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

@@ -100,14 +100,17 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public override operator fun ListPolynomial<C>.times(other: Int): ListPolynomial<C> =
-        if (other == 0) zero
-        else ListPolynomial(
-            coefficients
-                .toMutableList()
-                .apply {
-                    for (deg in indices) this[deg] = this[deg] * other
-                }
-        )
+        when (other) {
+            0 -> zero
+            1 -> this
+            else -> ListPolynomial(
+                coefficients
+                    .toMutableList()
+                    .apply {
+                        for (deg in indices) this[deg] = this[deg] * other
+                    }
+            )
+        }
 
     /**
      * Returns sum of the integer represented as a polynomial and the polynomial.
@@ -133,34 +136,39 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public override operator fun Int.minus(other: ListPolynomial<C>): ListPolynomial<C> =
-        if (this == 0) other
-        else
-            ListPolynomial(
-                other.coefficients
-                    .toMutableList()
-                    .apply {
-                        forEachIndexed { index, c -> if (index != 0) this[index] = -c }
+        ListPolynomial(
+            other.coefficients
+                .toMutableList()
+                .apply {
+                    if (this@minus == 0) {
+                        indices.forEach { this[it] = -this[it] }
+                    } else {
+                        (1..lastIndex).forEach { this[it] = -this[it] }
 
                         val result = this@minus - getOrElse(0) { constantZero }
 
-                        if(size == 0) add(result)
+                        if (size == 0) add(result)
                         else this[0] = result
                     }
-            )
+                }
+        )
     /**
      * Returns product of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
     public override operator fun Int.times(other: ListPolynomial<C>): ListPolynomial<C> =
-        if (this == 0) zero
-        else ListPolynomial(
-            other.coefficients
-                .toMutableList()
-                .apply {
-                    for (deg in indices) this[deg] = this@times * this[deg]
-                }
-        )
+        when (this) {
+            0 -> zero
+            1 -> other
+            else -> ListPolynomial(
+                other.coefficients
+                    .toMutableList()
+                    .apply {
+                        for (deg in indices) this[deg] = this@times * this[deg]
+                    }
+            )
+        }
 
     /**
      * Converts the integer [value] to polynomial.
@@ -192,7 +200,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             else ListPolynomial(
                 toMutableList()
                     .apply {
-                        forEachIndexed { index, c -> if (index != 0) this[index] = -c }
+                        (1 .. lastIndex).forEach { this[it] = -this[it] }
 
                         val result = if (size == 0) this@minus else this@minus - get(0)
 

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

@@ -98,14 +98,17 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public override operator fun NumberedPolynomial<C>.times(other: Int): NumberedPolynomial<C> =
-        if (other == 0) zero
-        else NumberedPolynomialAsIs(
-            coefficients
-                .toMutableMap()
-                .apply {
-                    for (degs in keys) this[degs] = this[degs]!! * other
-                }
-        )
+        when (other) {
+            0 -> zero
+            1 -> this
+            else -> NumberedPolynomialAsIs(
+                coefficients
+                    .toMutableMap()
+                    .apply {
+                        for (degs in keys) this[degs] = this[degs]!! * other
+                    }
+            )
+        }
 
     /**
      * Returns sum of the integer represented as a polynomial and the polynomial.
@@ -130,16 +133,20 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public override operator fun Int.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        if (this == 0) other
-        else
-            NumberedPolynomialAsIs(
-                other.coefficients
-                    .toMutableMap()
-                    .apply {
+        NumberedPolynomialAsIs(
+            other.coefficients
+                .toMutableMap()
+                .apply {
+                    if (this@minus == 0) {
+                        forEach { (key, value) -> this[key] = -value }
+                    } else {
+                        forEach { (key, value) -> if (key.isNotEmpty()) this[key] = -value }
+
                         val degs = emptyList<UInt>()
 
                         this[degs] = this@minus - getOrElse(degs) { constantZero }
                     }
+                }
             )
     /**
      * Returns product of the integer represented as a polynomial and the polynomial.
@@ -147,14 +154,17 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
      * The operation is equivalent to sum of [this] copies of [other].
      */
     public override operator fun Int.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        if (this == 0) zero
-        else NumberedPolynomialAsIs(
-            other.coefficients
-                .toMutableMap()
-                .apply {
-                    for (degs in keys) this[degs] = this@times * this[degs]!!
-                }
-        )
+        when (this) {
+            0 -> zero
+            1 -> other
+            else -> NumberedPolynomialAsIs(
+                other.coefficients
+                    .toMutableMap()
+                    .apply {
+                        for (degs in keys) this[degs] = this@times * this[degs]!!
+                    }
+            )
+        }
 
     /**
      * Converts the integer [value] to polynomial.
@@ -185,7 +195,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
             else NumberedPolynomialAsIs(
                 toMutableMap()
                     .apply {
-                        forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
+                        forEach { (degs, c) -> if (degs.isNotEmpty()) this[degs] = -c }
 
                         val degs = emptyList<UInt>()
 
@@ -266,7 +276,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
     override operator fun NumberedPolynomial<C>.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         NumberedPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
-                other.coefficients.mapValuesTo(this) { it.value }
+                coefficients.mapValuesTo(this) { it.value }
                 other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
             }
         )
@@ -276,7 +286,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
     override operator fun NumberedPolynomial<C>.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         NumberedPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
-                other.coefficients.mapValuesTo(this) { it.value }
+                coefficients.mapValuesTo(this) { it.value }
                 other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
             }
         )

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

@@ -119,11 +119,13 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
      * Substitutes provided polynomial [argument] into [this] polynomial.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
     public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = substitute(ring, argument)
     /**
      * Substitutes provided rational function [argument] into [this] polynomial.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
     public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
     /**
      * Substitutes provided constant [argument] into [this] rational function.
@@ -134,11 +136,13 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
      * Substitutes provided polynomial [argument] into [this] rational function.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
     public inline fun NumberedRationalFunction<C>.substitute(argument: Map<Int, NumberedPolynomial<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
     /**
      * Substitutes provided rational function [argument] into [this] rational function.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
     public inline fun NumberedRationalFunction<C>.substitute(argument: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
     /**
      * Substitutes provided constant [argument] into [this] polynomial.
@@ -149,11 +153,13 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
      * Substitutes provided polynomial [argument] into [this] polynomial.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
     public inline fun NumberedPolynomial<C>.substitute(argument: Buffer<NumberedPolynomial<C>>): NumberedPolynomial<C> = substitute(ring, argument)
     /**
      * Substitutes provided rational function [argument] into [this] polynomial.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
     public inline fun NumberedPolynomial<C>.substitute(argument: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
     /**
      * Substitutes provided constant [argument] into [this] rational function.
@@ -164,11 +170,13 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
      * Substitutes provided polynomial [arguments] into [this] rational function.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
     public inline fun NumberedRationalFunction<C>.substitute(arguments: Buffer<NumberedPolynomial<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
     /**
      * Substitutes provided rational function [arguments] into [this] rational function.
      */
     @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
     public inline fun NumberedRationalFunction<C>.substitute(arguments: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
     /**
      * Substitutes provided constant [arguments] into [this] polynomial.
@@ -222,7 +230,7 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
      * Substitutes provided [arguments] into [this] polynomial.
      */
     @Suppress("NOTHING_TO_INLINE")
-    @JvmName("invokePolynomial")
+    @JvmName("invokeRationalFunction")
     public inline operator fun NumberedPolynomial<C>.invoke(arguments: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
     /**
      * Substitutes provided [arguments] into [this] rational function.
@@ -234,6 +242,6 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
      * Substitutes provided [arguments] into [this] rational function.
      */
     @Suppress("NOTHING_TO_INLINE")
-    @JvmName("invokePolynomial")
+    @JvmName("invokeRationalFunction")
     public inline operator fun NumberedRationalFunction<C>.invoke(arguments: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
 }

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

@@ -6,8 +6,27 @@
 package space.kscience.kmath.functions
 
 
+/**
+ * Marks operations that are going to be optimized reimplementations by reducing number of boxings but currently is
+ * under development and is not stable (or even ready to use).
+ */
 @RequiresOptIn(
     message = "It's copy of operation with optimized boxing. It's currently unstable.",
     level = RequiresOptIn.Level.ERROR
 )
-internal annotation class UnstablePolynomialBoxingOptimization
+internal annotation class UnstablePolynomialBoxingOptimization
+
+/**
+ * Marks declarations that give access to internal entities of polynomials delicate structure. Thus, it allows to
+ * optimize performance a bit by skipping standard steps, but such skips may cause critical errors if something is
+ * implemented badly. Make sure you fully read and understand documentation and don't break internal contracts.
+ */
+@RequiresOptIn(
+    message = "This declaration gives access to delicate internal structure of polynomials. " +
+            "It allows to optimize performance by skipping unnecessary arguments check. " +
+            "But at the same time makes it easy to make a mistake " +
+            "that will cause wrong computation result or even runtime error. " +
+            "Make sure you fully read and understand documentation.",
+    level = RequiresOptIn.Level.WARNING
+)
+internal annotation class DelicatePolynomialAPI

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

@@ -37,6 +37,38 @@ internal inline fun <C> NumberedPolynomialAsIs(pairs: Collection<Pair<List<UInt>
 @PublishedApi
 internal inline fun <C> NumberedPolynomialAsIs(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
 
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is.
+ *
+ * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@Suppress("FunctionName", "NOTHING_TO_INLINE")
+@DelicatePolynomialAPI
+public inline fun <C> NumberedPolynomialWithoutCheck(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(coefs)
+
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The collections will be transformed to map with [toMap] and then will be used as is.
+ *
+ * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@Suppress("FunctionName", "NOTHING_TO_INLINE")
+@DelicatePolynomialAPI
+public inline fun <C> NumberedPolynomialWithoutCheck(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The array will be transformed to map with [toMap] and then will be used as is.
+ *
+ * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@Suppress("FunctionName", "NOTHING_TO_INLINE")
+@DelicatePolynomialAPI
+public inline fun <C> NumberedPolynomialWithoutCheck(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
+
 /**
  * Constructs [NumberedPolynomial] with provided coefficients map [coefs].
  *
@@ -245,11 +277,12 @@ public class NumberedPolynomialTermSignatureBuilder {
      * Declaring another power of the same variable will increase its degree by received degree.
      */
     public infix fun Int.inPowerOf(deg: UInt) {
-        if (this > signature.lastIndex) {
-            signature.addAll(List(this - signature.lastIndex - 1) { 0u })
+        val index = this - 1
+        if (index > signature.lastIndex) {
+            signature.addAll(List(index - signature.lastIndex - 1) { 0u })
             signature.add(deg)
         } else {
-            signature[this] += deg
+            signature[index] += deg
         }
     }
     /**
@@ -334,22 +367,26 @@ public class NumberedPolynomialBuilder<C>(
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
-/**
- * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of constants.
- *
- * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
- * ```
- * Int.algebra {
- *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
- *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
- *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
- *     }
- * }
- * ```
- */
-@UnstableKMathAPI
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> A.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(::add, initialCapacity).apply(block).build()
+///**
+// * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of constants.
+// *
+// * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+// * ```
+// * Int.algebra {
+// *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
+// *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+// *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+// *     }
+// * }
+// * ```
+// */
+// FIXME: For now this fabric does not let next two fabrics work. (See KT-52803.) Possible feature solutions:
+//  1. `LowPriorityInOverloadResolution` becomes public. Then it should be applied to this function.
+//  2. Union types are implemented. Then all three functions should be rewritten
+//     as one with single union type as a (context) receiver.
+//@UnstableKMathAPI
+//@Suppress("FunctionName")
+//public inline fun <C, A: Ring<C>> A.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(::add, initialCapacity).apply(block).build()
 /**
  * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of [NumberedPolynomial]s.
  *
@@ -365,7 +402,7 @@ public inline fun <C, A: Ring<C>> A.NumberedPolynomial(initialCapacity: Int = 0,
  */
 @UnstableKMathAPI
 @Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(initialCapacity: Int, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
+public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
 /**
  * Creates [NumberedPolynomial] with lambda [block] in context of [this] field of [NumberedRationalFunction]s.
  *
@@ -381,7 +418,7 @@ public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomi
  */
 @UnstableKMathAPI
 @Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(initialCapacity: Int, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
+public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 

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

@@ -86,7 +86,7 @@ public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>
 
 /**
  * Substitutes provided arguments [args] into [this] polynomial.
-     */ // TODO: To optimize boxing
+ */ // TODO: To optimize boxing
 @JvmName("substitutePolynomial")
 public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> =
     ring.numberedPolynomialSpace {

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

@@ -3,6 +3,8 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+@file:Suppress("LocalVariableName")
+
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.test.misc.*
@@ -28,25 +30,32 @@ class ListPolynomialTest {
                 ListPolynomial(Rational(-2)) + 2,
                 "test 3"
             )
-            assertEquals(
-                ListPolynomial(),
-                ListPolynomial<Rational>() + 0,
+            val polynomial_4 = ListPolynomial<Rational>()
+            assertSame(
+                polynomial_4,
+                polynomial_4 + 0,
                 "test 4"
             )
+            val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7))
+            assertSame(
+                polynomial_5,
+                polynomial_5 + 0,
+                "test 5"
+            )
             assertEquals(
                 ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)),
                 ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)) + 1,
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(-1)),
                 ListPolynomial(Rational(-2)) + 1,
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(2)),
                 ListPolynomial<Rational>() + 2,
-                "test 7"
+                "test 8"
             )
         }
     }
@@ -68,25 +77,32 @@ class ListPolynomialTest {
                 ListPolynomial(Rational(2)) - 2,
                 "test 3"
             )
-            assertEquals(
-                ListPolynomial(),
-                ListPolynomial<Rational>() - 0,
+            val polynomial_4 = ListPolynomial<Rational>()
+            assertSame(
+                polynomial_4,
+                polynomial_4 - 0,
                 "test 4"
             )
+            val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7))
+            assertEquals(
+                polynomial_5,
+                polynomial_5 - 0,
+                "test 5"
+            )
             assertEquals(
                 ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)),
                 ListPolynomial(Rational(2), Rational(0), Rational(0), Rational(0)) - 1,
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(1)),
                 ListPolynomial(Rational(2)) - 1,
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(-2)),
                 ListPolynomial<Rational>() - 2,
-                "test 7"
+                "test 8"
             )
         }
     }
@@ -103,6 +119,17 @@ class ListPolynomialTest {
                 ListPolynomial(7, 0, 49, 21, 14) * 15,
                 "test 2"
             )
+            val polynomial = ListPolynomial(22, 26, 13, 15, 26)
+            assertSame(
+                zero,
+                polynomial * 0,
+                "test 3"
+            )
+            assertSame(
+                polynomial,
+                polynomial * 1,
+                "test 4"
+            )
         }
     }
     @Test
@@ -123,25 +150,32 @@ class ListPolynomialTest {
                 2 + ListPolynomial(Rational(-2)),
                 "test 3"
             )
-            assertEquals(
-                ListPolynomial(),
-                0 + ListPolynomial(),
+            val polynomial_4 = ListPolynomial<Rational>()
+            assertSame(
+                polynomial_4,
+                0 + polynomial_4,
                 "test 4"
             )
+            val polynomial_5 = ListPolynomial<Rational>(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7))
+            assertSame(
+                polynomial_5,
+                0 + polynomial_5,
+                "test 5"
+            )
             assertEquals(
                 ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)),
                 1 + ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(-1)),
                 1 + ListPolynomial(Rational(-2)),
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(2)),
                 2 + ListPolynomial(),
-                "test 7"
+                "test 8"
             )
         }
     }
@@ -163,25 +197,30 @@ class ListPolynomialTest {
                 -2 - ListPolynomial(Rational(-2)),
                 "test 3"
             )
+            assertEquals(
+                ListPolynomial(Rational(-32, 9), Rational(-8, -9), Rational(8, 7)),
+                0 - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
+                "test 4"
+            )
             assertEquals(
                 ListPolynomial(),
                 0 - ListPolynomial(),
-                "test 4"
+                "test 5"
             )
             assertEquals(
                 ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)),
                 -1 - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(1)),
                 -1 - ListPolynomial(Rational(-2)),
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(-2)),
                 -2 - ListPolynomial(),
-                "test 7"
+                "test 8"
             )
         }
     }
@@ -198,6 +237,17 @@ class ListPolynomialTest {
                 15 * ListPolynomial(7, 0, 49, 21, 14),
                 "test 2"
             )
+            val polynomial = ListPolynomial(22, 26, 13, 15, 26)
+            assertSame(
+                zero,
+                0 * polynomial,
+                "test 3"
+            )
+            assertSame(
+                polynomial,
+                1 * polynomial,
+                "test 4"
+            )
         }
     }
     @Test

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

@@ -0,0 +1,111 @@
+/*
+ * 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.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.algebra
+import space.kscience.kmath.operations.invoke
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+
+class NumberedConstructorsTest {
+    @Test
+    @UnstableKMathAPI
+    fun testBuilder() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u, 0u, 3u) to 5,
+                listOf(0u, 1u) to -6,
+            ),
+            Int.algebra.numberedPolynomialSpace {
+                NumberedPolynomial {
+                    5 { 1 inPowerOf 2u; 3 inPowerOf 3u }
+                    (-6) { 2 inPowerOf 1u }
+                }
+            },
+            "test 1"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to -1,
+            ),
+            Int.algebra.numberedPolynomialSpace {
+                NumberedPolynomial {
+                    5 { }
+                    (-6) { }
+                }
+            },
+            "test 2"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u) to -1,
+            ),
+            Int.algebra.numberedPolynomialSpace {
+                NumberedPolynomial {
+                    5 { 1 inPowerOf 1u; 1 inPowerOf 1u }
+                    (-6) { 1 inPowerOf 2u }
+                }
+            },
+            "test 3"
+        )
+    }
+    @Test
+    @UnstableKMathAPI
+    fun testFabric() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u, 0u, 3u) to 5,
+                listOf(0u, 1u) to -6,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(2u, 0u, 3u) to 5,
+                    listOf(0u, 1u) to -6,
+                )
+            },
+            "test 1"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u, 0u, 3u) to 5,
+                listOf(0u, 1u) to -6,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(2u, 0u, 3u, 0u) to 5,
+                    listOf(0u, 1u, 0u, 0u) to -6,
+                )
+            },
+            "test 2"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to -1,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(0u) to 5,
+                    listOf(0u, 0u) to -6,
+                )
+            },
+            "test 3"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(0u) to 5,
+                    listOf(0u, 0u) to -5,
+                )
+            },
+            "test 4"
+        )
+    }
+}

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

@@ -7,6 +7,7 @@ package space.kscience.kmath.test.misc
 
 import space.kscience.kmath.functions.ListPolynomial
 import space.kscience.kmath.functions.ListPolynomialSpace
+import space.kscience.kmath.functions.PolynomialSpaceOverRing
 import space.kscience.kmath.operations.Ring
 
 
@@ -135,4 +136,7 @@ class IntModuloRing : Ring<IntModulo> {
 fun ListPolynomialSpace<IntModulo, IntModuloRing>.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
     ListPolynomial(coefs.map { IntModulo(it, ring.modulus) })
 fun IntModuloRing.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
-    ListPolynomial(coefs.map { IntModulo(it, modulus) })
+    ListPolynomial(coefs.map { IntModulo(it, modulus) })
+
+fun IntModuloRing.m(arg: Int) = IntModulo(arg, modulus)
+fun PolynomialSpaceOverRing<IntModulo, *, IntModuloRing>.m(arg: Int) = IntModulo(arg, ring.modulus)