Tests generation for numbered utilities in progress: finish map-wise substitutions. Also:

- Upgrade operations on Rational.
- Add new assertions.
- Changed a bit FIXME comments.

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

@@ -121,7 +121,7 @@ class ListPolynomialUtilTest {
     }
     @Test
     @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not.
-            //  Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should make denominator r^deg(p),
+            //  Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p),
             //  not r^(deg(p)(deg(p)+1)/2) as it is now.
     fun test_Polynomial_substitute_RationalFunction() {
         assertEquals(
@@ -589,7 +589,7 @@ class ListPolynomialUtilTest {
     }
     @Test
     @Ignore // FIXME: This tests work only for sane realisations of the substitutions. Currently, it is not.
-            //  Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should make denominator r^deg(p),
+            //  Sane algorithm for substitution p(q/r) (p, q, and r are polynomials) should return denominator r^deg(p),
             //  not r^(deg(p)(deg(p)+1)/2) as it is now.
     fun test_RationalFunction_substitute_RationalFunction() {
         assertEquals(

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

@@ -41,66 +41,105 @@ class Rational {
 
     operator fun unaryPlus(): Rational = this
     operator fun unaryMinus(): Rational = Rational(-this.numerator, this.denominator)
-    operator fun plus(other: Rational): Rational =
+    operator fun plus(other: Rational): Rational {
-        Rational(
+        val denominatorsGcd = gcd(denominator, other.denominator)
-            numerator * other.denominator + denominator * other.numerator,
+        val dividedThisDenominator = denominator / denominatorsGcd
-            denominator * other.denominator
+        val dividedOtherDenominator = other.denominator / denominatorsGcd
+        val numeratorCandidate = numerator * dividedOtherDenominator + dividedThisDenominator * other.numerator
+        val secondGcd = gcd(numeratorCandidate, denominatorsGcd)
+        return Rational(
+            numeratorCandidate / secondGcd,
+            dividedThisDenominator * (other.denominator / secondGcd),
+            toCheckInput = false
         )
+    }
     operator fun plus(other: Int): Rational =
         Rational(
             numerator + denominator * other.toLong(),
-            denominator
+            denominator,
+            toCheckInput = false
         )
     operator fun plus(other: Long): Rational =
         Rational(
             numerator + denominator * other,
-            denominator
+            denominator,
+            toCheckInput = false
         )
-    operator fun minus(other: Rational): Rational =
+    operator fun minus(other: Rational): Rational {
-        Rational(
+        val denominatorsGcd = gcd(denominator, other.denominator)
-            numerator * other.denominator - denominator * other.numerator,
+        val dividedThisDenominator = denominator / denominatorsGcd
-            denominator * other.denominator
+        val dividedOtherDenominator = other.denominator / denominatorsGcd
+        val numeratorCandidate = numerator * dividedOtherDenominator - dividedThisDenominator * other.numerator
+        val secondGcd = gcd(numeratorCandidate, denominatorsGcd)
+        return Rational(
+            numeratorCandidate / secondGcd,
+            dividedThisDenominator * (other.denominator / secondGcd),
+            toCheckInput = false
         )
+    }
     operator fun minus(other: Int): Rational =
         Rational(
             numerator - denominator * other.toLong(),
-            denominator
+            denominator,
+            toCheckInput = false
         )
     operator fun minus(other: Long): Rational =
         Rational(
             numerator - denominator * other,
-            denominator
+            denominator,
+            toCheckInput = false
         )
-    operator fun times(other: Rational): Rational =
+    operator fun times(other: Rational): Rational {
-        Rational(
+        val thisDenominatorAndOtherNumeratorGcd = gcd(denominator, other.numerator)
-            numerator * other.numerator,
+        val otherDenominatorAndThisNumeratorGcd = gcd(other.denominator, numerator)
-            denominator * other.denominator
+        return Rational(
+            (numerator / otherDenominatorAndThisNumeratorGcd) * (other.numerator / thisDenominatorAndOtherNumeratorGcd),
+            (denominator / thisDenominatorAndOtherNumeratorGcd) * (other.denominator / otherDenominatorAndThisNumeratorGcd),
+            toCheckInput = false
         )
-    operator fun times(other: Int): Rational =
+    }
-        Rational(
+    operator fun times(other: Int): Rational {
-            numerator * other.toLong(),
+        val other = other.toLong()
-            denominator
+        val denominatorAndOtherGcd = gcd(denominator, other)
+        return Rational(
+            numerator * (other / denominatorAndOtherGcd),
+            denominator / denominatorAndOtherGcd,
+            toCheckInput = false
         )
-    operator fun times(other: Long): Rational =
+    }
-        Rational(
+    operator fun times(other: Long): Rational {
-            numerator * other,
+        val denominatorAndOtherGcd = gcd(denominator, other)
-            denominator
+        return Rational(
+            numerator * (other / denominatorAndOtherGcd),
+            denominator / denominatorAndOtherGcd,
+            toCheckInput = false
         )
-    operator fun div(other: Rational): Rational =
+    }
-        Rational(
+    operator fun div(other: Rational): Rational {
-            numerator * other.denominator,
+        val denominatorsGcd = gcd(denominator, other.denominator)
-            denominator * other.numerator
+        val numeratorsGcd = gcd(numerator, other.numerator)
+        return Rational(
+            (numerator / numeratorsGcd) * (other.denominator / denominatorsGcd),
+            (denominator / denominatorsGcd) * (other.numerator / numeratorsGcd)
         )
-    operator fun div(other: Int): Rational =
+    }
-        Rational(
+    operator fun div(other: Int): Rational {
-            numerator,
+        val other = other.toLong()
-            denominator * other.toLong()
+        val numeratorAndOtherGcd = gcd(numerator, other)
+        return Rational(
+            numerator / numeratorAndOtherGcd,
+            denominator * (other / numeratorAndOtherGcd),
+            toCheckInput = false
         )
-    operator fun div(other: Long): Rational =
+    }
-        Rational(
+    operator fun div(other: Long): Rational {
-            numerator,
+        val numeratorAndOtherGcd = gcd(numerator, other)
-            denominator * other
+        return Rational(
+            numerator / numeratorAndOtherGcd,
+            denominator * (other / numeratorAndOtherGcd),
+            toCheckInput = false
         )
+    }
     override fun equals(other: Any?): Boolean =
         when (other) {
             is Rational -> numerator == other.numerator && denominator == other.denominator

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

@@ -5,6 +5,8 @@
 
 package space.kscience.kmath.test.misc
 
+import space.kscience.kmath.functions.NumberedPolynomial
+import space.kscience.kmath.functions.NumberedRationalFunction
 import kotlin.test.assertEquals
 
 
@@ -12,3 +14,35 @@ fun <T> assertContentEquals(expected: Map<T, Double>, actual: Map<T, Double>, ab
     assertEquals(expected.keys, actual.keys, message)
     for ((key, expectedValue) in expected) assertEquals(expectedValue, actual[key]!!, absoluteTolerance, message)
 }
+
+fun assertEquals(
+    expected: NumberedPolynomial<Double>,
+    actual: NumberedPolynomial<Double>,
+    absoluteTolerance: Double,
+    message: String? = null
+) = assertContentEquals(
+    expected.coefficients,
+    actual.coefficients,
+    absoluteTolerance,
+    message
+)
+
+fun assertEquals(
+    expected: NumberedRationalFunction<Double>,
+    actual: NumberedRationalFunction<Double>,
+    absoluteTolerance: Double,
+    message: String? = null
+) {
+    assertEquals(
+        expected.numerator,
+        actual.numerator,
+        absoluteTolerance,
+        message
+    )
+    assertEquals(
+        expected.denominator,
+        actual.denominator,
+        absoluteTolerance,
+        message
+    )
+}