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

@@ -447,7 +447,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
             callsInPlace(block, InvocationKind.EXACTLY_ONCE)
         }
         block()
-        while (elementAt(lastIndex).isZero()) removeAt(lastIndex)
+        while (isNotEmpty() && elementAt(lastIndex).isZero()) removeAt(lastIndex)
         return this
     }
     internal inline fun List<C>.applyAndRemoveZeros(block: MutableList<C>.() -> Unit) : List<C> =
@@ -456,7 +456,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
     internal inline fun MutableCoefficients(size: Int, init: (index: Int) -> C): MutableList<C> {
         val list = ArrayList<C>(size)
         repeat(size) { index -> list.add(init(index)) }
-        with(list) { while (elementAt(lastIndex).isZero()) removeAt(lastIndex) }
+        with(list) { while (isNotEmpty() && elementAt(lastIndex).isZero()) removeAt(lastIndex) }
         return list
     }
     @Suppress("FunctionName")
@@ -466,7 +466,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
         contract { callsInPlace(builderAction, InvocationKind.EXACTLY_ONCE) }
         return buildList {
             builderAction()
-            while (elementAt(lastIndex).isZero()) removeAt(lastIndex)
+            while (isNotEmpty() && elementAt(lastIndex).isZero()) removeAt(lastIndex)
         }
     }
     @OptIn(ExperimentalTypeInference::class)
@@ -474,7 +474,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
         contract { callsInPlace(builderAction, InvocationKind.EXACTLY_ONCE) }
         return buildList(capacity) {
             builderAction()
-            while (elementAt(lastIndex).isZero()) removeAt(lastIndex)
+            while (isNotEmpty() && elementAt(lastIndex).isZero()) removeAt(lastIndex)
         }
     }
 }

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/PolynomialTest.kt

@@ -5,11 +5,78 @@
 
 package space.kscience.kmath.functions
 
+import space.kscience.kmath.operations.BigInt
 import space.kscience.kmath.operations.algebra
+import space.kscience.kmath.operations.toBigInt
+import space.kscience.kmath.test.misc.Rational
+import space.kscience.kmath.test.misc.RationalField
+import space.kscience.kmath.test.misc.gcd
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
 class PolynomialTest {
+    @Test
+    fun test_Polynomial_Polynomial_plus() {
+        RationalField.polynomial {
+            // (5/9 - 8/9 x - 8/7 x^2) + (-5/7 + 5/1 x + 5/8 x^2) ?= -10/63 + 37/9 x - 29/56 x^2
+            assertEquals(
+                Polynomial(Rational(-10, 63), Rational(37, 9), Rational(-29, 56)),
+                Polynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) +
+                        Polynomial(Rational(-5, 7), Rational(5, 1), Rational(5, 8)),
+                "test 1"
+            )
+            // (-2/9 - 8/3 x) + (0 + 9/4 x + 2/4 x^2) ?= -2/9 - 5/12 x + 2/4 x^2
+            assertEquals(
+                Polynomial(Rational(-2, 9), Rational(-5, 12), Rational(2, 4)),
+                Polynomial(Rational(-2, 9), Rational(-8, 3)) +
+                        Polynomial(Rational(0), Rational(9, 4), Rational(2, 4)),
+                "test 2"
+            )
+            // (-4/7 - 2/6 x + 0 x^2 + 0 x^3) + (-6/3 - 7/2 x + 2/3 x^2) ?= -18/7 - 23/6 x + 2/3 x^2
+            assertEquals(
+                Polynomial(Rational(-18, 7), Rational(-23, 6), Rational(2, 3)),
+                Polynomial(Rational(-4, 7), Rational(-2, 6), Rational(0), Rational(0)) +
+                        Polynomial(Rational(-6, 3), Rational(-7, 2), Rational(2, 3)),
+                "test 3"
+            )
+            // (-2/4 - 6/9 x - 4/9 x^2) + (2/4 + 6/9 x + 4/9 x^2) ?= 0
+            assertEquals(
+                Polynomial(),
+                Polynomial(Rational(-2, 4), Rational(-6, 9), Rational(-4, 9)) +
+                        Polynomial(Rational(2, 4), Rational(6, 9), Rational(4, 9)),
+                "test 4"
+            )
+        }
+    }
+//    @Test
+//    fun test_Polynomial_Polynomial_minus() {
+//        RationalField.polynomial {
+//            assertEquals(
+//                Polynomial(Rational(1, 2), Rational(3, 5), Rational(-2)) +
+//                        Polynomial(Rational(3), Rational(7, 8), Rational(1, 9)),
+//                Polynomial(Rational(7, 2), Rational(59, 40), Rational(-17, 9)),
+//                "test 1"
+//            )
+//            assertEquals(
+//                Polynomial(Rational(1, 2), Rational(3, 5)) +
+//                        Polynomial(Rational(3), Rational(7, 8), Rational(1, 9)),
+//                Polynomial(Rational(7, 2), Rational(59, 40), Rational(1, 9)),
+//                "test 2"
+//            )
+//            assertEquals(
+//                Polynomial(Rational(1, 2), Rational(3, 5), Rational(0), Rational(0)) +
+//                        Polynomial(Rational(3), Rational(7, 8), Rational(1, 9)),
+//                Polynomial(Rational(7, 2), Rational(59, 40), Rational(1, 9)),
+//                "test 3"
+//            )
+//            assertEquals(
+//                Polynomial(Rational(1, 2), Rational(-3, 5), Rational(7, 3)) +
+//                        Polynomial(Rational(3), Rational(3, 5), Rational(-7, 3)),
+//                Polynomial(Rational(7, 2)),
+//                "test 4"
+//            )
+//        }
+//    }
     @Test
     fun simple_polynomial_test() {
         val polynomial : Polynomial<Double>

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/Rational.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.
+ */
+
+package space.kscience.kmath.test.misc
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.BigInt
+import space.kscience.kmath.operations.Field
+import space.kscience.kmath.operations.NumbersAddOps
+import space.kscience.kmath.operations.toBigInt
+import space.kscience.kmath.operations.BigInt.Companion.ZERO as I0
+import space.kscience.kmath.operations.BigInt.Companion.ONE as I1
+
+/**
+ * The class represents rational numbers.
+ *
+ * Instances contain [numerator] and [denominator] represented as [Long].
+ *
+ * Also [numerator] and [denominator] are coprime and [denominator] is positive.
+ *
+ * @author [Gleb Minaev](https://github.com/lounres)
+ */
+public class Rational: Comparable<Rational> {
+    public companion object {
+        /**
+         * Constant containing the zero (the additive identity) of the [Rational] field.
+         */
+        public val ZERO: Rational = Rational(I0)
+        /**
+         * Constant containing the one (the multiplicative identity) of the [Rational] field.
+         */
+        public val ONE: Rational = Rational(I1)
+    }
+
+    /**
+     * Numerator of the fraction. It's stored as non-negative coprime with [denominator] integer.
+     */
+    public val numerator: BigInt
+    /**
+     * Denominator of the fraction. It's stored as non-zero coprime with [numerator] integer.
+     */
+    public val denominator: BigInt
+
+    /**
+     * If [toCheckInput] is `true` before assigning values to [Rational.numerator] and [Rational.denominator] makes them coprime and makes
+     * denominator positive. Otherwise, just assigns the values.
+     *
+     * @throws ArithmeticException If denominator is zero.
+     */
+    internal constructor(numerator: BigInt, denominator: BigInt, toCheckInput: Boolean = true) {
+        if (toCheckInput) {
+            if (denominator == I0) throw ArithmeticException("/ by zero")
+
+            val greatestCommonDivider = gcd(numerator, denominator).let { if (denominator < I0) -it else it }
+
+            this.numerator = numerator / greatestCommonDivider
+            this.denominator = denominator / greatestCommonDivider
+        } else {
+            this.numerator = numerator
+            this.denominator = denominator
+        }
+    }
+
+    /**
+     * Before assigning values to [Rational.numerator] and [Rational.denominator] makes them coprime and makes
+     * denominator positive.
+     *
+     * @throws ArithmeticException If denominator is zero.
+     */
+    public constructor(numerator: BigInt, denominator: BigInt) : this(numerator, denominator, true)
+    public constructor(numerator: Int, denominator: BigInt) : this(numerator.toBigInt(), denominator, true)
+    public constructor(numerator: Long, denominator: BigInt) : this(numerator.toBigInt(), denominator, true)
+    public constructor(numerator: BigInt, denominator: Int) : this(numerator, denominator.toBigInt(), true)
+    public constructor(numerator: BigInt, denominator: Long) : this(numerator, denominator.toBigInt(), true)
+    public constructor(numerator: Int, denominator: Int) : this(numerator.toBigInt(), denominator.toBigInt(), true)
+    public constructor(numerator: Int, denominator: Long) : this(numerator.toBigInt(), denominator.toBigInt(), true)
+    public constructor(numerator: Long, denominator: Int) : this(numerator.toBigInt(), denominator.toBigInt(), true)
+    public constructor(numerator: Long, denominator: Long) : this(numerator.toBigInt(), denominator.toBigInt(), true)
+    public constructor(numerator: BigInt) : this(numerator, I1, false)
+    public constructor(numerator: Int) : this(numerator.toBigInt(), I1, false)
+    public constructor(numerator: Long) : this(numerator.toBigInt(), I1, false)
+
+    /**
+     * Returns the same instant.
+     */
+    public operator fun unaryPlus(): Rational = this
+
+    /**
+     * Returns negation of the instant of [Rational] field.
+     */
+    public operator fun unaryMinus(): Rational = Rational(-this.numerator, this.denominator)
+
+    /**
+     * Returns sum of the instants of [Rational] field.
+     */
+    public operator fun plus(other: Rational): Rational =
+        Rational(
+            numerator * other.denominator + denominator * other.numerator,
+            denominator * other.denominator
+        )
+
+    /**
+     * Returns sum of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun plus(other: BigInt): Rational =
+        Rational(
+            numerator + denominator * other,
+            denominator
+        )
+
+    /**
+     * Returns sum of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun plus(other: Int): Rational =
+        Rational(
+            numerator + denominator * other.toBigInt(),
+            denominator
+        )
+
+    /**
+     * Returns sum of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun plus(other: Long): Rational =
+        Rational(
+            numerator + denominator * other.toBigInt(),
+            denominator
+        )
+
+    /**
+     * Returns difference of the instants of [Rational] field.
+     */
+    public operator fun minus(other: Rational): Rational =
+        Rational(
+            numerator * other.denominator - denominator * other.numerator,
+            denominator * other.denominator
+        )
+
+    /**
+     * Returns difference of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun minus(other: BigInt): Rational =
+        Rational(
+            numerator - denominator * other,
+            denominator
+        )
+
+    /**
+     * Returns difference of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun minus(other: Int): Rational =
+        Rational(
+            numerator - denominator * other.toBigInt(),
+            denominator
+        )
+
+    /**
+     * Returns difference of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun minus(other: Long): Rational =
+        Rational(
+            numerator - denominator * other.toBigInt(),
+            denominator
+        )
+
+    /**
+     * Returns product of the instants of [Rational] field.
+     */
+    public operator fun times(other: Rational): Rational =
+        Rational(
+            numerator * other.numerator,
+            denominator * other.denominator
+        )
+
+    /**
+     * Returns product of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun times(other: BigInt): Rational =
+        Rational(
+            numerator * other,
+            denominator
+        )
+
+    /**
+     * Returns product of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun times(other: Int): Rational =
+        Rational(
+            numerator * other.toBigInt(),
+            denominator
+        )
+
+    /**
+     * Returns product of the instants of [Rational] field. [other] is represented as [Rational].
+     */
+    public operator fun times(other: Long): Rational =
+        Rational(
+            numerator * other.toBigInt(),
+            denominator
+        )
+
+    /**
+     * Returns quotient of the instants of [Rational] field.
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun div(other: Rational): Rational =
+        Rational(
+            numerator * other.denominator,
+            denominator * other.numerator
+        )
+
+    /**
+     * Returns quotient of the instants of [Rational] field. [other] is represented as [Rational].
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun div(other: BigInt): Rational =
+        Rational(
+            numerator,
+            denominator * other
+        )
+
+    /**
+     * Returns quotient of the instants of [Rational] field. [other] is represented as [Rational].
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun div(other: Int): Rational =
+        Rational(
+            numerator,
+            denominator * other.toBigInt()
+        )
+
+    /**
+     * Returns quotient of the instants of [Rational] field. [other] is represented as [Rational].
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun div(other: Long): Rational =
+        Rational(
+            numerator,
+            denominator * other.toBigInt()
+        )
+
+    /**
+     * Returns reminder from integral division.
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun rem(other: Rational): Rational =
+        Rational(
+            (numerator * other.denominator) % (denominator * other.numerator),
+            denominator * other.denominator
+        )
+
+    /**
+     * Returns reminder from integral division.
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun rem(other: BigInt): Rational =
+        Rational(
+            numerator % denominator * other,
+            denominator * other
+        )
+
+    /**
+     * Returns reminder from integral division.
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun rem(other: Int): Rational =
+        Rational(
+            numerator % denominator * other.toBigInt(),
+            denominator * other.toBigInt()
+        )
+
+    /**
+     * Returns reminder from integral division.
+     *
+     * @throws ArithmeticException if [other] is the zero of the field it can't be a divisor.
+     */
+    public operator fun rem(other: Long): Rational =
+        Rational(
+            numerator % denominator * other.toBigInt(),
+            denominator * other.toBigInt()
+        )
+
+    /**
+     * Checks equality of the instance to [other].
+     *
+     * [BigInt], [Int] and [Long] values are also checked as Rational ones.
+     */
+    override fun equals(other: Any?): Boolean =
+        when (other) {
+            is Rational -> numerator == other.numerator && denominator == other.denominator
+            is BigInt -> numerator == other && denominator == I1
+            is Int -> numerator == other && denominator == I1
+            is Long -> numerator == other && denominator == I1
+            else -> false
+        }
+
+    /**
+     * Compares the instance to [other] as [Comparable.compareTo].
+     *
+     * @see Comparable.compareTo
+     */
+    override operator fun compareTo(other: Rational): Int = (numerator * other.denominator).compareTo(other.numerator * denominator)
+
+    /**
+     * Compares the instance to [other] as [Comparable.compareTo].
+     *
+     * [Integer] values are also checked as Rational ones.
+     *
+     * @see Comparable.compareTo
+     */
+    public operator fun compareTo(other: BigInt): Int = (numerator).compareTo(denominator * other)
+
+    /**
+     * Compares the instance to [other] as [Comparable.compareTo].
+     *
+     * [Int] values are also checked as Rational ones.
+     *
+     * @see Comparable.compareTo
+     */
+    public operator fun compareTo(other: Int): Int = (numerator).compareTo(denominator * other.toBigInt())
+
+    /**
+     * Compares the instance to [other] as [Comparable.compareTo].
+     *
+     * [Long] values are also checked as Rational ones.
+     *
+     * @see Comparable.compareTo
+     */
+    public operator fun compareTo(other: Long): Int = (numerator).compareTo(denominator * other.toBigInt())
+
+    public override fun hashCode(): Int = 31 * numerator.hashCode() + denominator.hashCode()
+
+//    /** Creates a range from this value to the specified [other] value. */
+//    operator fun rangeTo(other: JBInt) = ClosedRationalRange(this, other.toRational())
+//    /** Creates a range from this value to the specified [other] value. */
+//    operator fun rangeTo(other: Rational) = ClosedRationalRange(this, other)
+//    /** Creates a range from this value to the specified [other] value. */
+//    operator fun rangeTo(other: Int) = ClosedRationalRange(this, other.toRational())
+//    /** Creates a range from this value to the specified [other] value. */
+//    operator fun rangeTo(other: Long) = ClosedRationalRange(this, other.toRational())
+
+    public fun toRational(): Rational = this
+
+    public fun toBigInt(): BigInt = numerator / denominator
+
+//    public fun toInt(): Int = (numerator / denominator).toInt()
+//
+//    public fun toLong(): Long = (numerator / denominator).toLong()
+//
+//    public fun toDouble(): Double = (numerator.toDouble() / denominator.toDouble())
+//
+//    public fun toFloat(): Float = (numerator.toFloat() / denominator.toFloat())
+
+    public override fun toString(): String = if (denominator == I1) "$numerator" else "$numerator/$denominator"
+}
+
+
+/**
+ * Algebraic structure for rational numbers.
+ */
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+@OptIn(UnstableKMathAPI::class)
+public object RationalField : Field<Rational>, NumbersAddOps<Rational> {
+    override inline val zero: Rational get() = Rational.ZERO
+    override inline val one: Rational get() = Rational.ONE
+
+    override inline fun number(value: Number): Rational = Rational(value.toLong())
+
+    override inline fun add(left: Rational, right: Rational): Rational = left + right
+    override inline fun multiply(left: Rational, right: Rational): Rational = left * right
+    override inline fun divide(left: Rational, right: Rational): Rational = left / right
+    override inline fun scale(a: Rational, value: Double): Rational = a * number(value)
+
+    override inline fun Rational.unaryMinus(): Rational = -this
+    override inline fun Rational.plus(arg: Rational): Rational = this + arg
+    override inline fun Rational.minus(arg: Rational): Rational = this - arg
+    override inline fun Rational.times(arg: Rational): Rational = this * arg
+    override inline fun Rational.div(arg: Rational): Rational = this / arg
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/RationalWithMemorization.kt

@@ -0,0 +1,113 @@
+/*
+ * 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.test.misc
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.*
+
+class RationalWithMemorization private constructor(
+    val value: Rational,
+    override val memory : OperationsMemory
+): WithMemorization {
+    public companion object {
+        /**
+         * Constant containing the zero (the additive identity) of the [Rational] field.
+         */
+        public val ZERO: RationalWithMemorization = RationalWithMemorization(Rational.ZERO, object : Endpoint {})
+        /**
+         * Constant containing the one (the multiplicative identity) of the [Rational] field.
+         */
+        public val ONE: RationalWithMemorization = RationalWithMemorization(Rational.ONE, object : Endpoint {})
+    }
+    public constructor(numerator: BigInt, denominator: BigInt) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: Int, denominator: BigInt) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: Long, denominator: BigInt) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: BigInt, denominator: Int) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: BigInt, denominator: Long) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: Int, denominator: Int) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: Int, denominator: Long) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: Long, denominator: Int) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: Long, denominator: Long) : this(Rational(numerator, denominator), object : Endpoint {})
+    public constructor(numerator: BigInt) : this(Rational(numerator), object : Endpoint {})
+    public constructor(numerator: Int) : this(Rational(numerator), object : Endpoint {})
+    public constructor(numerator: Long) : this(Rational(numerator), object : Endpoint {})
+
+    public operator fun unaryPlus(): RationalWithMemorization = this
+    public operator fun unaryMinus(): RationalWithMemorization = RationalWithMemorization(
+        -value,
+        object : Negation {
+            override val negated: OperationsMemory = memory
+        }
+    )
+    public operator fun plus(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
+        value + other.value,
+        object : Sum {
+            override val augend: OperationsMemory = memory
+            override val addend: OperationsMemory = other.memory
+        }
+    )
+    public operator fun minus(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
+        value - other.value,
+        object : Difference {
+            override val minuend: OperationsMemory = memory
+            override val subtrahend: OperationsMemory = other.memory
+        }
+    )
+    public operator fun times(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
+        value * other.value,
+        object : Product {
+            override val multiplicand: OperationsMemory = memory
+            override val multiplier: OperationsMemory = other.memory
+        }
+    )
+    public operator fun div(other: RationalWithMemorization): RationalWithMemorization = RationalWithMemorization(
+        value / other.value,
+        object : Quotient {
+            override val dividend: OperationsMemory = memory
+            override val divisor: OperationsMemory = other.memory
+        }
+    )
+
+    public override fun equals(other: Any?): Boolean =
+        other is RationalWithMemorization && value == other.value
+
+    public override fun hashCode(): Int = value.hashCode()
+
+    public override fun toString(): String = value.toString()
+}
+
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+public object RationalWithMemorizationRing : Ring<RationalWithMemorization> {
+    override inline val zero: RationalWithMemorization get() = RationalWithMemorization.ZERO
+    override inline val one: RationalWithMemorization get() = RationalWithMemorization.ONE
+
+    override inline fun add(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left + right
+    override inline fun multiply(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left * right
+
+    override inline fun RationalWithMemorization.unaryMinus(): RationalWithMemorization = -this
+    override inline fun RationalWithMemorization.plus(arg: RationalWithMemorization): RationalWithMemorization = this + arg
+    override inline fun RationalWithMemorization.minus(arg: RationalWithMemorization): RationalWithMemorization = this - arg
+    override inline fun RationalWithMemorization.times(arg: RationalWithMemorization): RationalWithMemorization = this * arg
+}
+
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+public object RationalWithMemorizationField : Field<RationalWithMemorization> {
+    override inline val zero: RationalWithMemorization get() = RationalWithMemorization.ZERO
+    override inline val one: RationalWithMemorization get() = RationalWithMemorization.ONE
+
+    override inline fun number(value: Number): RationalWithMemorization = RationalWithMemorization(value.toLong())
+
+    override inline fun add(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left + right
+    override inline fun multiply(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left * right
+    override inline fun divide(left: RationalWithMemorization, right: RationalWithMemorization): RationalWithMemorization = left / right
+    override inline fun scale(a: RationalWithMemorization, value: Double): RationalWithMemorization = a * number(value)
+
+    override inline fun RationalWithMemorization.unaryMinus(): RationalWithMemorization = -this
+    override inline fun RationalWithMemorization.plus(arg: RationalWithMemorization): RationalWithMemorization = this + arg
+    override inline fun RationalWithMemorization.minus(arg: RationalWithMemorization): RationalWithMemorization = this - arg
+    override inline fun RationalWithMemorization.times(arg: RationalWithMemorization): RationalWithMemorization = this * arg
+    override inline fun RationalWithMemorization.div(arg: RationalWithMemorization): RationalWithMemorization = this / arg
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/memorization.kt

@@ -0,0 +1,51 @@
+/*
+ * 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.test.misc
+
+sealed interface OperationsMemory
+
+interface Endpoint: OperationsMemory
+
+interface Negation: OperationsMemory {
+    val negated: OperationsMemory
+}
+
+interface Sum: OperationsMemory {
+    val augend: OperationsMemory
+    val addend: OperationsMemory
+}
+
+interface Difference: OperationsMemory {
+    val minuend: OperationsMemory
+    val subtrahend: OperationsMemory
+}
+
+interface Product: OperationsMemory {
+    val multiplicand: OperationsMemory
+    val multiplier: OperationsMemory
+}
+
+interface Quotient: OperationsMemory {
+    val dividend: OperationsMemory
+    val divisor: OperationsMemory
+}
+
+
+fun equalMemories(one: OperationsMemory, other: OperationsMemory) : Boolean =
+    when(one) {
+        is Negation -> other is Negation && equalMemories(one.negated, other.negated)
+        is Sum -> other is Sum && equalMemories(one.augend, other.augend) && equalMemories(one.addend, other.addend)
+        is Difference -> other is Difference && equalMemories(one.minuend, other.minuend) && equalMemories(one.subtrahend, other.subtrahend)
+        is Product -> other is Product && equalMemories(one.multiplicand, other.multiplicand) && equalMemories(one.multiplier, other.multiplier)
+        is Quotient -> other is Quotient && equalMemories(one.dividend, other.dividend) && equalMemories(one.divisor, other.divisor)
+        is Endpoint -> one === other
+    }
+
+interface WithMemorization {
+    val memory: OperationsMemory
+}
+
+fun equalMemories(one: WithMemorization, other: WithMemorization) : Boolean = equalMemories(one.memory, other.memory)

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/misc.kt

@@ -0,0 +1,25 @@
+/*
+ * 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.test.misc
+
+import space.kscience.kmath.operations.*
+import space.kscience.kmath.operations.BigInt.Companion.ZERO as I0
+
+// TODO: Move to corresponding module "kmath-number-theory"
+
+/**
+ * Computes [Greatest Common Divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of [a] and [b].
+ *
+ * It's computed by [Euclidean algorithm](https://en.wikipedia.org/wiki/Greatest_common_divisor#Euclidean_algorithm).
+ * Hence, its time complexity is $$O(\log(a+b))$$ (see [Wolfram MathWorld](https://mathworld.wolfram.com/EuclideanAlgorithm.html)).
+ */
+public tailrec fun gcd(a: BigInt, b: BigInt): BigInt = if (a == I0) abs(b) else gcd(b % a, a)
+
+/**
+ * Computes [Greatest Common Divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of the [values].
+ */
+public fun gcd(vararg values: BigInt): BigInt = values.reduce(::gcd)
+public fun gcd(values: Iterable<BigInt>): BigInt = values.reduce(::gcd)