Fix scalar multiplication in BigInt, implement testers for fields, rings and spaces and apply them to ComplexFieldTest, BigIntAlgebraTest and RealFieldTest

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/BigInt.kt

@@ -22,8 +22,9 @@ object BigIntField : Field<BigInt> {
     override val one: BigInt = BigInt.ONE
 
     override fun add(a: BigInt, b: BigInt): BigInt = a.plus(b)
+    override fun number(value: Number): BigInt = value.toLong().toBigInt()
 
-    override fun multiply(a: BigInt, k: Number): BigInt = a.times(k.toLong())
+    override fun multiply(a: BigInt, k: Number): BigInt = a.times(number(k))
 
     override fun multiply(a: BigInt, b: BigInt): BigInt = a.times(b)
 

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntAlgebraTest.kt

@@ -1,9 +1,13 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.operations.internal.RingVerifier
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
-class BigIntAlgebraTest {
+internal class BigIntAlgebraTest {
+    @Test
+    fun verify() = BigIntField { RingVerifier(this, +"42", +"10", +"-12", 10).verify() }
+
     @Test
     fun testKBigIntegerRingSum() {
         val res = BigIntField {

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt

@@ -1,5 +1,6 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.operations.internal.FieldVerifier
 import kotlin.math.PI
 import kotlin.math.abs
 import kotlin.test.Test
@@ -7,6 +8,9 @@ import kotlin.test.assertEquals
 import kotlin.test.assertTrue
 
 internal class ComplexFieldTest {
+    @Test
+    fun verify() = ComplexField { FieldVerifier(this, 42.0 * i, 66.0 + 28 * i, 2.0 + 0 * i, 5).verify() }
+
     @Test
     fun testAddition() {
         assertEquals(Complex(42, 42), ComplexField { Complex(16, 16) + Complex(26, 26) })

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/RealFieldTest.kt

@@ -1,14 +1,16 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.operations.internal.FieldVerifier
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
-class RealFieldTest {
+internal class RealFieldTest {
+    @Test
+    fun verify() = FieldVerifier(RealField, 42.0, 66.0, 2.0, 5).verify()
+
     @Test
     fun testSqrt() {
-        val sqrt = RealField {
-            sqrt(25 * one)
-        }
+        val sqrt = RealField { sqrt(25 * one) }
         assertEquals(5.0, sqrt)
     }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/internal/AlgebraicVerifier.kt

@@ -0,0 +1,9 @@
+package scientifik.kmath.operations.internal
+
+import scientifik.kmath.operations.Algebra
+
+internal interface AlgebraicVerifier<T, out A> where A : Algebra<T> {
+    val algebra: A
+
+    fun verify()
+}

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/internal/FieldVerifier.kt

@@ -0,0 +1,24 @@
+package scientifik.kmath.operations.internal
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.invoke
+import kotlin.test.assertEquals
+import kotlin.test.assertNotEquals
+
+internal class FieldVerifier<T>(override val algebra: Field<T>, a: T, b: T, c: T, x: Number) :
+    RingVerifier<T>(algebra, a, b, c, x) {
+
+    override fun verify() {
+        super.verify()
+
+        algebra {
+            assertNotEquals(a / b, b / a, "Division in $algebra is not anti-commutative.")
+            assertNotEquals((a / b) / c, a / (b / c), "Division in $algebra is associative.")
+            assertEquals((a + b) / c, (a / c) + (b / c), "Division in $algebra is not right-distributive.")
+            assertEquals(a, a / one, "$one in $algebra is not neutral division element.")
+            assertEquals(one, one / a * a, "$algebra does not provide single reciprocal element.")
+            assertEquals(zero / a, zero, "$zero in $algebra is not left neutral element for division.")
+            assertEquals(-one, a / (-a), "Division by sign reversal element in $algebra does not give ${-one}.")
+        }
+    }
+}

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/internal/RingVerifier.kt

@@ -0,0 +1,28 @@
+package scientifik.kmath.operations.internal
+
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.operations.invoke
+import kotlin.test.assertEquals
+
+internal open class RingVerifier<T>(override val algebra: Ring<T>, a: T, b: T, c: T, x: Number) :
+    SpaceVerifier<T>(algebra, a, b, c, x) {
+    override fun verify() {
+        super.verify()
+
+        algebra {
+            assertEquals(a * b, a * b, "Multiplication in $algebra is not commutative.")
+            assertEquals(a * b * c, a * (b * c), "Multiplication in $algebra is not associative.")
+            assertEquals(c * (a + b), (c * a) + (c * b), "Multiplication in $algebra is not distributive.")
+            assertEquals(a * one, one * a, "$one in $algebra is not a neutral multiplication element.")
+            assertEquals(a, one * a, "$one in $algebra is not a neutral multiplication element.")
+            assertEquals(a, a * one, "$one in $algebra is not a neutral multiplication element.")
+            assertEquals(a, one * a, "$one in $algebra is not a neutral multiplication element.")
+            assertEquals(a, a * one * one, "Multiplication by $one in $algebra is not idempotent.")
+            assertEquals(a, a * one * one * one, "Multiplication by $one in $algebra is not idempotent.")
+            assertEquals(a, a * one * one * one * one, "Multiplication by $one in $algebra is not idempotent.")
+            assertEquals(zero, a * zero, "Multiplication by $zero in $algebra doesn't give $zero.")
+            assertEquals(zero, zero * a, "Multiplication by $zero in $algebra doesn't give $zero.")
+            assertEquals(a * zero, a * zero, "Multiplication by $zero in $algebra doesn't give $zero.")
+        }
+    }
+}

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/internal/SpaceVerifier.kt

@@ -0,0 +1,33 @@
+package scientifik.kmath.operations.internal
+
+import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.invoke
+import kotlin.test.assertEquals
+import kotlin.test.assertNotEquals
+
+internal open class SpaceVerifier<T>(
+    override val algebra: Space<T>,
+    val a: T,
+    val b: T,
+    val c: T,
+    val x: Number
+) :
+    AlgebraicVerifier<T, Space<T>> {
+    override fun verify() {
+        algebra {
+            assertEquals(a + b, b + a, "Addition in $algebra is not commutative.")
+            assertEquals(a + b + c, a + (b + c), "Addition in $algebra is not associative.")
+            assertEquals(x * (a + b), x * a + x * b, "Addition in $algebra is not distributive.")
+            assertEquals((a + b) * x, a * x + b * x, "Addition in $algebra is not distributive.")
+            assertEquals(a + zero, zero + a, "$zero in $algebra is not a neutral addition element.")
+            assertEquals(a, a + zero, "$zero in $algebra is not a neutral addition element.")
+            assertEquals(a, zero + a, "$zero in $algebra is not a neutral addition element.")
+            assertEquals(a - b, -(b - a), "Subtraction in $algebra is not anti-commutative.")
+            assertNotEquals(a - b - c, a - (b - c), "Subtraction in $algebra is associative.")
+            assertEquals(x * (a - b), x * a - x * b, "Subtraction in $algebra is not distributive.")
+            assertEquals(a, a - zero, "$zero in $algebra is not a neutral addition element.")
+            assertEquals(a * x, x * a, "Multiplication by scalar in $algebra is not commutative.")
+            assertEquals(x * (a + b), (x * a) + (x * b), "Multiplication by scalar in $algebra is not distributive.")
+        }
+    }
+}