing<C, ListPolynomial<C>, A> {
+    /**
+     * Returns sum of the polynomial and the integer represented as a polynomial.
+     *
+     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+     */
+    public override operator fun ListPolynomial<C>.plus(other: Int): ListPolynomial<C> =
+        if (other == 0) this
+        else
+            ListPolynomial(
+                coefficients
+                    .toMutableList()
+                    .apply {
+                        val result = getOrElse(0) { constantZero } + other
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+    /**
+     * Returns difference between the polynomial and the integer represented as a polynomial.
+     *
+     * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
+     */
+    public override operator fun ListPolynomial<C>.minus(other: Int): ListPolynomial<C> =
+        if (other == 0) this
+        else
+            ListPolynomial(
+                coefficients
+                    .toMutableList()
+                    .apply {
+                        val result = getOrElse(0) { constantZero } - other
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+    /**
+     * Returns product of the polynomial and the integer represented as a polynomial.
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public override operator fun ListPolynomial<C>.times(other: Int): ListPolynomial<C> =
+        when (other) {
+            0 -> zero
+            1 -> this
+            else -> ListPolynomial(
+                coefficients
+                    .toMutableList()
+                    .apply {
+                        for (deg in indices) this[deg] = this[deg] * other
+                    }
+            )
+        }
+
+    /**
+     * Returns sum of the integer represented as a polynomial and the polynomial.
+     *
+     * The operation is equivalent to adding [this] copies of unit polynomial to [other].
+     */
+    public override operator fun Int.plus(other: ListPolynomial<C>): ListPolynomial<C> =
+        if (this == 0) other
+        else
+            ListPolynomial(
+                other.coefficients
+                    .toMutableList()
+                    .apply {
+                        val result = this@plus + getOrElse(0) { constantZero }
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+    /**
+     * Returns difference between the integer represented as a polynomial and the polynomial.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
+     */
+    public override operator fun Int.minus(other: ListPolynomial<C>): ListPolynomial<C> =
+        ListPolynomial(
+            other.coefficients
+                .toMutableList()
+                .apply {
+                    if (this@minus == 0) {
+                        indices.forEach { this[it] = -this[it] }
+                    } else {
+                        (1..lastIndex).forEach { this[it] = -this[it] }
+
+                        val result = this@minus - getOrElse(0) { constantZero }
+
+                        if (size == 0) add(result)
+                        else this[0] = result
+                    }
+                }
+        )
+    /**
+     * Returns product of the integer represented as a polynomial and the polynomial.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public override operator fun Int.times(other: ListPolynomial<C>): ListPolynomial<C> =
+        when (this) {
+            0 -> zero
+            1 -> other
+            else -> ListPolynomial(
+                other.coefficients
+                    .toMutableList()
+                    .apply {
+                        for (deg in indices) this[deg] = this@times * this[deg]
+                    }
+            )
+        }
+
+    /**
+     * Returns sum of the constant represented as a polynomial and the polynomial.
+     */
+    public override operator fun C.plus(other: ListPolynomial<C>): ListPolynomial<C> =
+        with(other.coefficients) {
+            if (isEmpty()) ListPolynomial(listOf(this@plus))
+            else ListPolynomial(
+                toMutableList()
+                    .apply {
+                        val result = if (size == 0) this@plus else this@plus + get(0)
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+        }
+    /**
+     * Returns difference between the constant represented as a polynomial and the polynomial.
+     */
+    public override operator fun C.minus(other: ListPolynomial<C>): ListPolynomial<C> =
+        with(other.coefficients) {
+            if (isEmpty()) ListPolynomial(listOf(this@minus))
+            else ListPolynomial(
+                toMutableList()
+                    .apply {
+                        (1 .. lastIndex).forEach { this[it] = -this[it] }
+
+                        val result = if (size == 0) this@minus else this@minus - get(0)
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+        }
+    /**
+     * Returns product of the constant represented as a polynomial and the polynomial.
+     */
+    public override operator fun C.times(other: ListPolynomial<C>): ListPolynomial<C> =
+        ListPolynomial(
+            other.coefficients
+                .toMutableList()
+                .apply {
+                    for (deg in indices) this[deg] = this@times * this[deg]
+                }
+        )
+
+    /**
+     * Returns sum of the constant represented as a polynomial and the polynomial.
+     */
+    public override operator fun ListPolynomial<C>.plus(other: C): ListPolynomial<C> =
+        with(coefficients) {
+            if (isEmpty()) ListPolynomial(listOf(other))
+            else ListPolynomial(
+                toMutableList()
+                    .apply {
+                        val result = if (size == 0) other else get(0) + other
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+        }
+    /**
+     * Returns difference between the constant represented as a polynomial and the polynomial.
+     */
+    public override operator fun ListPolynomial<C>.minus(other: C): ListPolynomial<C> =
+        with(coefficients) {
+            if (isEmpty()) ListPolynomial(listOf(-other))
+            else ListPolynomial(
+                toMutableList()
+                    .apply {
+                        val result = if (size == 0) other else get(0) - other
+
+                        if(size == 0) add(result)
+                        else this[0] = result
+                    }
+            )
+        }
+    /**
+     * Returns product of the constant represented as a polynomial and the polynomial.
+     */
+    public override operator fun ListPolynomial<C>.times(other: C): ListPolynomial<C> =
+        ListPolynomial(
+            coefficients
+                .toMutableList()
+                .apply {
+                    for (deg in indices) this[deg] = this[deg] * other
+                }
+        )
+
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public override fun number(value: C): ListPolynomial<C> = ListPolynomial(listOf(value))
+
+    /**
+     * Returns negation of the polynomial.
+     */
+    public override operator fun ListPolynomial<C>.unaryMinus(): ListPolynomial<C> =
+        ListPolynomial(coefficients.map { -it })
+    /**
+     * Returns sum of the polynomials.
+     */
+    public override operator fun ListPolynomial<C>.plus(other: ListPolynomial<C>): ListPolynomial<C> {
+        val thisDegree = degree
+        val otherDegree = other.degree
+        return ListPolynomial(
+            List(max(thisDegree, otherDegree) + 1) {
+                when {
+                    it > thisDegree -> other.coefficients[it]
+                    it > otherDegree -> coefficients[it]
+                    else -> coefficients[it] + other.coefficients[it]
+                }
+            }
+        )
+    }
+    /**
+     * Returns difference of the polynomials.
+     */
+    public override operator fun ListPolynomial<C>.minus(other: ListPolynomial<C>): ListPolynomial<C> {
+        val thisDegree = degree
+        val otherDegree = other.degree
+        return ListPolynomial(
+            List(max(thisDegree, otherDegree) + 1) {
+                when {
+                    it > thisDegree -> -other.coefficients[it]
+                    it > otherDegree -> coefficients[it]
+                    else -> coefficients[it] - other.coefficients[it]
+                }
+            }
+        )
+    }
+    /**
+     * Returns product of the polynomials.
+     */
+    public override operator fun ListPolynomial<C>.times(other: ListPolynomial<C>): ListPolynomial<C> {
+        val thisDegree = degree
+        val otherDegree = other.degree
+        return ListPolynomial(
+            List(thisDegree + otherDegree + 1) { d ->
+                (max(0, d - otherDegree)..min(thisDegree, d))
+                    .map { coefficients[it] * other.coefficients[d - it] }
+                    .reduce { acc, rational -> acc + rational }
+            }
+        )
+    }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */ // TODO: To optimize boxing
+    override fun power(arg: ListPolynomial<C>, exponent: UInt): ListPolynomial<C> = super.power(arg, exponent)
+
+    /**
+     * Instance of zero polynomial (zero of the polynomial ring).
+     */
+    override val zero: ListPolynomial<C> = ListPolynomial(emptyList())
+    /**
+     * Instance of unit polynomial (unit of the polynomial ring).
+     */
+    override val one: ListPolynomial<C> by lazy { ListPolynomial(listOf(constantOne)) }
+
+    /**
+     * 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 ListPolynomial<C>.degree: Int get() = coefficients.lastIndex
+
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
+    /**
+     * Evaluates value of [this] polynomial on provided [argument].
+     */
+    public inline fun ListPolynomial<C>.substitute(argument: C): C = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] polynomial.
+     */
+    public inline fun ListPolynomial<C>.substitute(argument: ListPolynomial<C>): ListPolynomial<C> = substitute(ring, argument)
+
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    public inline fun ListPolynomial<C>.asFunction(): (C) -> C = asFunctionOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    public inline fun ListPolynomial<C>.asFunctionOfConstant(): (C) -> C = asFunctionOfConstantOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    public inline fun ListPolynomial<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListPolynomial<C> = asFunctionOfPolynomialOver(ring)
+
+    /**
+     * Evaluates value of [this] polynomial on provided [argument].
+     */
+    public inline operator fun ListPolynomial<C>.invoke(argument: C): C = substitute(ring, argument)
+    /**
+     * Evaluates value of [this] polynomial on provided [argument].
+     */
+    public inline operator fun ListPolynomial<C>.invoke(argument: ListPolynomial<C>): ListPolynomial<C> = substitute(ring, argument)
+}
+
+/**
+ * Space of polynomials constructed over ring.
+ *
+ * @param C the type of constants. Polynomials have them as a coefficients in their terms.
+ * @param A type of underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
+ */
+public class ScalableListPolynomialSpace<C, A>(
+    ring: A,
+) : ListPolynomialSpace<C, A>(ring), ScaleOperations<ListPolynomial<C>> where A : Ring<C>, A : ScaleOperations<C> {
+    override fun scale(a: ListPolynomial<C>, value: Double): ListPolynomial<C> =
+        ring { ListPolynomial(a.coefficients.map { scale(it, value) }) }
+}
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListRationalFunction.kt
similarity index 100%
rename from kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListRationalFunction.kt
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedRationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedRationalFunction.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedRationalFunction.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedRationalFunction.kt
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/Polynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/Polynomial.kt
new file mode 100644
index 000000000..61ea5a342
--- /dev/null
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/Polynomial.kt
@@ -0,0 +1,502 @@
+/*
+ * 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
+import kotlin.js.JsName
+import kotlin.jvm.JvmName
+
+
+/**
+ * Abstraction of polynomials.
+ */
+public interface Polynomial<C>
+
+/**
+ * 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 coefficients in their terms.
+ * @param P the type of polynomials.
+ */
+@Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE") // FIXME: Waiting for KT-31420
+public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
+    /**
+     * Returns sum of the constant and the integer represented as a constant (member of underlying ring).
+     *
+     * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
+     */
+    public operator fun C.plus(other: Int): C
+    /**
+     * Returns difference between the constant and the integer represented as a constant (member of underlying ring).
+     *
+     * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
+     */
+    public operator fun C.minus(other: Int): C
+    /**
+     * Returns product of the constant and the integer represented as a constant (member of underlying ring).
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public operator fun C.times(other: Int): C
+
+    /**
+     * Returns sum of the integer represented as a constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
+     */
+    public operator fun Int.plus(other: C): C
+    /**
+     * Returns difference between the integer represented as a constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
+     */
+    public operator fun Int.minus(other: C): C
+    /**
+     * Returns product of the integer represented as a constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public operator fun Int.times(other: C): C
+
+    /**
+     * Converts the integer [value] to constant.
+     */
+    public fun constantNumber(value: Int): C = constantOne * value
+    /**
+     * Converts the integer to constant.
+     */
+    public fun Int.asConstant(): C = constantNumber(this)
+
+    /**
+     * Returns sum of the polynomial and the integer represented as a polynomial.
+     *
+     * The operation is equivalent to adding [other] copies of unit polynomial to [this].
+     */
+    public operator fun P.plus(other: Int): P = addMultipliedByDoubling(this, one, other)
+    /**
+     * Returns difference between the polynomial and the integer represented as a polynomial.
+     *
+     * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
+     */
+    public operator fun P.minus(other: Int): P = addMultipliedByDoubling(this, one, -other)
+    /**
+     * Returns product of the polynomial and the integer represented as a polynomial.
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public operator fun P.times(other: Int): P = multiplyByDoubling(this, other)
+
+    /**
+     * Returns sum of the integer represented as a polynomial and the polynomial.
+     *
+     * The operation is equivalent to adding [this] copies of unit polynomial to [other].
+     */
+    public operator fun Int.plus(other: P): P = addMultipliedByDoubling(other, one, this)
+    /**
+     * Returns difference between the integer represented as a polynomial and the polynomial.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
+     */
+    public operator fun Int.minus(other: P): P = addMultipliedByDoubling(-other, one, this)
+    /**
+     * Returns product of the integer represented as a polynomial and the polynomial.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public operator fun Int.times(other: P): P = multiplyByDoubling(other, this)
+
+    /**
+     * Converts the integer [value] to polynomial.
+     */
+    public fun number(value: Int): P = number(constantNumber(value))
+    /**
+     * Converts the integer to polynomial.
+     */
+    public fun Int.asPolynomial(): P = number(this)
+
+    /**
+     * Returns the same constant.
+     */
+    @JvmName("unaryPlusConstant")
+    @JsName("unaryPlusConstant")
+    public operator fun C.unaryPlus(): C = this
+    /**
+     * Returns negation of the constant.
+     */
+    @JvmName("unaryMinusConstant")
+    @JsName("unaryMinusConstant")
+    public operator fun C.unaryMinus(): C
+    /**
+     * Returns sum of the constants.
+     */
+    @JvmName("plusConstantConstant")
+    @JsName("plusConstantConstant")
+    public operator fun C.plus(other: C): C
+    /**
+     * Returns difference of the constants.
+     */
+    @JvmName("minusConstantConstant")
+    @JsName("minusConstantConstant")
+    public operator fun C.minus(other: C): C
+    /**
+     * Returns product of the constants.
+     */
+    @JvmName("timesConstantConstant")
+    @JsName("timesConstantConstant")
+    public operator fun C.times(other: C): C
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("powerConstant")
+    @JsName("powerConstant")
+    public fun power(arg: C, exponent: UInt) : C
+
+    /**
+     * 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
+
+    /**
+     * Returns sum of the constant represented as a polynomial and the polynomial.
+     */
+    public operator fun C.plus(other: P): P
+    /**
+     * Returns difference between the constant represented as a polynomial and the polynomial.
+     */
+    public operator fun C.minus(other: P): P
+    /**
+     * Returns product of the constant represented as a polynomial and the polynomial.
+     */
+    public operator fun C.times(other: P): P
+
+    /**
+     * Returns sum of the constant represented as a polynomial and the polynomial.
+     */
+    public operator fun P.plus(other: C): P
+    /**
+     * Returns difference between the constant represented as a polynomial and the polynomial.
+     */
+    public operator fun P.minus(other: C): P
+    /**
+     * Returns product of the constant represented as a polynomial and the polynomial.
+     */
+    public operator fun P.times(other: C): P
+
+    /**
+     * Converts the constant [value] to polynomial.
+     */
+    public fun number(value: C): P = one * value
+    /**
+     * Converts the constant to polynomial.
+     */
+    public fun C.asPolynomial(): P = number(this)
+
+    /**
+     * Returns the same polynomial.
+     */
+    public override operator fun P.unaryPlus(): P = this
+    /**
+     * Returns negation of the polynomial.
+     */
+    public override operator fun P.unaryMinus(): P
+    /**
+     * Returns sum of the polynomials.
+     */
+    public override operator fun P.plus(other: P): P
+    /**
+     * Returns difference of the polynomials.
+     */
+    public override operator fun P.minus(other: P): P
+    /**
+     * Returns product of the polynomials.
+     */
+    public override operator fun P.times(other: P): P
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    public override fun power(arg: P, exponent: UInt) : P = exponentiateBySquaring(arg, exponent)
+
+    /**
+     * Instance of zero polynomial (zero of the polynomial ring).
+     */
+    public override val zero: P
+    /**
+     * Instance of unit polynomial (unit of the polynomial ring).
+     */
+    public override val one: P
+
+    /**
+     * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
+     * zero, degree is -1.
+     */
+    public val P.degree: Int
+
+    override fun add(left: P, right: P): P = left + right
+    override fun multiply(left: P, right: P): P = left * right
+}
+
+/**
+ * Abstraction of ring of polynomials of type [P] over ring of constants of type [C]. It also assumes that there is
+ * provided [ring] (of type [A]), that provides constant-wise operations.
+ *
+ * @param C the type of constants. Polynomials have them as coefficients in their terms.
+ * @param P the type of polynomials.
+ * @param A the type of algebraic structure (precisely, of ring) provided for constants.
+ */
+@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420
+public interface PolynomialSpaceOverRing<C, P: Polynomial<C>, A: Ring<C>> : PolynomialSpace<C, P> {
+
+    /**
+     * Underlying ring of constants. Its operations on constants are inherited by local operations on constants.
+     */
+    public val ring: A
+
+    /**
+     * Returns sum of the constant and the integer represented as a constant (member of underlying ring).
+     *
+     * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
+     */
+    public override operator fun C.plus(other: Int): C = ring { addMultipliedByDoubling(this@plus, one, other) }
+    /**
+     * Returns difference between the constant and the integer represented as a constant (member of underlying ring).
+     *
+     * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
+     */
+    public override operator fun C.minus(other: Int): C = ring { addMultipliedByDoubling(this@minus, one, -other) }
+    /**
+     * Returns product of the constant and the integer represented as a constant (member of underlying ring).
+     *
+     * The operation is equivalent to sum of [other] copies of [this].
+     */
+    public override operator fun C.times(other: Int): C = ring { multiplyByDoubling(this@times, other) }
+
+    /**
+     * Returns sum of the integer represented as a constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
+     */
+    public override operator fun Int.plus(other: C): C = ring { addMultipliedByDoubling(other, one, this@plus) }
+    /**
+     * Returns difference between the integer represented as a constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
+     */
+    public override operator fun Int.minus(other: C): C = ring { addMultipliedByDoubling(-other, one, this@minus) }
+    /**
+     * Returns product of the integer represented as a constant (member of underlying ring) and the constant.
+     *
+     * The operation is equivalent to sum of [this] copies of [other].
+     */
+    public override operator fun Int.times(other: C): C = ring { multiplyByDoubling(other, this@times) }
+
+    /**
+     * Returns negation of the constant.
+     */
+    @JvmName("unaryMinusConstant")
+    public override operator fun C.unaryMinus(): C = ring { -this@unaryMinus }
+    /**
+     * Returns sum of the constants.
+     */
+    @JvmName("plusConstantConstant")
+    public override operator fun C.plus(other: C): C = ring { this@plus + other }
+    /**
+     * Returns difference of the constants.
+     */
+    @JvmName("minusConstantConstant")
+    public override operator fun C.minus(other: C): C = ring { this@minus - other }
+    /**
+     * Returns product of the constants.
+     */
+    @JvmName("timesConstantConstant")
+    public override operator fun C.times(other: C): C = ring { this@times * other }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("powerConstant")
+    override fun power(arg: C, exponent: UInt): C = ring { power(arg, exponent) }
+
+    /**
+     * Instance of zero constant (zero of the underlying ring).
+     */
+    public override val constantZero: C get() = ring.zero
+    /**
+     * Instance of unit constant (unit of the underlying ring).
+     */
+    public override val constantOne: C get() = ring.one
+}
+
+/**
+ * Abstraction of ring of polynomials of type [P] of variables of type [V] and over ring of constants of type [C].
+ *
+ * @param C the type of constants. Polynomials have them as coefficients in their terms.
+ * @param V the type of variables. Polynomials have them in representations of terms.
+ * @param P the type of polynomials.
+ */
+@Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420
+public interface MultivariatePolynomialSpace<C, V, P: Polynomial<C>>: PolynomialSpace<C, P> {
+    /**
+     * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
+    @JvmName("plusVariableInt")
+    public operator fun V.plus(other: Int): P
+    /**
+     * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
+    @JvmName("minusVariableInt")
+    public operator fun V.minus(other: Int): P
+    /**
+     * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
+    @JvmName("timesVariableInt")
+    public operator fun V.times(other: Int): P
+
+    /**
+     * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("plusIntVariable")
+    public operator fun Int.plus(other: V): P
+    /**
+     * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("minusIntVariable")
+    public operator fun Int.minus(other: V): P
+    /**
+     * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("timesIntVariable")
+    public operator fun Int.times(other: V): P
+
+    /**
+     * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
+    @JvmName("plusVariableConstant")
+    public operator fun V.plus(other: C): P
+    /**
+     * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
+    @JvmName("minusVariableConstant")
+    public operator fun V.minus(other: C): P
+    /**
+     * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
+    @JvmName("timesVariableConstant")
+    public operator fun V.times(other: C): P
+
+    /**
+     * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("plusConstantVariable")
+    public operator fun C.plus(other: V): P
+    /**
+     * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("minusConstantVariable")
+    public operator fun C.minus(other: V): P
+    /**
+     * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("timesConstantVariable")
+    public operator fun C.times(other: V): P
+
+    /**
+     * Represents the variable as a monic monomial.
+     */
+    @JvmName("unaryPlusVariable")
+    public operator fun V.unaryPlus(): P
+    /**
+     * Returns negation of representation of the variable as a monic monomial.
+     */
+    @JvmName("unaryMinusVariable")
+    public operator fun V.unaryMinus(): P
+    /**
+     * Returns sum of the variables represented as monic monomials.
+     */
+    @JvmName("plusVariableVariable")
+    public operator fun V.plus(other: V): P
+    /**
+     * Returns difference between the variables represented as monic monomials.
+     */
+    @JvmName("minusVariableVariable")
+    public operator fun V.minus(other: V): P
+    /**
+     * Returns product of the variables represented as monic monomials.
+     */
+    @JvmName("timesVariableVariable")
+    public operator fun V.times(other: V): P
+
+    /**
+     * Represents the [variable] as a monic monomial.
+     */
+    @JvmName("numberVariable")
+    public fun number(variable: V): P = +variable
+    /**
+     * Represents the variable as a monic monomial.
+     */
+    @JvmName("asPolynomialVariable")
+    public fun V.asPolynomial(): P = number(this)
+
+    /**
+     * Returns sum of the variable represented as a monic monomial and the polynomial.
+     */
+    @JvmName("plusVariablePolynomial")
+    public operator fun V.plus(other: P): P
+    /**
+     * Returns difference between the variable represented as a monic monomial and the polynomial.
+     */
+    @JvmName("minusVariablePolynomial")
+    public operator fun V.minus(other: P): P
+    /**
+     * Returns product of the variable represented as a monic monomial and the polynomial.
+     */
+    @JvmName("timesVariablePolynomial")
+    public operator fun V.times(other: P): P
+
+    /**
+     * Returns sum of the polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("plusPolynomialVariable")
+    public operator fun P.plus(other: V): P
+    /**
+     * Returns difference between the polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("minusPolynomialVariable")
+    public operator fun P.minus(other: V): P
+    /**
+     * Returns product of the polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("timesPolynomialVariable")
+    public operator fun P.times(other: V): P
+
+    /**
+     * 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 P.degrees: Map<V, UInt>
+    /**
+     * Counts degree of the polynomial by the specified [variable].
+     */
+    public fun P.degreeBy(variable: V): UInt = degrees.getOrElse(variable) { 0u }
+    /**
+     * Counts degree of the polynomial by the specified [variables].
+     */
+    public fun P.degreeBy(variables: Collection<V>): UInt
+    /**
+     * Set of all variables that appear in the polynomial in positive exponents.
+     */
+    public val P.variables: Set<V> get() = degrees.keys
+    /**
+     * Count of all variables that appear in the polynomial in positive exponents.
+     */
+    public val P.countOfVariables: Int get() = variables.size
+}
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/RationalFunction.kt
similarity index 99%
rename from kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/RationalFunction.kt
index 1782dba74..f664ae9db 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/RationalFunction.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/RationalFunction.kt
@@ -5,7 +5,8 @@
 
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.operations.*
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.invoke
 import kotlin.js.JsName
 import kotlin.jvm.JvmName
 
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/algebraicStub.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/algebraicStub.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/algebraicStub.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/algebraicStub.kt
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
similarity index 99%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
index 4e799cb43..e3b35facc 100644
--- a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
@@ -8,9 +8,9 @@ package space.kscience.kmath.functions
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.Field
-import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.algebra
+import space.kscience.kmath.operations.invoke
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 import kotlin.jvm.JvmName
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/listConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/listConstructors.kt
new file mode 100644
index 000000000..e95361724
--- /dev/null
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/listConstructors.kt
@@ -0,0 +1,92 @@
+/*
+ * 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
+
+
+/**
+ * Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed
+ * if [reverse] parameter is true.
+ */
+@Suppress("FunctionName")
+public fun <C> ListPolynomial(coefficients: List<C>, reverse: Boolean = false): ListPolynomial<C> =
+    ListPolynomial(with(coefficients) { if (reverse) reversed() else this })
+
+/**
+ * Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed
+ * if [reverse] parameter is true.
+ */
+@Suppress("FunctionName")
+public fun <C> ListPolynomial(vararg coefficients: C, reverse: Boolean = false): ListPolynomial<C> =
+    ListPolynomial(with(coefficients) { if (reverse) reversed() else toList() })
+
+/**
+ * Represents [this] constant as a [ListPolynomial].
+ */
+public fun <C> C.asListPolynomial() : ListPolynomial<C> = ListPolynomial(listOf(this))
+
+
+// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
+
+/**
+ * Constructs [ListRationalFunction] instance with numerator and denominator constructed with provided
+ * [numeratorCoefficients] and [denominatorCoefficients]. The both collections of coefficients will be reversed if
+ * [reverse] parameter is true.
+ */
+@Suppress("FunctionName")
+public fun <C> ListRationalFunction(numeratorCoefficients: List<C>, denominatorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
+    ListRationalFunction<C>(
+        ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
+        ListPolynomial( with(denominatorCoefficients) { if (reverse) reversed() else this } )
+    )
+/**
+ * Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator.
+ */
+@Suppress("FunctionName")
+public fun <C, A: Ring<C>> A.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
+    ListRationalFunction<C>(numerator, ListPolynomial(listOf(one)))
+/**
+ * Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator.
+ */
+@Suppress("FunctionName")
+public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
+    ListRationalFunction<C>(numerator, polynomialOne)
+/**
+ * Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit
+ * denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true.
+ */
+@Suppress("FunctionName")
+public fun <C, A: Ring<C>> A.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
+    ListRationalFunction<C>(
+        ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
+        ListPolynomial(listOf(one))
+    )
+/**
+ * Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit
+ * denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true.
+ */
+@Suppress("FunctionName")
+public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
+    ListRationalFunction<C>(
+        ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
+        polynomialOne
+    )
+
+/**
+ * Represents [this] constant as a rational function.
+ */ // FIXME: When context receivers will be ready, delete this function and uncomment the following two
+public fun <C, A: Ring<C>> C.asListRationalFunction(ring: A) : ListRationalFunction<C> = ring.ListRationalFunction(asListPolynomial())
+///**
+// * Represents [this] constant as a rational function.
+// */
+//context(A)
+//public fun <C, A: Ring<C>> C.asListRationalFunction() : ListRationalFunction<C> = ListRationalFunction(asListPolynomial())
+///**
+// * Represents [this] constant as a rational function.
+// */
+//context(ListRationalFunctionSpace<C, A>)
+//public fun <C, A: Ring<C>> C.asListRationalFunction() : ListRationalFunction<C> = ListRationalFunction(asListPolynomial())
\ No newline at end of file
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/listUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/listUtil.kt
new file mode 100644
index 000000000..4f3f6d88e
--- /dev/null
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/listUtil.kt
@@ -0,0 +1,255 @@
+/*
+ * 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.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.*
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+import kotlin.math.max
+import kotlin.math.pow
+
+
+/**
+ * Creates a [ListPolynomialSpace] over a received ring.
+ */
+public inline val <C, A : Ring<C>> A.listPolynomialSpace: ListPolynomialSpace<C, A>
+    get() = ListPolynomialSpace(this)
+
+/**
+ * Creates a [ListPolynomialSpace]'s scope over a received ring.
+ */ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block]
+public inline fun <C, A : Ring<C>, R> A.listPolynomialSpace(block: ListPolynomialSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return ListPolynomialSpace(this).block()
+}
+
+/**
+ * Creates a [ScalableListPolynomialSpace] over a received scalable ring.
+ */
+public inline val <C, A> A.scalableListPolynomialSpace: ScalableListPolynomialSpace<C, A> where A : Ring<C>, A : ScaleOperations<C>
+    get() = ScalableListPolynomialSpace(this)
+
+/**
+ * Creates a [ScalableListPolynomialSpace]'s scope over a received scalable ring.
+ */ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block]
+public inline fun <C, A, R> A.scalableListPolynomialSpace(block: ScalableListPolynomialSpace<C, A>.() -> R): R where A : Ring<C>, A : ScaleOperations<C> {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return ScalableListPolynomialSpace(this).block()
+}
+
+/**
+ * Creates a [ListRationalFunctionSpace] over a received ring.
+ */
+public inline val <C, A : Ring<C>> A.listRationalFunctionSpace: ListRationalFunctionSpace<C, A>
+    get() = ListRationalFunctionSpace(this)
+
+/**
+ * Creates a [ListRationalFunctionSpace]'s scope over a received ring.
+ */ // TODO: When context will be ready move [ListRationalFunctionSpace] and add [A] to context receivers of [block]
+public inline fun <C, A : Ring<C>, R> A.listRationalFunctionSpace(block: ListRationalFunctionSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return ListRationalFunctionSpace(this).block()
+}
+
+
+/**
+ * Evaluates value of [this] Double polynomial on provided Double argument.
+ */
+public fun ListPolynomial<Double>.substitute(arg: Double): Double =
+    coefficients.reduceIndexedOrNull { index, acc, c ->
+        acc + c * arg.pow(index)
+    } ?: .0
+
+/**
+ * Evaluates value of [this] polynomial on provided argument.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */
+public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
+    if (coefficients.isEmpty()) return zero
+    var result: C = coefficients.last()
+    for (j in coefficients.size - 2 downTo 0) {
+        result = (arg * result) + coefficients[j]
+    }
+    return result
+}
+
+/**
+ * Substitutes provided polynomial [arg] into [this] polynomial.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */ // TODO: To optimize boxing
+public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> =
+    ring.listPolynomialSpace {
+        if (coefficients.isEmpty()) return zero
+        var result: ListPolynomial<C> = coefficients.last().asPolynomial()
+        for (j in coefficients.size - 2 downTo 0) {
+            result = (arg * result) + coefficients[j]
+        }
+        return result
+    }
+
+/**
+ * Substitutes provided rational function [arg] into [this] polynomial.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */ // TODO: To optimize boxing
+public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListRationalFunction<C>) : ListRationalFunction<C> =
+    ring.listRationalFunctionSpace {
+        if (coefficients.isEmpty()) return zero
+        var result: ListRationalFunction<C> = coefficients.last().asRationalFunction()
+        for (j in coefficients.size - 2 downTo 0) {
+            result = (arg * result) + coefficients[j]
+        }
+        return result
+    }
+
+/**
+ * Evaluates value of [this] Double rational function in provided Double argument.
+ */
+public fun ListRationalFunction<Double>.substitute(arg: Double): Double =
+    numerator.substitute(arg) / denominator.substitute(arg)
+
+/**
+ * Evaluates value of [this] polynomial for provided argument.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */
+public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
+    numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+}
+
+/**
+ * Substitutes provided polynomial [arg] into [this] rational function.
+ */ // TODO: To optimize boxing
+public fun <C> ListRationalFunction<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListRationalFunction<C> =
+    ring.listRationalFunctionSpace {
+        numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+    }
+
+/**
+ * Substitutes provided rational function [arg] into [this] rational function.
+ */ // TODO: To optimize boxing
+public fun <C> ListRationalFunction<C>.substitute(ring: Ring<C>, arg: ListRationalFunction<C>) : ListRationalFunction<C> =
+    ring.listRationalFunctionSpace {
+        numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+    }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfConstantOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfPolynomialOver(ring: A): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfRationalFunctionOver(ring: A): (ListRationalFunction<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Field<C>> ListRationalFunction<C>.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Field<C>> ListRationalFunction<C>.asFunctionOfConstantOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListRationalFunction<C>.asFunctionOfPolynomialOver(ring: A): (ListPolynomial<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListRationalFunction<C>.asFunctionOfRationalFunctionOver(ring: A): (ListRationalFunction<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Returns algebraic derivative of received polynomial.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.derivative(
+    ring: A,
+): ListPolynomial<C> where  A : Ring<C>, A : NumericAlgebra<C> = ring {
+    ListPolynomial(
+        buildList(max(0, coefficients.size - 1)) {
+            for (deg in 1 .. coefficients.lastIndex) add(number(deg) * coefficients[deg])
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial of specified [order]. The [order] should be non-negative integer.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.nthDerivative(
+    ring: A,
+    order: Int,
+): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = ring {
+    require(order >= 0) { "Order of derivative must be non-negative" }
+    ListPolynomial(
+        buildList(max(0, coefficients.size - order)) {
+            for (deg in order.. coefficients.lastIndex)
+                add((deg - order + 1 .. deg).fold(coefficients[deg]) { acc, d -> acc * number(d) })
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.antiderivative(
+    ring: A,
+): ListPolynomial<C> where  A : Field<C>, A : NumericAlgebra<C> = ring {
+    ListPolynomial(
+        buildList(coefficients.size + 1) {
+            add(zero)
+            coefficients.mapIndexedTo(this) { index, t -> t / number(index + 1) }
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial of specified [order]. The [order] should be non-negative integer.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.nthAntiderivative(
+    ring: A,
+    order: Int,
+): ListPolynomial<C> where  A : Field<C>, A : NumericAlgebra<C> = ring {
+    require(order >= 0) { "Order of antiderivative must be non-negative" }
+    ListPolynomial(
+        buildList(coefficients.size + order) {
+            repeat(order) { add(zero) }
+            coefficients.mapIndexedTo(this) { index, c -> (1..order).fold(c) { acc, i -> acc / number(index + i) } }
+        }
+    )
+}
+
+/**
+ * Computes a definite integral of [this] polynomial in the specified [range].
+ */
+@UnstableKMathAPI
+public fun <C : Comparable<C>> ListPolynomial<C>.integrate(
+    ring: Field<C>,
+    range: ClosedRange<C>,
+): C = ring {
+    val antiderivative = antiderivative(ring)
+    antiderivative.substitute(ring, range.endInclusive) - antiderivative.substitute(ring, range.start)
+}
\ No newline at end of file
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/misc.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/misc.kt
new file mode 100644
index 000000000..76f1c294e
--- /dev/null
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/misc.kt
@@ -0,0 +1,22 @@
+/*
+ * 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
+
+
+/**
+ * Marks declarations that give access to internal entities of polynomials delicate structure. Thus, it allows to
+ * optimize performance a bit by skipping standard steps, but such skips may cause critical errors if something is
+ * implemented badly. Make sure you fully read and understand documentation and don't break internal contracts.
+ */
+@RequiresOptIn(
+    message = "This declaration gives access to delicate internal structure of polynomials. " +
+            "It allows to optimize performance by skipping unnecessary arguments check. " +
+            "But at the same time makes it easy to make a mistake " +
+            "that will cause wrong computation result or even runtime error. " +
+            "Make sure you fully read and understand documentation.",
+    level = RequiresOptIn.Level.ERROR
+)
+public annotation class DelicatePolynomialAPI
\ No newline at end of file
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt
diff --git a/kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt
similarity index 100%
rename from kmath-polynomialX/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt
rename to kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt
diff --git a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt
similarity index 99%
rename from kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt
rename to kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt
index 081cf06e4..80476050b 100644
--- a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt
+++ b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledConstructorsTest.kt
@@ -6,13 +6,13 @@
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.algebra
-import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.functions.testUtils.t
 import space.kscience.kmath.functions.testUtils.x
 import space.kscience.kmath.functions.testUtils.y
 import space.kscience.kmath.functions.testUtils.z
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.algebra
+import space.kscience.kmath.operations.invoke
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
diff --git a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt
similarity index 99%
rename from kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt
rename to kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt
index d2d417a02..bde1386da 100644
--- a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt
+++ b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialTest.kt
@@ -11,15 +11,15 @@ import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.functions.testUtils.IntModuloRing
 import space.kscience.kmath.functions.testUtils.Rational
 import space.kscience.kmath.functions.testUtils.RationalField
-import space.kscience.kmath.functions.testUtils.o
+import space.kscience.kmath.functions.testUtils.iota
 import space.kscience.kmath.functions.testUtils.m
-import kotlin.test.*
+import space.kscience.kmath.functions.testUtils.o
+import space.kscience.kmath.functions.testUtils.s
+import space.kscience.kmath.functions.testUtils.t
 import space.kscience.kmath.functions.testUtils.x
 import space.kscience.kmath.functions.testUtils.y
 import space.kscience.kmath.functions.testUtils.z
-import space.kscience.kmath.functions.testUtils.t
-import space.kscience.kmath.functions.testUtils.s
-import space.kscience.kmath.functions.testUtils.iota
+import kotlin.test.*
 
 
 // TODO: Тесты на конвертацию.
diff --git a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt
similarity index 99%
rename from kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt
rename to kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt
index 37329a318..88ee1cbb8 100644
--- a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt
+++ b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/LabeledPolynomialUtilTest.kt
@@ -6,16 +6,15 @@
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.functions.testUtils.Rational
 import space.kscience.kmath.functions.testUtils.RationalField
+import space.kscience.kmath.functions.testUtils.iota
+import space.kscience.kmath.functions.testUtils.x
+import space.kscience.kmath.functions.testUtils.y
+import space.kscience.kmath.misc.UnstableKMathAPI
 import kotlin.test.Ignore
 import kotlin.test.Test
 import kotlin.test.assertEquals
-import space.kscience.kmath.functions.testUtils.x
-import space.kscience.kmath.functions.testUtils.y
-import space.kscience.kmath.functions.testUtils.iota
-import space.kscience.kmath.functions.testUtils.assertEquals
 
 class LabeledPolynomialUtilTest {
     @Test
diff --git a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt
similarity index 100%
rename from kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt
rename to kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt
diff --git a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt
similarity index 100%
rename from kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt
rename to kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialTest.kt
diff --git a/kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt
similarity index 100%
rename from kmath-polynomialX/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt
rename to kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt
diff --git a/settings.gradle.kts b/settings.gradle.kts
index 543d08001..bdd83d04e 100644
--- a/settings.gradle.kts
+++ b/settings.gradle.kts
@@ -27,8 +27,8 @@ include(
     ":kmath-coroutines",
     ":kmath-functions",
     ":test-utils-functions",
-    ":kmath-polynomialX",
-    ":test-utils-polynomialX",
+    ":kmath-polynomial",
+    ":test-utils-polynomial",
     ":kmath-histograms",
     ":kmath-commons",
     ":kmath-viktor",
diff --git a/test-utils-polynomialX/build.gradle.kts b/test-utils-polynomial/build.gradle.kts
similarity index 63%
rename from test-utils-polynomialX/build.gradle.kts
rename to test-utils-polynomial/build.gradle.kts
index f20e1b8bb..e10e1f2b1 100644
--- a/test-utils-polynomialX/build.gradle.kts
+++ b/test-utils-polynomial/build.gradle.kts
@@ -7,9 +7,7 @@ kotlin.sourceSets {
     commonMain {
         dependencies {
             api(projects.kmathCore)
-            api(projects.kmathFunctions)
-            api(projects.testUtilsFunctions)
-            api(projects.kmathPolynomialX)
+            api(projects.kmathPolynomial)
             api(kotlin("test"))
         }
     }
diff --git a/test-utils-polynomialX/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt b/test-utils-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt
similarity index 100%
rename from test-utils-polynomialX/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt
rename to test-utils-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/BufferUtils.kt
diff --git a/test-utils-polynomialX/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt b/test-utils-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt
similarity index 100%
rename from test-utils-polynomialX/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt
rename to test-utils-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/assertion.kt
diff --git a/test-utils-polynomialX/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/misc.kt b/test-utils-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/misc.kt
similarity index 100%
rename from test-utils-polynomialX/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/misc.kt
rename to test-utils-polynomial/src/commonMain/kotlin/space/kscience/kmath/functions/testUtils/misc.kt