Added some test. Fixed bug in algebraicStub.kt

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

@@ -139,7 +139,7 @@ internal tailrec fun <C> Ring<C>.exponentiationBySquaring(arg: C, exponent: UInt
 internal tailrec fun <C> RingOps<C>.multiplyExponentiationBySquaring(base: C, arg: C, exponent: UInt): C =
     when {
         exponent == 0u -> base
-        exponent == 1u -> base + arg
+        exponent == 1u -> base * arg
         exponent and 1u == 0u -> multiplyExponentiationBySquaring(base, arg * arg, exponent shr 1)
         exponent and 1u == 1u -> multiplyExponentiationBySquaring(base * arg, arg * arg, exponent shr 1)
         else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")

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

@@ -0,0 +1,589 @@
+/*
+ * 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.invoke
+import space.kscience.kmath.operations.Field
+import kotlin.jvm.JvmInline
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+@JvmInline
+value class Expr(val expr: String)
+
+object ExprRing : Field<Expr> {
+    override fun Expr.unaryMinus(): Expr = Expr("-${expr}")
+    override fun add(left: Expr, right: Expr): Expr = Expr("(${left.expr} + ${right.expr})")
+    override fun multiply(left: Expr, right: Expr): Expr = Expr("(${left.expr} * ${right.expr})")
+    override val zero: Expr = Expr("0")
+    override val one: Expr = Expr("1")
+    override fun divide(left: Expr, right: Expr): Expr = Expr("(${left.expr} / ${right.expr})")
+    override fun scale(a: Expr, value: Double): Expr = Expr("(${a.expr} / $value)")
+}
+
+class AlgebraicStubTest {
+    @Test
+    fun test_addMultipliedBySquaring_for_UInt() {
+        ExprRing {
+            assertEquals(
+                "57",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 0u).expr,
+                "tried addMultipliedBySquaring(57, 179, 0u)"
+            )
+            assertEquals(
+                "(57 + 179)",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 1u).expr,
+                "tried addMultipliedBySquaring(57, 179, 1u)"
+            )
+            assertEquals(
+                "(57 + (179 + 179))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 2u).expr,
+                "tried addMultipliedBySquaring(57, 179, 2u)"
+            )
+            assertEquals(
+                "((57 + 179) + (179 + 179))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 3u).expr,
+                "tried addMultipliedBySquaring(57, 179, 3u)"
+            )
+            assertEquals(
+                "(57 + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 4u).expr,
+                "tried addMultipliedBySquaring(57, 179, 4u)"
+            )
+            assertEquals(
+                "((57 + 179) + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 5u).expr,
+                "tried addMultipliedBySquaring(57, 179, 5u)"
+            )
+            assertEquals(
+                "((57 + (179 + 179)) + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 6u).expr,
+                "tried addMultipliedBySquaring(57, 179, 6u)"
+            )
+            assertEquals(
+                "(((57 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 7u).expr,
+                "tried addMultipliedBySquaring(57, 179, 7u)"
+            )
+            assertEquals(
+                "(57 + (((179 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179))))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 8u).expr,
+                "tried addMultipliedBySquaring(57, 179, 8u)"
+            )
+        }
+    }
+    @Test
+    fun test_multiplyBySquaring_for_UInt() {
+        ExprRing {
+            assertEquals(
+                "0",
+                multiplyBySquaring(Expr("57"), 0u).expr,
+                "tried multiplyBySquaring(57, 0u)"
+            )
+            assertEquals(
+                "57",
+                multiplyBySquaring(Expr("57"), 1u).expr,
+                "tried multiplyBySquaring(57, 1u)"
+            )
+            assertEquals(
+                "(57 + 57)",
+                multiplyBySquaring(Expr("57"), 2u).expr,
+                "tried multiplyBySquaring(57, 2u)"
+            )
+            assertEquals(
+                "(57 + (57 + 57))",
+                multiplyBySquaring(Expr("57"), 3u).expr,
+                "tried multiplyBySquaring(57, 3u)"
+            )
+            assertEquals(
+                "((57 + 57) + (57 + 57))",
+                multiplyBySquaring(Expr("57"), 4u).expr,
+                "tried multiplyBySquaring(57, 4u)"
+            )
+            assertEquals(
+                "(57 + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 5u).expr,
+                "tried multiplyBySquaring(57, 5u)"
+            )
+            assertEquals(
+                "((57 + 57) + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 6u).expr,
+                "tried multiplyBySquaring(57, 6u)"
+            )
+            assertEquals(
+                "((57 + (57 + 57)) + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 7u).expr,
+                "tried multiplyBySquaring(57, 7u)"
+            )
+            assertEquals(
+                "(((57 + 57) + (57 + 57)) + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 8u).expr,
+                "tried multiplyBySquaring(57, 8u)"
+            )
+        }
+    }
+    @Test
+    fun test_addMultipliedBySquaring_for_Int() {
+        ExprRing {
+            assertEquals(
+                "57",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 0).expr,
+                "tried addMultipliedBySquaring(57, 179, 0)"
+            )
+            assertEquals(
+                "(57 + 179)",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 1).expr,
+                "tried addMultipliedBySquaring(57, 179, 1)"
+            )
+            assertEquals(
+                "(57 + -179)",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -1).expr,
+                "tried addMultipliedBySquaring(57, 179, -1)"
+            )
+            assertEquals(
+                "(57 + (179 + 179))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 2).expr,
+                "tried addMultipliedBySquaring(57, 179, 2)"
+            )
+            assertEquals(
+                "(57 + (-179 + -179))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -2).expr,
+                "tried addMultipliedBySquaring(57, 179, -2)"
+            )
+            assertEquals(
+                "((57 + 179) + (179 + 179))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 3).expr,
+                "tried addMultipliedBySquaring(57, 179, 3)"
+            )
+            assertEquals(
+                "((57 + -179) + (-179 + -179))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -3).expr,
+                "tried addMultipliedBySquaring(57, 179, -3)"
+            )
+            assertEquals(
+                "(57 + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 4).expr,
+                "tried addMultipliedBySquaring(57, 179, 4)"
+            )
+            assertEquals(
+                "(57 + ((-179 + -179) + (-179 + -179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -4).expr,
+                "tried addMultipliedBySquaring(57, 179, -4)"
+            )
+            assertEquals(
+                "((57 + 179) + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 5).expr,
+                "tried addMultipliedBySquaring(57, 179, 5)"
+            )
+            assertEquals(
+                "((57 + -179) + ((-179 + -179) + (-179 + -179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -5).expr,
+                "tried addMultipliedBySquaring(57, 179, -5)"
+            )
+            assertEquals(
+                "((57 + (179 + 179)) + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 6).expr,
+                "tried addMultipliedBySquaring(57, 179, 6)"
+            )
+            assertEquals(
+                "((57 + (-179 + -179)) + ((-179 + -179) + (-179 + -179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -6).expr,
+                "tried addMultipliedBySquaring(57, 179, -6)"
+            )
+            assertEquals(
+                "(((57 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 7).expr,
+                "tried addMultipliedBySquaring(57, 179, 7)"
+            )
+            assertEquals(
+                "(((57 + -179) + (-179 + -179)) + ((-179 + -179) + (-179 + -179)))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -7).expr,
+                "tried addMultipliedBySquaring(57, 179, -7)"
+            )
+            assertEquals(
+                "(57 + (((179 + 179) + (179 + 179)) + ((179 + 179) + (179 + 179))))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), 8).expr,
+                "tried addMultipliedBySquaring(57, 179, 8)"
+            )
+            assertEquals(
+                "(57 + (((-179 + -179) + (-179 + -179)) + ((-179 + -179) + (-179 + -179))))",
+                addMultipliedBySquaring(Expr("57"), Expr("179"), -8).expr,
+                "tried addMultipliedBySquaring(57, 179, -8)"
+            )
+        }
+    }
+    @Test
+    fun test_multiplyBySquaring_for_Int() {
+        ExprRing {
+            assertEquals(
+                "0",
+                multiplyBySquaring(Expr("57"), 0).expr,
+                "tried multiplyBySquaring(57, 0)"
+            )
+            assertEquals(
+                "57",
+                multiplyBySquaring(Expr("57"), 1).expr,
+                "tried multiplyBySquaring(57, 1)"
+            )
+            assertEquals(
+                "-57",
+                multiplyBySquaring(Expr("57"), -1).expr,
+                "tried multiplyBySquaring(57, -1)"
+            )
+            assertEquals(
+                "(57 + 57)",
+                multiplyBySquaring(Expr("57"), 2).expr,
+                "tried multiplyBySquaring(57, 2)"
+            )
+            assertEquals(
+                "(-57 + -57)",
+                multiplyBySquaring(Expr("57"), -2).expr,
+                "tried multiplyBySquaring(57, -2)"
+            )
+            assertEquals(
+                "(57 + (57 + 57))",
+                multiplyBySquaring(Expr("57"), 3).expr,
+                "tried multiplyBySquaring(57, 3)"
+            )
+            assertEquals(
+                "(-57 + (-57 + -57))",
+                multiplyBySquaring(Expr("57"), -3).expr,
+                "tried multiplyBySquaring(57, -3)"
+            )
+            assertEquals(
+                "((57 + 57) + (57 + 57))",
+                multiplyBySquaring(Expr("57"), 4).expr,
+                "tried multiplyBySquaring(57, 4)"
+            )
+            assertEquals(
+                "((-57 + -57) + (-57 + -57))",
+                multiplyBySquaring(Expr("57"), -4).expr,
+                "tried multiplyBySquaring(57, -4)"
+            )
+            assertEquals(
+                "(57 + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 5).expr,
+                "tried multiplyBySquaring(57, 5)"
+            )
+            assertEquals(
+                "(-57 + ((-57 + -57) + (-57 + -57)))",
+                multiplyBySquaring(Expr("57"), -5).expr,
+                "tried multiplyBySquaring(57, -5)"
+            )
+            assertEquals(
+                "((57 + 57) + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 6).expr,
+                "tried multiplyBySquaring(57, 6)"
+            )
+            assertEquals(
+                "((-57 + -57) + ((-57 + -57) + (-57 + -57)))",
+                multiplyBySquaring(Expr("57"), -6).expr,
+                "tried multiplyBySquaring(57, -6)"
+            )
+            assertEquals(
+                "((57 + (57 + 57)) + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 7).expr,
+                "tried multiplyBySquaring(57, 7)"
+            )
+            assertEquals(
+                "((-57 + (-57 + -57)) + ((-57 + -57) + (-57 + -57)))",
+                multiplyBySquaring(Expr("57"), -7).expr,
+                "tried multiplyBySquaring(57, -7)"
+            )
+            assertEquals(
+                "(((57 + 57) + (57 + 57)) + ((57 + 57) + (57 + 57)))",
+                multiplyBySquaring(Expr("57"), 8).expr,
+                "tried multiplyBySquaring(57, 8)"
+            )
+            assertEquals(
+                "(((-57 + -57) + (-57 + -57)) + ((-57 + -57) + (-57 + -57)))",
+                multiplyBySquaring(Expr("57"), -8).expr,
+                "tried multiplyBySquaring(57, -8)"
+            )
+        }
+    }
+    @Test
+    fun test_multiplyExponentiationBySquaring_for_UInt() {
+        ExprRing {
+            assertEquals(
+                "57",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 0u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 0u)"
+            )
+            assertEquals(
+                "(57 * 179)",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 1u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 1u)"
+            )
+            assertEquals(
+                "(57 * (179 * 179))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 2u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 2u)"
+            )
+            assertEquals(
+                "((57 * 179) * (179 * 179))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 3u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 3u)"
+            )
+            assertEquals(
+                "(57 * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 4u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 4u)"
+            )
+            assertEquals(
+                "((57 * 179) * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 5u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 5u)"
+            )
+            assertEquals(
+                "((57 * (179 * 179)) * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 6u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 6u)"
+            )
+            assertEquals(
+                "(((57 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 7u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 7u)"
+            )
+            assertEquals(
+                "(57 * (((179 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 8u).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 8u)"
+            )
+        }
+    }
+    @Test
+    fun test_exponentiationBySquaring_for_UInt() {
+        ExprRing {
+            assertEquals(
+                "0",
+                exponentiationBySquaring(Expr("57"), 0u).expr,
+                "tried exponentiationBySquaring(57, 0u)"
+            )
+            assertEquals(
+                "57",
+                exponentiationBySquaring(Expr("57"), 1u).expr,
+                "tried exponentiationBySquaring(57, 1u)"
+            )
+            assertEquals(
+                "(57 * 57)",
+                exponentiationBySquaring(Expr("57"), 2u).expr,
+                "tried exponentiationBySquaring(57, 2u)"
+            )
+            assertEquals(
+                "(57 * (57 * 57))",
+                exponentiationBySquaring(Expr("57"), 3u).expr,
+                "tried exponentiationBySquaring(57, 3u)"
+            )
+            assertEquals(
+                "((57 * 57) * (57 * 57))",
+                exponentiationBySquaring(Expr("57"), 4u).expr,
+                "tried exponentiationBySquaring(57, 4u)"
+            )
+            assertEquals(
+                "(57 * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 5u).expr,
+                "tried exponentiationBySquaring(57, 5u)"
+            )
+            assertEquals(
+                "((57 * 57) * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 6u).expr,
+                "tried exponentiationBySquaring(57, 6u)"
+            )
+            assertEquals(
+                "((57 * (57 * 57)) * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 7u).expr,
+                "tried exponentiationBySquaring(57, 7u)"
+            )
+            assertEquals(
+                "(((57 * 57) * (57 * 57)) * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 8u).expr,
+                "tried exponentiationBySquaring(57, 8u)"
+            )
+        }
+    }
+    @Test
+    fun test_multiplyExponentiationBySquaring_for_Int() {
+        ExprRing {
+            assertEquals(
+                "57",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 0).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 0)"
+            )
+            assertEquals(
+                "(57 * 179)",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 1).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 1)"
+            )
+            assertEquals(
+                "(57 * (1 / 179))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -1).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -1)"
+            )
+            assertEquals(
+                "(57 * (179 * 179))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 2).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 2)"
+            )
+            assertEquals(
+                "(57 * ((1 / 179) * (1 / 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -2).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -2)"
+            )
+            assertEquals(
+                "((57 * 179) * (179 * 179))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 3).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 3)"
+            )
+            assertEquals(
+                "((57 * (1 / 179)) * ((1 / 179) * (1 / 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -3).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -3)"
+            )
+            assertEquals(
+                "(57 * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 4).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 4)"
+            )
+            assertEquals(
+                "(57 * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -4).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -4)"
+            )
+            assertEquals(
+                "((57 * 179) * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 5).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 5)"
+            )
+            assertEquals(
+                "((57 * (1 / 179)) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -5).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -5)"
+            )
+            assertEquals(
+                "((57 * (179 * 179)) * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 6).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 6)"
+            )
+            assertEquals(
+                "((57 * ((1 / 179) * (1 / 179))) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -6).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -6)"
+            )
+            assertEquals(
+                "(((57 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179)))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 7).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 7)"
+            )
+            assertEquals(
+                "(((57 * (1 / 179)) * ((1 / 179) * (1 / 179))) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -7).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -7)"
+            )
+            assertEquals(
+                "(57 * (((179 * 179) * (179 * 179)) * ((179 * 179) * (179 * 179))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), 8).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, 8)"
+            )
+            assertEquals(
+                "(57 * ((((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179))) * (((1 / 179) * (1 / 179)) * ((1 / 179) * (1 / 179)))))",
+                multiplyExponentiationBySquaring(Expr("57"), Expr("179"), -8).expr,
+                "tried multiplyExponentiationBySquaring(57, 179, -8)"
+            )
+        }
+    }
+    @Test
+    fun test_exponentiationBySquaring_for_Int() {
+        ExprRing {
+            assertEquals(
+                "0",
+                exponentiationBySquaring(Expr("57"), 0).expr,
+                "tried exponentiationBySquaring(57, 0)"
+            )
+            assertEquals(
+                "57",
+                exponentiationBySquaring(Expr("57"), 1).expr,
+                "tried exponentiationBySquaring(57, 1)"
+            )
+            assertEquals(
+                "(1 / 57)",
+                exponentiationBySquaring(Expr("57"), -1).expr,
+                "tried exponentiationBySquaring(57, -1)"
+            )
+            assertEquals(
+                "(57 * 57)",
+                exponentiationBySquaring(Expr("57"), 2).expr,
+                "tried exponentiationBySquaring(57, 2)"
+            )
+            assertEquals(
+                "((1 / 57) * (1 / 57))",
+                exponentiationBySquaring(Expr("57"), -2).expr,
+                "tried exponentiationBySquaring(57, -2)"
+            )
+            assertEquals(
+                "(57 * (57 * 57))",
+                exponentiationBySquaring(Expr("57"), 3).expr,
+                "tried exponentiationBySquaring(57, 3)"
+            )
+            assertEquals(
+                "((1 / 57) * ((1 / 57) * (1 / 57)))",
+                exponentiationBySquaring(Expr("57"), -3).expr,
+                "tried exponentiationBySquaring(57, -3)"
+            )
+            assertEquals(
+                "((57 * 57) * (57 * 57))",
+                exponentiationBySquaring(Expr("57"), 4).expr,
+                "tried exponentiationBySquaring(57, 4)"
+            )
+            assertEquals(
+                "(((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57)))",
+                exponentiationBySquaring(Expr("57"), -4).expr,
+                "tried exponentiationBySquaring(57, -4)"
+            )
+            assertEquals(
+                "(57 * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 5).expr,
+                "tried exponentiationBySquaring(57, 5)"
+            )
+            assertEquals(
+                "((1 / 57) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))",
+                exponentiationBySquaring(Expr("57"), -5).expr,
+                "tried exponentiationBySquaring(57, -5)"
+            )
+            assertEquals(
+                "((57 * 57) * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 6).expr,
+                "tried exponentiationBySquaring(57, 6)"
+            )
+            assertEquals(
+                "(((1 / 57) * (1 / 57)) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))",
+                exponentiationBySquaring(Expr("57"), -6).expr,
+                "tried exponentiationBySquaring(57, -6)"
+            )
+            assertEquals(
+                "((57 * (57 * 57)) * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 7).expr,
+                "tried exponentiationBySquaring(57, 7)"
+            )
+            assertEquals(
+                "(((1 / 57) * ((1 / 57) * (1 / 57))) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))",
+                exponentiationBySquaring(Expr("57"), -7).expr,
+                "tried exponentiationBySquaring(57, -7)"
+            )
+            assertEquals(
+                "(((57 * 57) * (57 * 57)) * ((57 * 57) * (57 * 57)))",
+                exponentiationBySquaring(Expr("57"), 8).expr,
+                "tried exponentiationBySquaring(57, 8)"
+            )
+            assertEquals(
+                "((((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))) * (((1 / 57) * (1 / 57)) * ((1 / 57) * (1 / 57))))",
+                exponentiationBySquaring(Expr("57"), -8).expr,
+                "tried exponentiationBySquaring(57, -8)"
+            )
+        }
+    }
+}

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

@@ -12,11 +12,12 @@ import kotlin.test.assertEquals
 class PolynomialTest {
     @Test
     fun simple_polynomial_test() {
+        val polynomial : Polynomial<Double>
         Double.algebra.scalablePolynomial {
             val x = Polynomial(listOf(0.0, 1.0))
-            val polynomial = x * x - 2 * x + 1
+            polynomial = x * x - 2 * x + 1
-            assertEquals(0.0, polynomial.substitute(1.0), 0.001)
         }
+        assertEquals(0.0, polynomial.substitute(1.0), 0.001)
     }
     @Test
     fun testIntegration() {