Added support of power function to abstract structures.

Implemented exponentiation by squaring as default implementation of `power`. Updated docs in algebraicStub.kt and updated realisations in it.

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

@@ -71,19 +71,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
-    public operator fun P.plus(other: Int): P = optimizedAddMultiplied(this, one, other)
+    public operator fun P.plus(other: Int): P = addMultipliedBySquaring(this, one, other)
     /**
      * Returns difference between the polynomial and the integer represented as polynomial.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
-    public operator fun P.minus(other: Int): P = optimizedAddMultiplied(this, one, -other)
+    public operator fun P.minus(other: Int): P = addMultipliedBySquaring(this, one, -other)
     /**
      * Returns product of the polynomial and the integer represented as polynomial.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
-    public operator fun P.times(other: Int): P = optimizedMultiply(this, other)
+    public operator fun P.times(other: Int): P = multiplyBySquaring(this, other)
     // endregion
 
     // region Integer-polynomial relation
@@ -92,19 +92,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
-    public operator fun Int.plus(other: P): P = optimizedAddMultiplied(other, one, this)
+    public operator fun Int.plus(other: P): P = addMultipliedBySquaring(other, one, this)
     /**
      * Returns difference between the integer represented as polynomial and the polynomial.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
-    public operator fun Int.minus(other: P): P = optimizedAddMultiplied(-other, one, this)
+    public operator fun Int.minus(other: P): P = addMultipliedBySquaring(-other, one, this)
     /**
      * Returns product of the integer represented as polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
-    public operator fun Int.times(other: P): P = optimizedMultiply(other, this)
+    public operator fun Int.times(other: P): P = multiplyBySquaring(other, this)
     // endregion
 
     // region Constant-constant relation
@@ -138,6 +138,12 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
     @JvmName("constantTimes")
     @JsName("constantTimes")
     public operator fun C.times(other: C): C
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("constantPower")
+    @JsName("constantPower")
+    public fun power(arg: C, exponent: UInt) : C
 
     /**
      * Check if the instant is zero constant.
@@ -225,6 +231,10 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
      * Returns product of the polynomials.
      */
     public override operator fun P.times(other: P): P
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    public override fun power(arg: P, exponent: UInt) : P = exponentiationBySquaring(arg, exponent)
 
     /**
      * Check if the instant is zero polynomial.
@@ -331,19 +341,19 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
      *
      * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
      */
-    public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) }
+    public override operator fun C.plus(other: Int): C = ring { addMultipliedBySquaring(this@plus, one, other) }
     /**
      * Returns difference between the constant and the integer represented as constant (member of underlying ring).
      *
      * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
      */
-    public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) }
+    public override operator fun C.minus(other: Int): C = ring { addMultipliedBySquaring(this@minus, one, -other) }
     /**
      * Returns product of the constant and the integer represented as constant (member of underlying ring).
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
-    public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) }
+    public override operator fun C.times(other: Int): C = ring { multiplyBySquaring(this@times, other) }
     // endregion
 
     // region Integer-constant relation
@@ -352,19 +362,19 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
      *
      * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
      */
-    public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) }
+    public override operator fun Int.plus(other: C): C = ring { addMultipliedBySquaring(other, one, this@plus) }
     /**
      * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
      */
-    public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) }
+    public override operator fun Int.minus(other: C): C = ring { addMultipliedBySquaring(-other, one, this@minus) }
     /**
      * Returns product of the integer represented as constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
-    public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) }
+    public override operator fun Int.times(other: C): C = ring { multiplyBySquaring(other, this@times) }
     // endregion
 
     // region Constant-constant relation
@@ -388,6 +398,11 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
      */
     @JvmName("constantTimes")
     public override operator fun C.times(other: C): C = ring { this@times * other }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("constantPower")
+    override fun power(arg: C, exponent: UInt): C = ring { power(arg, exponent) }
 
     /**
      * Instance of zero constant (zero of the underlying ring).

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

@@ -120,19 +120,19 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
-    public operator fun R.plus(other: Int): R = optimizedAddMultiplied(this, one, other)
+    public operator fun R.plus(other: Int): R = addMultipliedBySquaring(this, one, other)
     /**
      * Returns difference between the rational function and the integer represented as rational function.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
-    public operator fun R.minus(other: Int): R = optimizedAddMultiplied(this, one, -other)
+    public operator fun R.minus(other: Int): R = addMultipliedBySquaring(this, one, -other)
     /**
      * Returns product of the rational function and the integer represented as rational function.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
-    public operator fun R.times(other: Int): R = optimizedMultiply(this, other)
+    public operator fun R.times(other: Int): R = multiplyBySquaring(this, other)
     // endregion
 
     // region Integer-Rational relation
@@ -141,19 +141,19 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
-    public operator fun Int.plus(other: R): R = optimizedAddMultiplied(other, one, this)
+    public operator fun Int.plus(other: R): R = addMultipliedBySquaring(other, one, this)
     /**
      * Returns difference between the integer represented as rational function and the rational function.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
-    public operator fun Int.minus(other: R): R = optimizedAddMultiplied(-other, one, this)
+    public operator fun Int.minus(other: R): R = addMultipliedBySquaring(-other, one, this)
     /**
      * Returns product of the integer represented as rational function and the rational function.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
-    public operator fun Int.times(other: R): R = optimizedMultiply(other, this)
+    public operator fun Int.times(other: R): R = multiplyBySquaring(other, this)
     // endregion
 
     // region Constant-constant relation
@@ -187,6 +187,12 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
     @JvmName("constantTimes")
     @JsName("constantTimes")
     public operator fun C.times(other: C): C
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("constantPower")
+    @JsName("constantPower")
+    public fun power(arg: C, exponent: UInt) : C
 
     /**
      * Check if the instant is zero constant.
@@ -274,6 +280,10 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Returns product of the polynomials.
      */
     public operator fun P.times(other: P): P
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    public fun power(arg: P, exponent: UInt) : P
 
     /**
      * Check if the instant is zero polynomial.
@@ -400,6 +410,10 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
      * Returns product of the rational functions.
      */
     public override operator fun R.times(other: R): R
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    public override fun power(arg: R, exponent: UInt) : R = exponentiationBySquaring(arg, exponent)
 
     /**
      * Check if the instant is zero rational function.
@@ -536,19 +550,19 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
      *
      * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
      */
-    public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) }
+    public override operator fun C.plus(other: Int): C = ring { addMultipliedBySquaring(this@plus, one, other) }
     /**
      * Returns difference between the constant and the integer represented as constant (member of underlying ring).
      *
      * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
      */
-    public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) }
+    public override operator fun C.minus(other: Int): C = ring { addMultipliedBySquaring(this@minus, one, -other) }
     /**
      * Returns product of the constant and the integer represented as constant (member of underlying ring).
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
-    public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) }
+    public override operator fun C.times(other: Int): C = ring { multiplyBySquaring(this@times, other) }
     // endregion
 
     // region Integer-constant relation
@@ -557,19 +571,19 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
      *
      * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
      */
-    public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) }
+    public override operator fun Int.plus(other: C): C = ring { addMultipliedBySquaring(other, one, this@plus) }
     /**
      * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
      */
-    public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) }
+    public override operator fun Int.minus(other: C): C = ring { addMultipliedBySquaring(-other, one, this@minus) }
     /**
      * Returns product of the integer represented as constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
-    public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) }
+    public override operator fun Int.times(other: C): C = ring { multiplyBySquaring(other, this@times) }
     // endregion
 
     // region Constant-constant relation
@@ -598,6 +612,11 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
      */
     @JvmName("constantTimes")
     public override operator fun C.times(other: C): C = ring { this@times * other }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("constantPower")
+    public override fun power(arg: C, exponent: UInt) : C = ring { power(arg, exponent) }
 
     /**
      * Instance of zero constant (zero of the underlying ring).
@@ -740,6 +759,11 @@ public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<
      */
     @JvmName("constantTimes")
     public override operator fun C.times(other: C): C = polynomialRing { this@times * other }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    @JvmName("constantPower")
+    public override fun power(arg: C, exponent: UInt) : C = polynomialRing { power(arg, exponent) }
 
     /**
      * Check if the instant is zero constant.
@@ -827,6 +851,10 @@ public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<
      * Returns product of the polynomials.
      */
     public override operator fun P.times(other: P): P = polynomialRing { this@times * other }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */
+    public override fun power(arg: P, exponent: UInt) : P = polynomialRing { power(arg, exponent) }
 
     /**
      * Check if the instant is zero polynomial.

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

@@ -5,53 +5,54 @@
 
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.operations.Group
+import space.kscience.kmath.operations.*
 
 
 // TODO: All of this should be moved to algebraic structures' place for utilities
 // TODO: Move receiver to context receiver
 /**
- * Multiplication of element and integer.
+ * Returns product of [arg] and integer [multiplier].
  *
- * @receiver the multiplicand.
+ * @param arg the multiplicand.
- * @param other the multiplier.
+ * @param multiplier the integer multiplier.
- * @return the difference.
+ * @return product of the multiplicand [arg] and the multiplier [multiplier].
  * @author Gleb Minaev
  */
-internal fun <C> Group<C>.optimizedMultiply(arg: C, other: Int): C =
+internal fun <C> Group<C>.multiplyBySquaring(arg: C, multiplier: Int): C =
-    if (other >= 0) optimizedMultiply(arg, other.toUInt())
+    if (multiplier >= 0) multiplyBySquaring(arg, multiplier.toUInt())
-    else optimizedMultiply(arg, (-other).toUInt())
+    else multiplyBySquaring(-arg, (-multiplier).toUInt())
 
 // TODO: Move receiver to context receiver
 /**
  * Adds product of [arg] and [multiplier] to [base].
  *
- * @receiver the algebra to provide multiplication.
  * @param base the augend.
  * @param arg the multiplicand.
- * @param multiplier the multiplier.
+ * @param multiplier the integer multiplier.
  * @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier].
  * @author Gleb Minaev
  */
-internal fun <C> Group<C>.optimizedAddMultiplied(base: C, arg: C, multiplier: Int): C =
+internal fun <C> GroupOps<C>.addMultipliedBySquaring(base: C, arg: C, multiplier: Int): C =
-    if (multiplier >= 0) optimizedAddMultiplied(base, arg, multiplier.toUInt())
+    if (multiplier >= 0) addMultipliedBySquaring(base, arg, multiplier.toUInt())
-    else optimizedAddMultiplied(base, arg, (-multiplier).toUInt())
+    else addMultipliedBySquaring(base, -arg, (-multiplier).toUInt())
 
 // TODO: Move receiver to context receiver
 /**
- * Multiplication of element and integer.
+ * Returns product of [arg] and integer [multiplier].
  *
- * @receiver the multiplicand.
+ * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
- * @param other the multiplier.
+ *
- * @return the difference.
+ * @param arg the multiplicand.
+ * @param multiplier the integer multiplier.
+ * @return product of the multiplicand [arg] and the multiplier [multiplier].
  * @author Gleb Minaev
  */
-internal tailrec fun <C> Group<C>.optimizedMultiply(arg: C, other: UInt): C =
+internal tailrec fun <C> Group<C>.multiplyBySquaring(arg: C, multiplier: UInt): C =
     when {
-        other == 0u -> zero
+        multiplier == 0u -> zero
-        other == 1u -> arg
+        multiplier == 1u -> arg
-        other % 2u == 0u -> optimizedMultiply(arg + arg, other / 2u)
+        multiplier and 1u == 0u -> multiplyBySquaring(arg + arg, multiplier shr 1)
-        other % 2u == 1u -> optimizedAddMultiplied(arg, arg + arg, other / 2u)
+        multiplier and 1u == 1u -> addMultipliedBySquaring(arg, arg + arg, multiplier shr 1)
         else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")
     }
 
@@ -59,18 +60,87 @@ internal tailrec fun <C> Group<C>.optimizedMultiply(arg: C, other: UInt): C =
 /**
  * Adds product of [arg] and [multiplier] to [base].
  *
- * @receiver the algebra to provide multiplication.
+ * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
+ *
  * @param base the augend.
  * @param arg the multiplicand.
- * @param multiplier the multiplier.
+ * @param multiplier the integer multiplier.
  * @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier].
  * @author Gleb Minaev
  */
-internal tailrec fun <C> Group<C>.optimizedAddMultiplied(base: C, arg: C, multiplier: UInt): C =
+internal tailrec fun <C> GroupOps<C>.addMultipliedBySquaring(base: C, arg: C, multiplier: UInt): C =
     when {
         multiplier == 0u -> base
         multiplier == 1u -> base + arg
-        multiplier % 2u == 0u -> optimizedAddMultiplied(base, arg + arg, multiplier / 2u)
+        multiplier and 1u == 0u -> addMultipliedBySquaring(base, arg + arg, multiplier shr 1)
-        multiplier % 2u == 1u -> optimizedAddMultiplied(base + arg, arg + arg, multiplier / 2u)
+        multiplier and 1u == 1u -> addMultipliedBySquaring(base + arg, arg + arg, multiplier shr 1)
+        else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")
+    }
+
+// TODO: Move receiver to context receiver
+/**
+ * Raises [arg] to the integer power [exponent].
+ *
+ * @param arg the base of the power.
+ * @param exponent the exponent of the power.
+ * @return [arg] raised to the power [exponent].
+ * @author Gleb Minaev
+ */
+internal fun <C> Field<C>.exponentiationBySquaring(arg: C, exponent: Int): C =
+    if (exponent >= 0) exponentiationBySquaring(arg, exponent.toUInt())
+    else exponentiationBySquaring(one / arg, (-exponent).toUInt())
+
+// TODO: Move receiver to context receiver
+/**
+ * Multiplies [base] and [arg] raised to the integer power [exponent].
+ *
+ * @param base the multiplicand.
+ * @param arg the base of the power.
+ * @param exponent the exponent of the power.
+ * @return product of [base] and [arg] raised to the power [exponent].
+ * @author Gleb Minaev
+ */
+internal fun <C> Field<C>.multiplyExponentiationBySquaring(base: C, arg: C, exponent: Int): C =
+    if (exponent >= 0) multiplyExponentiationBySquaring(base, arg, exponent.toUInt())
+    else multiplyExponentiationBySquaring(base, one / arg, (-exponent).toUInt())
+
+// TODO: Move receiver to context receiver
+/**
+ * Raises [arg] to the integer power [exponent].
+ *
+ * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
+ *
+ * @param arg the base of the power.
+ * @param exponent the exponent of the power.
+ * @return [arg] raised to the power [exponent].
+ * @author Gleb Minaev
+ */
+internal tailrec fun <C> Ring<C>.exponentiationBySquaring(arg: C, exponent: UInt): C =
+    when {
+        exponent == 0u -> zero
+        exponent == 1u -> arg
+        exponent and 1u == 0u -> exponentiationBySquaring(arg * arg, exponent shr 1)
+        exponent and 1u == 1u -> multiplyExponentiationBySquaring(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")
+    }
+
+// TODO: Move receiver to context receiver
+/**
+ * Multiplies [base] and [arg] raised to the integer power [exponent].
+ *
+ * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
+ *
+ * @param base the multiplicand.
+ * @param arg the base of the power.
+ * @param exponent the exponent of the power.
+ * @return product of [base] and [arg] raised to the power [exponent].
+ * @author Gleb Minaev
+ */
+internal tailrec fun <C> RingOps<C>.multiplyExponentiationBySquaring(base: C, arg: C, exponent: UInt): C =
+    when {
+        exponent == 0u -> base
+        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/commonMain/kotlin/space/kscience/kmath/functions/labeledPolynomialUtil.kt

@@ -351,7 +351,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
                                 }
                             }
                         },
-                        optimizedMultiply(c, degs[variable]!!)
+                        multiplyBySquaring(c, degs[variable]!!)
                     )
                 }
         }
@@ -382,7 +382,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
                                 }
                             }
                         },
-                        cleanedVariables.fold(c) { acc, variable -> optimizedMultiply(acc, degs[variable]!!) }
+                        cleanedVariables.fold(c) { acc, variable -> multiplyBySquaring(acc, degs[variable]!!) }
                     )
                 }
         }
@@ -415,7 +415,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
                         },
                         degs[variable]!!.let { deg ->
                             (deg downTo deg - order + 1u)
-                                .fold(c) { acc, ord -> optimizedMultiply(acc, ord) }
+                                .fold(c) { acc, ord -> multiplyBySquaring(acc, ord) }
                         }
                     )
                 }
@@ -451,7 +451,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
                         filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
                             degs[index]!!.let { deg ->
                                 (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> optimizedMultiply(acc2, ord) }
+                                    .fold(acc1) { acc2, ord -> multiplyBySquaring(acc2, ord) }
                             }
                         }
                     )
@@ -478,7 +478,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
                     }
                     put(
                         newDegs,
-                        c / optimizedMultiply(one, newDegs[variable]!!)
+                        c / multiplyBySquaring(one, newDegs[variable]!!)
                     )
                 }
         }
@@ -505,7 +505,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
                     }
                     put(
                         newDegs,
-                        cleanedVariables.fold(c) { acc, variable -> acc / optimizedMultiply(one, newDegs[variable]!!) }
+                        cleanedVariables.fold(c) { acc, variable -> acc / multiplyBySquaring(one, newDegs[variable]!!) }
                     )
                 }
         }
@@ -534,7 +534,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo
                         newDegs,
                         newDegs[variable]!!.let { deg ->
                             (deg downTo  deg - order + 1u)
-                                .fold(c) { acc, ord -> acc / optimizedMultiply(one, ord) }
+                                .fold(c) { acc, ord -> acc / multiplyBySquaring(one, ord) }
                         }
                     )
                 }
@@ -565,7 +565,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo
                         filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
                             newDegs[index]!!.let { deg ->
                                 (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> acc2 / optimizedMultiply(one, ord) }
+                                    .fold(acc1) { acc2, ord -> acc2 / multiplyBySquaring(one, ord) }
                             }
                         }
                     )

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

@@ -393,7 +393,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
                                 else -> return@forEach
                             }
                         }.cleanUp(),
-                        optimizedMultiply(c, degs[variable])
+                        multiplyBySquaring(c, degs[variable])
                     )
                 }
         }
@@ -424,7 +424,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
                                 else -> return@forEach
                             }
                         }.cleanUp(),
-                        cleanedVariables.fold(c) { acc, variable -> optimizedMultiply(acc, degs[variable]) }
+                        cleanedVariables.fold(c) { acc, variable -> multiplyBySquaring(acc, degs[variable]) }
                     )
                 }
         }
@@ -456,7 +456,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
                         }.cleanUp(),
                         degs[variable].let { deg ->
                             (deg downTo deg - order + 1u)
-                                .fold(c) { acc, ord -> optimizedMultiply(acc, ord) }
+                                .fold(c) { acc, ord -> multiplyBySquaring(acc, ord) }
                         }
                     )
                 }
@@ -489,7 +489,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
                         filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
                             degs[index].let { deg ->
                                 (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> optimizedMultiply(acc2, ord) }
+                                    .fold(acc1) { acc2, ord -> multiplyBySquaring(acc2, ord) }
                             }
                         }
                     )
@@ -512,7 +512,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
                 .forEach { (degs, c) ->
                     put(
                         List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u },
-                        c / optimizedMultiply(one, degs[variable])
+                        c / multiplyBySquaring(one, degs[variable])
                     )
                 }
         }
@@ -536,7 +536,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
                 .forEach { (degs, c) ->
                     put(
                         List(max(maxRespectedVariable + 1, degs.size)) { if (it !in variables) degs[it] else degs[it] + 1u },
-                        cleanedVariables.fold(c) { acc, variable -> acc / optimizedMultiply(one, degs[variable]) }
+                        cleanedVariables.fold(c) { acc, variable -> acc / multiplyBySquaring(one, degs[variable]) }
                     )
                 }
         }
@@ -561,7 +561,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectT
                         List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order },
                         degs[variable].let { deg ->
                             (deg downTo deg - order + 1u)
-                                .fold(c) { acc, ord -> acc / optimizedMultiply(one, ord) }
+                                .fold(c) { acc, ord -> acc / multiplyBySquaring(one, ord) }
                         }
                     )
                 }
@@ -589,7 +589,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectT
                         filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
                             degs[index].let { deg ->
                                 (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> acc2 / optimizedMultiply(one, ord) }
+                                    .fold(acc1) { acc2, ord -> acc2 / multiplyBySquaring(one, ord) }
                             }
                         }
                     )