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

@@ -220,7 +220,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
     public override operator fun C.minus(other: Polynomial<C>): Polynomial<C> =
         if (this.isZero()) other
         else with(other.coefficients) {
-            if (isEmpty()) Polynomial(listOf(-this@minus))
+            if (isEmpty()) Polynomial(listOf(this@minus))
             else Polynomial(
                 toMutableList()
                     .apply {

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

@@ -6,11 +6,11 @@
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.operations.algebra
-import space.kscience.kmath.test.misc.Rational
-import space.kscience.kmath.test.misc.RationalField
+import space.kscience.kmath.test.misc.*
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
+
 class PolynomialTest {
     @Test
     fun test_Polynomial_Int_plus() {
@@ -93,6 +93,116 @@ class PolynomialTest {
         }
     }
     @Test
+    fun test_Polynomial_Int_times() {
+        IntModuloRing(35).polynomial {
+            assertEquals(
+                Polynomial(34, 2, 1, 20, 2),
+                Polynomial(22, 26, 13, 15, 26) * 27,
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(),
+                Polynomial(7, 0, 49, 21, 14) * 15,
+                "test 2"
+            )
+        }
+    }
+    @Test
+    fun test_Int_Polynomial_plus() {
+        RationalField.polynomial {
+            assertEquals(
+                Polynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
+                -3 + Polynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(Rational(0), Rational(0), Rational(0), Rational(0)),
+                2 + Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 2"
+            )
+            assertEquals(
+                Polynomial(),
+                2 + Polynomial(Rational(-2)),
+                "test 3"
+            )
+            assertEquals(
+                Polynomial(),
+                0 + Polynomial(),
+                "test 4"
+            )
+            assertEquals(
+                Polynomial(Rational(-1), Rational(0), Rational(0), Rational(0)),
+                1 + Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 5"
+            )
+            assertEquals(
+                Polynomial(Rational(-1)),
+                1 + Polynomial(Rational(-2)),
+                "test 6"
+            )
+            assertEquals(
+                Polynomial(Rational(2)),
+                2 + Polynomial(),
+                "test 7"
+            )
+        }
+    }
+    @Test
+    fun test_Int_Polynomial_minus() {
+        RationalField.polynomial {
+            assertEquals(
+                Polynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
+                3 - Polynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(Rational(0), Rational(0), Rational(0), Rational(0)),
+                -2 - Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 2"
+            )
+            assertEquals(
+                Polynomial(),
+                -2 - Polynomial(Rational(-2)),
+                "test 3"
+            )
+            assertEquals(
+                Polynomial(),
+                0 - Polynomial(),
+                "test 4"
+            )
+            assertEquals(
+                Polynomial(Rational(1), Rational(0), Rational(0), Rational(0)),
+                -1 - Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 5"
+            )
+            assertEquals(
+                Polynomial(Rational(1)),
+                -1 - Polynomial(Rational(-2)),
+                "test 6"
+            )
+            assertEquals(
+                Polynomial(Rational(-2)),
+                -2 - Polynomial(),
+                "test 7"
+            )
+        }
+    }
+    @Test
+    fun test_Int_Polynomial_times() {
+        IntModuloRing(35).polynomial {
+            assertEquals(
+                Polynomial(34, 2, 1, 20, 2),
+                27 * Polynomial(22, 26, 13, 15, 26),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(),
+                15 * Polynomial(7, 0, 49, 21, 14),
+                "test 2"
+            )
+        }
+    }
+    @Test
     fun test_Polynomial_Constant_plus() {
         RationalField.polynomial {
             assertEquals(
@@ -173,6 +283,116 @@ class PolynomialTest {
         }
     }
     @Test
+    fun test_Polynomial_Constant_times() {
+        IntModuloRing(35).polynomial {
+            assertEquals(
+                Polynomial(34, 2, 1, 20, 2),
+                Polynomial(22, 26, 13, 15, 26) * number(27),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(),
+                Polynomial(7, 0, 49, 21, 14) * number(15),
+                "test 2"
+            )
+        }
+    }
+    @Test
+    fun test_Constant_Polynomial_plus() {
+        RationalField.polynomial {
+            assertEquals(
+                Polynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
+                Rational(-3) + Polynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(Rational(0), Rational(0), Rational(0), Rational(0)),
+                Rational(2) + Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 2"
+            )
+            assertEquals(
+                Polynomial(),
+                Rational(2) + Polynomial(Rational(-2)),
+                "test 3"
+            )
+            assertEquals(
+                Polynomial(),
+                Rational(0) + Polynomial(),
+                "test 4"
+            )
+            assertEquals(
+                Polynomial(Rational(-1), Rational(0), Rational(0), Rational(0)),
+                Rational(1) + Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 5"
+            )
+            assertEquals(
+                Polynomial(Rational(-1)),
+                Rational(1) + Polynomial(Rational(-2)),
+                "test 6"
+            )
+            assertEquals(
+                Polynomial(Rational(2)),
+                Rational(2) + Polynomial(),
+                "test 7"
+            )
+        }
+    }
+    @Test
+    fun test_Constant_Polynomial_minus() {
+        RationalField.polynomial {
+            assertEquals(
+                Polynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
+                Rational(3) - Polynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(Rational(0), Rational(0), Rational(0), Rational(0)),
+                Rational(-2) - Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 2"
+            )
+            assertEquals(
+                Polynomial(),
+                Rational(-2) - Polynomial(Rational(-2)),
+                "test 3"
+            )
+            assertEquals(
+                Polynomial(),
+                Rational(0) - Polynomial(),
+                "test 4"
+            )
+            assertEquals(
+                Polynomial(Rational(1), Rational(0), Rational(0), Rational(0)),
+                Rational(-1) - Polynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
+                "test 5"
+            )
+            assertEquals(
+                Polynomial(Rational(1)),
+                Rational(-1) - Polynomial(Rational(-2)),
+                "test 6"
+            )
+            assertEquals(
+                Polynomial(Rational(-2)),
+                Rational(-2) - Polynomial(),
+                "test 7"
+            )
+        }
+    }
+    @Test
+    fun test_Constant_Polynomial_times() {
+        IntModuloRing(35).polynomial {
+            assertEquals(
+                Polynomial(34, 2, 1, 20, 2),
+                27 * Polynomial(22, 26, 13, 15, 26),
+                "test 1"
+            )
+            assertEquals(
+                Polynomial(),
+                15 * Polynomial(7, 0, 49, 21, 14),
+                "test 2"
+            )
+        }
+    }
+    @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

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

@@ -0,0 +1,142 @@
+/*
+ * 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.functions.Polynomial
+import space.kscience.kmath.functions.PolynomialSpace
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.Ring
+
+
+class IntModulo {
+    val residue: Int
+    val modulus: Int
+
+    @PublishedApi
+    internal constructor(residue: Int, modulus: Int, toCheckInput: Boolean = true) {
+        if (toCheckInput) {
+            require(modulus != 0) { "modulus can not be zero" }
+            this.modulus = if (modulus < 0) -modulus else modulus
+            this.residue = residue.mod(modulus)
+        } else {
+            this.residue = residue
+            this.modulus = modulus
+        }
+    }
+
+    constructor(residue: Int, modulus: Int) : this(residue, modulus, true)
+
+    operator fun unaryPlus(): IntModulo = this
+    operator fun unaryMinus(): IntModulo =
+        IntModulo(
+            if (residue == 0) 0 else modulus - residue,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun plus(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not add two residue different modulo" }
+        return IntModulo(
+            (residue + other.residue) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun plus(other: Int): IntModulo =
+        IntModulo(
+            (residue + other) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun minus(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not subtract two residue different modulo" }
+        return IntModulo(
+            (residue - other.residue) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun minus(other: Int): IntModulo =
+        IntModulo(
+            (residue - other) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun times(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not multiply two residue different modulo" }
+        return IntModulo(
+            (residue * other.residue) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun times(other: Int): IntModulo =
+        IntModulo(
+            (residue * other) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun div(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not divide two residue different modulo" }
+        val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other.residue, modulus)
+        require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
+        return IntModulo(
+            (residue * reciprocalCandidate) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun div(other: Int): IntModulo {
+        val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other, modulus)
+        require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
+        return IntModulo(
+            (residue * reciprocalCandidate) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    override fun equals(other: Any?): Boolean =
+        when (other) {
+            is IntModulo -> residue == other.residue && modulus == other.modulus
+            else -> false
+        }
+
+    override fun hashCode(): Int = residue.hashCode()
+
+    override fun toString(): String = "$residue mod $modulus"
+}
+
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+@OptIn(UnstableKMathAPI::class)
+class IntModuloRing : Ring<IntModulo> {
+
+    val modulus: Int
+
+    constructor(modulus: Int) {
+        require(modulus != 0) { "modulus can not be zero" }
+        this.modulus = if (modulus < 0) -modulus else modulus
+    }
+
+    override inline val zero: IntModulo get() = IntModulo(0, modulus, toCheckInput = false)
+    override inline val one: IntModulo get() = IntModulo(0, modulus, toCheckInput = false)
+
+    fun number(arg: Int) = IntModulo(arg, modulus, toCheckInput = false)
+
+    override inline fun add(left: IntModulo, right: IntModulo): IntModulo = left + right
+    override inline fun multiply(left: IntModulo, right: IntModulo): IntModulo = left * right
+
+    override inline fun IntModulo.unaryMinus(): IntModulo = -this
+    override inline fun IntModulo.plus(arg: IntModulo): IntModulo = this + arg
+    override inline fun IntModulo.minus(arg: IntModulo): IntModulo = this - arg
+    override inline fun IntModulo.times(arg: IntModulo): IntModulo = this * arg
+    inline fun IntModulo.div(arg: IntModulo): IntModulo = this / arg
+}
+
+fun PolynomialSpace<IntModulo, IntModuloRing>.number(arg: Int) = IntModulo(arg, ring.modulus, toCheckInput = false)
+
+fun PolynomialSpace<IntModulo, IntModuloRing>.Polynomial(vararg coefs: Int): Polynomial<IntModulo> =
+    Polynomial(coefs.map { IntModulo(it, ring.modulus) })
+fun IntModuloRing.Polynomial(vararg coefs: Int): Polynomial<IntModulo> =
+    Polynomial(coefs.map { IntModulo(it, modulus) })

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

@@ -114,10 +114,6 @@ class Rational {
     override fun toString(): String = if (denominator == 1L) "$numerator" else "$numerator/$denominator"
 }
 
-
-/**
- * Algebraic structure for rational numbers.
- */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 @OptIn(UnstableKMathAPI::class)
 object RationalField : Field<Rational>, NumbersAddOps<Rational> {

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

@@ -5,8 +5,27 @@
 
 package space.kscience.kmath.test.misc
 
-import kotlin.math.abs
-
 // TODO: Move to corresponding module "kmath-number-theory"
 
+import kotlin.math.abs
+
+
+data class BezoutIdentityWithGCD<T>(val first: T, val second: T, val gcd: T)
+
 tailrec fun gcd(a: Long, b: Long): Long = if (a == 0L) abs(b) else gcd(b % a, a)
+
+fun bezoutIdentityWithGCD(a: Int, b: Int): BezoutIdentityWithGCD<Int> =
+    when {
+        a < 0 && b < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, -second, gcd) }
+        a < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, second, gcd) }
+        b < 0 -> with(bezoutIdentityWithGCDInternalLogic(a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(first, -second, gcd) }
+        else -> bezoutIdentityWithGCDInternalLogic(a, b, 1, 0, 0, 1)
+    }
+
+internal tailrec fun bezoutIdentityWithGCDInternalLogic(a: Int, b: Int, m1: Int, m2: Int, m3: Int, m4: Int): BezoutIdentityWithGCD<Int> =
+    if (b == 0) BezoutIdentityWithGCD(m1, m3, a)
+    else {
+        val quotient = a / b
+        val reminder = a % b
+        bezoutIdentityWithGCDInternalLogic(b, reminder, m2, m1 - quotient * m2, m4, m3 - quotient * m4)
+    }