diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt
index 12bf9f839..b07674a1e 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/LabeledPolynomial.kt
@@ -150,12 +150,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         else with(coefficients) {
             if (isEmpty()) other.asPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } + other
-                    }
+                withPutOrChanged(emptyMap(), other.asConstant()) { it -> it + other }
             )
         }
     /**
@@ -168,12 +163,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         else with(coefficients) {
             if (isEmpty()) (-other).asPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } - other
-                    }
+                withPutOrChanged(emptyMap(), (-other).asConstant()) { it -> it - other }
             )
         }
     /**
@@ -186,11 +176,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             0 -> zero
             1 -> this
             else -> LabeledPolynomialAsIs(
-                coefficients
-                    .toMutableMap()
-                    .apply {
-                        for (degs in keys) this[degs] = this[degs]!! * other
-                    }
+                coefficients.mapValues { (_, value) -> value * other }
             )
         }
 
@@ -204,12 +190,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         else with(other.coefficients) {
             if (isEmpty()) this@plus.asPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = this@plus + getOrElse(degs) { constantZero }
-                    }
+                withPutOrChanged(emptyMap(), this@plus.asConstant()) { it -> this@plus + it }
             )
         }
     /**
@@ -218,18 +199,14 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public override operator fun Int.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        if (this == 0) -other
-        else with(other.coefficients) {
-            if (isEmpty()) this@minus.asPolynomial()
-            else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        forEach { (key, value) -> if (key.isNotEmpty()) this[key] = -value }
-
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = this@minus - getOrElse(degs) { constantZero }
-                    }
+        when {
+            this == 0 -> -other
+            other.coefficients.isEmpty() -> this@minus.asPolynomial()
+            else -> LabeledPolynomialAsIs(
+                buildMap(other.coefficients.size + 1) {
+                    put(emptyMap(), asConstant())
+                    other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC })
+                }
             )
         }
     /**
@@ -242,11 +219,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             0 -> zero
             1 -> other
             else -> LabeledPolynomialAsIs(
-                other.coefficients
-                    .toMutableMap()
-                    .apply {
-                        for (degs in keys) this[degs] = this@times * this[degs]!!
-                    }
+                other.coefficients.mapValues { (_, value) -> this@times * value }
             )
         }
 
@@ -305,41 +278,26 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         with(other.coefficients) {
             if (isEmpty()) this@plus.asLabeledPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = this@plus + getOrElse(degs) { constantZero }
-                    }
+                withPutOrChanged(emptyMap(), this@plus) { it -> this@plus + it }
             )
         }
     /**
      * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        with(other.coefficients) {
-            if (isEmpty()) this@minus.asLabeledPolynomial()
-            else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
-
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = this@minus - getOrElse(degs) { constantZero }
-                    }
-            )
-        }
+        if (other.coefficients.isEmpty()) this@minus.asPolynomial()
+        else LabeledPolynomialAsIs(
+            buildMap(other.coefficients.size + 1) {
+                put(emptyMap(), this@minus)
+                other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC })
+            }
+        )
     /**
      * Returns product of the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         LabeledPolynomialAsIs(
-            other.coefficients
-                .toMutableMap()
-                .apply {
-                    for (degs in keys) this[degs] = this@times * this[degs]!!
-                }
+            other.coefficients.mapValues { this@times * it.value }
         )
 
     /**
@@ -349,12 +307,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         with(coefficients) {
             if (isEmpty()) other.asLabeledPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } + other
-                    }
+                withPutOrChanged(emptyMap(), other) { it -> it + other }
             )
         }
     /**
@@ -364,12 +317,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         with(coefficients) {
             if (isEmpty()) other.asLabeledPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyMap<Symbol, UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } - other
-                    }
+                withPutOrChanged(emptyMap(), -other) { it -> it - other }
             )
         }
     /**
@@ -377,11 +325,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      */
     override operator fun LabeledPolynomial<C>.times(other: C): LabeledPolynomial<C> =
         LabeledPolynomialAsIs(
-            coefficients
-                .toMutableMap()
-                .apply {
-                    for (degs in keys) this[degs] = this[degs]!! * other
-                }
+            coefficients.mapValues { it.value * other }
         )
 
     /**
@@ -441,38 +385,27 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         with(other.coefficients) {
             if (isEmpty()) this@plus.asPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = mapOf(this@plus to 1U)
-
-                        this[degs] = constantOne + getOrElse(degs) { constantZero }
-                    }
+                withPutOrChanged(mapOf(this@plus to 1U), constantOne) { it -> constantOne + it }
             )
         }
     /**
      * Returns difference between the variable represented as a monic monomial and the polynomial.
      */
     public override operator fun Symbol.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        with(other.coefficients) {
-            if (isEmpty()) this@minus.asPolynomial()
-            else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val theVariableDegs = mapOf(this@minus to 1U)
-
-                        forEach { (degs, c) -> if(degs != theVariableDegs) this[degs] = -c }
-
-                        this[theVariableDegs] = constantOne - getOrElse(theVariableDegs) { constantZero }
-                    }
-            )
-        }
+        if (other.coefficients.isEmpty()) this@minus.asPolynomial()
+        else LabeledPolynomialAsIs(
+            buildMap(other.coefficients.size + 1) {
+                put(mapOf(this@minus to 1U), constantOne)
+                other.coefficients.copyMapToBy(this, { _, c -> -c }) { currentC, newC -> currentC - newC }
+            }
+        )
     /**
      * Returns product of the variable represented as a monic monomial and the polynomial.
      */
     public override operator fun Symbol.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         LabeledPolynomialAsIs(
             other.coefficients
-                .mapKeys { (degs, _) -> degs.toMutableMap().also{ it[this] = if (this in it) it[this]!! + 1U else 1U } }
+                .mapKeys { (degs, _) -> degs.withPutOrChanged(this, 1u) { it -> it + 1u } }
         )
 
     /**
@@ -482,12 +415,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         with(coefficients) {
             if (isEmpty()) other.asPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = mapOf(other to 1U)
-
-                        this[degs] = constantOne + getOrElse(degs) { constantZero }
-                    }
+                withPutOrChanged(mapOf(other to 1U), constantOne) { it -> it + constantOne }
             )
         }
     /**
@@ -497,12 +425,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         with(coefficients) {
             if (isEmpty()) other.asPolynomial()
             else LabeledPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = mapOf(other to 1U)
-
-                        this[degs] = getOrElse(degs) { constantZero } - constantOne
-                    }
+                withPutOrChanged(mapOf(other to 1U), -constantOne) { it -> it - constantOne }
             )
         }
     /**
@@ -511,7 +434,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     public override operator fun LabeledPolynomial<C>.times(other: Symbol): LabeledPolynomial<C> =
         LabeledPolynomialAsIs(
             coefficients
-                .mapKeys { (degs, _) -> degs.toMutableMap().also{ it[other] = if (other in it) it[other]!! + 1U else 1U } }
+                .mapKeys { (degs, _) -> degs.withPutOrChanged(other, 1u) { it -> it + 1u } }
         )
 
     /**
@@ -526,10 +449,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      */
     override operator fun LabeledPolynomial<C>.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         LabeledPolynomialAsIs(
-            buildMap(coefficients.size + other.coefficients.size) {
-                coefficients.mapValuesTo(this) { it.value }
-                other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
-            }
+            mergeBy(coefficients, other.coefficients) { c1, c2 -> c1 + c2 }
         )
     /**
      * Returns difference of the polynomials.
@@ -537,8 +457,8 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     override operator fun LabeledPolynomial<C>.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         LabeledPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
-                coefficients.mapValuesTo(this) { it.value }
-                other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
+                coefficients.copyTo(this)
+                other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC })
             }
         )
     /**
@@ -548,10 +468,9 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         LabeledPolynomialAsIs(
             buildMap(coefficients.size * other.coefficients.size) {
                 for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
-                    val degs = degs1.toMutableMap()
-                    degs2.mapValuesTo(degs) { (variable, deg) -> degs.getOrElse(variable) { 0u } + deg }
+                    val degs = mergeBy(degs1, degs2) { deg1, deg2 -> deg1 + deg2 }
                     val c = c1 * c2
-                    this[degs] = if (degs in this) this[degs]!! + c else c
+                    this.putOrChange(degs, c) { it -> it + c }
                 }
             }
         )
@@ -581,10 +500,8 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     public override val LabeledPolynomial<C>.degrees: Map<Symbol, UInt>
         get() =
             buildMap {
-                coefficients.entries.forEach { (degs, _) ->
-                    degs.mapValuesTo(this) { (variable, deg) ->
-                        max(getOrElse(variable) { 0u }, deg)
-                    }
+                coefficients.keys.forEach { degs ->
+                    degs.copyToBy(this, ::max)
                 }
             }
     /**
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt
index 91b9c7658..17c42ac8c 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/ListPolynomial.kt
@@ -109,11 +109,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             0 -> zero
             1 -> this
             else -> ListPolynomial(
-                coefficients
-                    .toMutableList()
-                    .apply {
-                        for (deg in indices) this[deg] = this[deg] * other
-                    }
+                coefficients.map { it * other }
             )
         }
 
@@ -167,11 +163,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             0 -> zero
             1 -> other
             else -> ListPolynomial(
-                other.coefficients
-                    .toMutableList()
-                    .apply {
-                        for (deg in indices) this[deg] = this@times * this[deg]
-                    }
+                other.coefficients.map { this@times * it }
             )
         }
 
@@ -214,11 +206,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
      */
     public override operator fun C.times(other: ListPolynomial<C>): ListPolynomial<C> =
         ListPolynomial(
-            other.coefficients
-                .toMutableList()
-                .apply {
-                    for (deg in indices) this[deg] = this@times * this[deg]
-                }
+            other.coefficients.map { this@times * it }
         )
 
     /**
@@ -258,11 +246,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
      */
     public override operator fun ListPolynomial<C>.times(other: C): ListPolynomial<C> =
         ListPolynomial(
-            coefficients
-                .toMutableList()
-                .apply {
-                    for (deg in indices) this[deg] = this[deg] * other
-                }
+            coefficients.map { it * other }
         )
 
     /**
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt
index 96c96e555..14c03ff7c 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/NumberedPolynomial.kt
@@ -71,13 +71,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         if (other == 0) this
         else
             NumberedPolynomialAsIs(
-                coefficients
-                    .toMutableMap()
-                    .apply {
-                        val degs = emptyList<UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } + other
-                    }
+                coefficients.withPutOrChanged(emptyList(), other.asConstant()) { it -> it + other }
             )
     /**
      * Returns difference between the polynomial and the integer represented as a polynomial.
@@ -88,13 +82,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         if (other == 0) this
         else
             NumberedPolynomialAsIs(
-                coefficients
-                    .toMutableMap()
-                    .apply {
-                        val degs = emptyList<UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } - other
-                    }
+                coefficients.withPutOrChanged(emptyList(), (-other).asConstant()) { it -> it - other }
             )
     /**
      * Returns product of the polynomial and the integer represented as a polynomial.
@@ -106,11 +94,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
             0 -> zero
             1 -> this
             else -> NumberedPolynomialAsIs(
-                coefficients
-                    .toMutableMap()
-                    .apply {
-                        for (degs in keys) this[degs] = this[degs]!! * other
-                    }
+                coefficients.mapValues { it.value * other }
             )
         }
 
@@ -123,13 +107,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         if (this == 0) other
         else
             NumberedPolynomialAsIs(
-                other.coefficients
-                    .toMutableMap()
-                    .apply {
-                        val degs = emptyList<UInt>()
-
-                        this[degs] = this@plus + getOrElse(degs) { constantZero }
-                    }
+                other.coefficients.withPutOrChanged(emptyList(), this@plus.asConstant()) { it -> this@plus + it }
             )
     /**
      * Returns difference between the integer represented as a polynomial and the polynomial.
@@ -162,11 +140,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
             0 -> zero
             1 -> other
             else -> NumberedPolynomialAsIs(
-                other.coefficients
-                    .toMutableMap()
-                    .apply {
-                        for (degs in keys) this[degs] = this@times * this[degs]!!
-                    }
+                other.coefficients.mapValues { this@times * it.value }
             )
         }
 
@@ -177,12 +151,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         with(other.coefficients) {
             if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this@plus))
             else NumberedPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyList<UInt>()
-
-                        this[degs] = this@plus + getOrElse(degs) { constantZero }
-                    }
+                withPutOrChanged(emptyList(), this@plus) { it -> this@plus + it }
             )
         }
     /**
@@ -207,11 +176,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
      */
     override operator fun C.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         NumberedPolynomialAsIs(
-            other.coefficients
-                .toMutableMap()
-                .apply {
-                    for (degs in keys) this[degs] = this@times * this[degs]!!
-                }
+            other.coefficients.mapValues { this@times * it.value }
         )
 
     /**
@@ -221,12 +186,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         with(coefficients) {
             if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to other))
             else NumberedPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyList<UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } + other
-                    }
+                withPutOrChanged(emptyList(), other) { it -> it + other }
             )
         }
     /**
@@ -236,12 +196,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
         with(coefficients) {
             if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to other))
             else NumberedPolynomialAsIs(
-                toMutableMap()
-                    .apply {
-                        val degs = emptyList<UInt>()
-
-                        this[degs] = getOrElse(degs) { constantZero } - other
-                    }
+                withPutOrChanged(emptyList(), -other) { it -> it - other }
             )
         }
     /**
@@ -249,11 +204,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
      */
     override operator fun NumberedPolynomial<C>.times(other: C): NumberedPolynomial<C> =
         NumberedPolynomialAsIs(
-            coefficients
-                .toMutableMap()
-                .apply {
-                    for (degs in keys) this[degs] = this[degs]!! * other
-                }
+            coefficients.mapValues { it.value * other }
         )
 
     /**
@@ -274,10 +225,7 @@ 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) {
-                coefficients.mapValuesTo(this) { it.value }
-                other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
-            }
+            mergeBy(coefficients, other.coefficients) { c1, c2 -> c1 + c2 }
         )
     /**
      * Returns difference of the polynomials.
@@ -285,8 +233,8 @@ 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) {
-                coefficients.mapValuesTo(this) { it.value }
-                other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
+                coefficients.copyTo(this)
+                other.coefficients.copyMapToBy(this, { _, c -> -c }, { currentC, newC -> currentC - newC })
             }
         )
     /**
@@ -300,7 +248,7 @@ public class NumberedPolynomialSpace<C, A : Ring<C>>(
                         (0..max(degs1.lastIndex, degs2.lastIndex))
                             .map { degs1.getOrElse(it) { 0U } + degs2.getOrElse(it) { 0U } }
                     val c = c1 * c2
-                    this[degs] = if (degs in this) this[degs]!! + c else c
+                    putOrChange(degs, c) { it -> it + c }
                 }
             }
         )
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/collectionUtils.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/collectionUtils.kt
new file mode 100644
index 000000000..1d3da4c8b
--- /dev/null
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/collectionUtils.kt
@@ -0,0 +1,500 @@
+/*
+ * 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 kotlin.contracts.InvocationKind.*
+import kotlin.contracts.contract
+
+
+/**
+ * Applies the [transformation][transform] to the value corresponding to the given [key] or null instead if it's not
+ * present.
+ *
+ * @param key key to check.
+ * @param transform transformation to apply.
+ * @return result of the transformation
+ */
+internal inline fun <K, V> MutableMap<in K, V>.applyToKey(key: K, transform: (currentValue: V?) -> V): V {
+    contract {
+        callsInPlace(transform, EXACTLY_ONCE)
+    }
+    return transform(get(key)).also { this[key] = it }
+}
+
+/**
+ * Depending on presence of value corresponding to the given [key] either puts new value calculated by [valueOnPut] or
+ * changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut lazily calculated value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * current value as a parameter.
+ * @return result value corresponding to the [key].
+ */
+internal inline fun <K, V> MutableMap<K, V>.putOrChange(key: K, valueOnPut: () -> V, transformOnChange: (currentValue: V) -> V): V {
+    contract {
+        callsInPlace(valueOnPut, AT_MOST_ONCE)
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    @Suppress("UNCHECKED_CAST")
+    return (if (key !in this) valueOnPut() else transformOnChange(get(key) as V)).also { this[key] = it }
+}
+
+/**
+ * Depending on presence of value corresponding to the given [key] either puts new value [valueOnPut] or
+ * changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * current value as a parameter.
+ * @return result value corresponding to the [key].
+ */
+internal inline fun <K, V> MutableMap<K, V>.putOrChange(key: K, valueOnPut: V, transformOnChange: (currentValue: V) -> V): V {
+    contract {
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return putOrChange<K, V>(key, { valueOnPut }, transformOnChange)
+}
+
+/**
+ * Depending on presence of value corresponding to the given [key] either puts new value [valueOnPut] or
+ * changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * current value and new value as parameters.
+ * @return result value corresponding to the [key].
+ */
+internal inline fun <K, V> MutableMap<K, V>.putOrChange(key: K, valueOnPut: V, transformOnChange: (currentValue: V, newValue: V) -> V): V {
+    contract {
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return putOrChange<K, V>(key, { valueOnPut }, { transformOnChange(it, valueOnPut) })
+}
+
+/**
+ * Depending on presence of value corresponding to the given [key] either puts new value [valueOnPut] or
+ * changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * the [key], current value, and new value as parameters.
+ * @return result value corresponding to the [key].
+ */
+internal inline fun <K, V> MutableMap<K, V>.putOrChange(key: K, valueOnPut: V, transformOnChange: (key: K, currentValue: V, newValue: V) -> V): V {
+    contract {
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return putOrChange<K, V>(key, { valueOnPut }, { transformOnChange(key, it, valueOnPut) })
+}
+
+/**
+ * Creates copy of [the map][this] and applies the [transformation][transform] to the value corresponding to the given
+ * [key] in the copy or null instead if it's not present.
+ *
+ * @param key key to check.
+ * @param transform transformation to apply.
+ * @return the copy of [the map][this].
+ */
+internal inline fun <K, V> Map<in K, V>.withAppliedToKey(key: K, transform: (currentValue: V?) -> V): Map<K, V> {
+    contract {
+        callsInPlace(transform, EXACTLY_ONCE)
+    }
+    return buildMap(size) {
+        putAll(this)
+        applyToKey(key, transform)
+    }
+}
+
+/**
+ * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new
+ * value calculated by [valueOnPut] or changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut lazily calculated value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * current value as a parameter.
+ * @return the copy of [the map][this].
+ */
+internal inline fun <K, V> Map<K, V>.withPutOrChanged(key: K, valueOnPut: () -> V, transformOnChange: (currentValue: V) -> V): Map<K, V> {
+    contract {
+        callsInPlace(valueOnPut, AT_MOST_ONCE)
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return buildMap(size + 1) {
+        putAll(this@withPutOrChanged)
+        putOrChange(key, valueOnPut, transformOnChange)
+    }
+}
+
+/**
+ * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new
+ * value [valueOnPut] or changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * current value as a parameter.
+ * @return the copy of [the map][this].
+ */
+internal inline fun <K, V> Map<K, V>.withPutOrChanged(key: K, valueOnPut: V, transformOnChange: (currentValue: V) -> V): Map<K, V> {
+    contract {
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return withPutOrChanged<K, V>(key, { valueOnPut }, transformOnChange)
+}
+
+/**
+ * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new
+ * value [valueOnPut] or changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * current value and new value as parameters.
+ * @return the copy of [the map][this].
+ */
+internal inline fun <K, V> Map<K, V>.withPutOrChanged(key: K, valueOnPut: V, transformOnChange: (currentValue: V, newValue: V) -> V): Map<K, V> {
+    contract {
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return withPutOrChanged<K, V>(key, { valueOnPut }, { transformOnChange(it, valueOnPut) })
+}
+
+/**
+ * Creates copy of [the map][this] and depending on presence of value corresponding to the given [key] either puts new
+ * value [valueOnPut] or changes the present value with [transformOnChange].
+ *
+ * @param key key to check.
+ * @param valueOnPut value to put in case of absence of the [key].
+ * @param transformOnChange transform to apply to current value corresponding to the [key] in case of its presence. Uses
+ * the [key], current value, and new value as parameters.
+ * @return the copy of [the map][this].
+ */
+internal inline fun <K, V> Map<K, V>.withPutOrChanged(key: K, valueOnPut: V, transformOnChange: (key: K, currentValue: V, newValue: V) -> V): Map<K, V> {
+    contract {
+        callsInPlace(transformOnChange, AT_MOST_ONCE)
+    }
+    return withPutOrChanged<K, V>(key, { valueOnPut }, { transformOnChange(key, it, valueOnPut) })
+}
+
+/**
+ * Copies entries of [this map][this] to the [destination] map overriding present ones if needed.
+ *
+ * @receiver map to be copied.
+ * @param destination map to receive copies.
+ * @return the [destination].
+ */
+internal fun <K, V, D: MutableMap<K, V>> Map<K, V>.copyTo(destination: D): D {
+    for ((key, value) in this) {
+        destination[key] = value
+    }
+    return destination
+}
+
+/**
+ * Copies entries of [this map][this] to the [destination] map merging present entries with new ones using [resolve]
+ * lambda.
+ *
+ * @receiver map to be copied.
+ * @param destination map to receive copies.
+ * @param resolve lambda function that resolves overriding. It takes a key, current value corresponding to the key, and
+ * a new one and returns value to associate to the key.
+ * @return the [destination].
+ */
+internal inline fun <K, V: W, W, D: MutableMap<K, W>> Map<out K, V>.copyToBy(destination: D, resolve: (key: K, currentValue: W, newValue: V) -> W): D {
+    for ((key, value) in this) {
+        destination.putOrChange(key, value) { it -> resolve(key, it, value) }
+    }
+    return destination
+}
+
+/**
+ * Copies entries of [this map][this] to the [destination] map merging present entries with new ones using [resolve]
+ * lambda.
+ *
+ * @receiver map to be copied.
+ * @param destination map to receive copies.
+ * @param resolve lambda function that resolves overriding. It takes current value corresponding to some key, and
+ * a new one and returns value to associate to the key.
+ * @return the [destination].
+ */
+internal inline fun <K, V: W, W, D: MutableMap<K, W>> Map<out K, V>.copyToBy(destination: D, resolve: (currentValue: W, newValue: V) -> W): D =
+    copyToBy(destination) { _, currentValue, newValue -> resolve(currentValue, newValue) }
+
+/**
+ * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting
+ * entries to the [destination] map overriding present ones if needed. Is equivalent to
+ * ```kotlin
+ * this.mapValues(transform).copyTo(destination)
+ * ```
+ *
+ * @receiver map to be transformed and copied.
+ * @param destination map to receive copies.
+ * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is
+ * the same as initial entry.
+ * @return the [destination].
+ */
+internal inline fun <K, V, W, D: MutableMap<K, W>> Map<out K, V>.copyMapTo(destination: D, transform: (Map.Entry<K, V>) -> W): D {
+    for (entry in this) {
+        destination[entry.key] = transform(entry)
+    }
+    return destination
+}
+
+/**
+ * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting
+ * entries to the [destination] map overriding present ones if needed. Is equivalent to
+ * ```kotlin
+ * this.mapValues(transform).copyTo(destination)
+ * ```
+ *
+ * @receiver map to be transformed and copied.
+ * @param destination map to receive copies.
+ * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is
+ * the same as initial entry.
+ * @return the [destination].
+ */
+internal inline fun <K, V, W, D: MutableMap<K, W>> Map<out K, V>.copyMapTo(destination: D, transform: (key: K, value: V) -> W): D =
+    copyMapTo(destination) { (key, value) -> transform(key, value) }
+
+/**
+ * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting
+ * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to
+ * ```kotlin
+ * this.mapValues(transform).copyToBy(destination, resolve)
+ * ```
+ *
+ * @receiver map to be transformed and copied.
+ * @param destination map to receive copies.
+ * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is
+ * the same as initial entry.
+ * @param resolve lambda function that resolves overriding. It takes a key, current value corresponding to the key, and
+ * a new one and returns value to associate to the key.
+ * @return the [destination].
+ */
+internal inline fun <K, V, W, D: MutableMap<K, W>> Map<out K, V>.copyMapToBy(destination: D, transform: (Map.Entry<K, V>) -> W, resolve: (key: K, currentValue: W, newValue: V) -> W): D {
+    for (entry in this) {
+        val (key, value) = entry
+        destination.putOrChange(key, transform(entry)) { it -> resolve(key, it, value) }
+    }
+    return destination
+}
+
+/**
+ * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting
+ * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to
+ * ```kotlin
+ * this.mapValues(transform).copyToBy(destination, resolve)
+ * ```
+ *
+ * @receiver map to be transformed and copied.
+ * @param destination map to receive copies.
+ * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is
+ * the same as initial entry.
+ * @param resolve lambda function that resolves overriding. It takes a key, current value corresponding to the key, and
+ * a new one and returns value to associate to the key.
+ * @return the [destination].
+ */
+internal inline fun <K, V, W, D: MutableMap<K, W>> Map<out K, V>.copyMapToBy(destination: D, transform: (key: K, value: V) -> W, resolve: (key: K, currentValue: W, newValue: V) -> W): D =
+    copyMapToBy(destination, { (key, value) -> transform(key, value) }, resolve)
+
+/**
+ * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting
+ * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to
+ * ```kotlin
+ * this.mapValues(transform).copyToBy(destination, resolve)
+ * ```
+ *
+ * @receiver map to be transformed and copied.
+ * @param destination map to receive copies.
+ * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is
+ * the same as initial entry.
+ * @param resolve lambda function that resolves overriding. It takes current value corresponding to some key, and
+ * a new one and returns value to associate to the key.
+ * @return the [destination].
+ */
+internal inline fun <K, V, W, D: MutableMap<K, W>> Map<out K, V>.copyMapToBy(destination: D, transform: (Map.Entry<K, V>) -> W, resolve: (currentValue: W, newValue: V) -> W): D =
+    copyMapToBy(destination, transform, { _, currentValue, newValue -> resolve(currentValue, newValue) })
+
+/**
+ * Transforms values of entries of [this map][this] with [the given transformation][transform] and copies resulting
+ * entries to the [destination] map merging present entries with new ones using [resolve] lambda. Is equivalent to
+ * ```kotlin
+ * this.mapValues(transform).copyToBy(destination, resolve)
+ * ```
+ *
+ * @receiver map to be transformed and copied.
+ * @param destination map to receive copies.
+ * @param transform generates value of transformed entry using initial entry as an argument. Key of transformed entry is
+ * the same as initial entry.
+ * @param resolve lambda function that resolves overriding. It takes current value corresponding to some key, and
+ * a new one and returns value to associate to the key.
+ * @return the [destination].
+ */
+internal inline fun <K, V, W, D: MutableMap<K, W>> Map<out K, V>.copyMapToBy(destination: D, transform: (key: K, value: V) -> W, resolve: (currentValue: W, newValue: V) -> W): D =
+    copyMapToBy(destination, { (key, value) -> transform(key, value) }, { _, currentValue, newValue -> resolve(currentValue, newValue) })
+
+// TODO: Docs
+internal fun <K, V, D: MutableMap<K, V>> mergeTo(map1: Map<out K, V>, map2: Map<out K, V>, destination: D): D {
+    for ((key, value) in map1) {
+        destination.put(key, value)
+    }
+    for ((key, value) in map2) {
+        destination.put(key, value)
+    }
+    return destination
+}
+
+// TODO: Docs
+internal inline fun <K, V1: W, V2: W, W, D: MutableMap<K, W>> mergeToBy(map1: Map<out K, V1>, map2: Map<out K, V2>, destination: D, resolve: (key: K, value1: V1, value2: V2) -> W): D {
+    for (key in map2.keys) {
+        destination.remove(key)
+    }
+    for ((key, value) in map1) {
+        destination.put(key, value)
+    }
+    for ((key, value) in map2) {
+        @Suppress("UNCHECKED_CAST")
+        destination.putOrChange(key, value) { it -> resolve(key, it as V1, value) }
+    }
+    return destination
+}
+
+// TODO: Docs
+internal inline fun <K, V1: W, V2: W, W, D: MutableMap<K, W>> mergeToBy(map1: Map<K, V1>, map2: Map<K, V2>, destination: D, resolve: (value1: V1, value2: V2) -> W): D =
+    mergeToBy(map1, map2, destination) { _, value1, value2 -> resolve(value1, value2) }
+
+// TODO: Docs
+internal fun <K, V1: W, V2: W, W> merge(map1: Map<K, V1>, map2: Map<K, V2>): Map<K, W> {
+    val result = LinkedHashMap<K, W>(map1.size + map2.size)
+    return mergeTo(map1, map2, result)
+}
+
+// TODO: Docs
+internal inline fun <K, V1: W, V2: W, W> mergeBy(map1: Map<K, V1>, map2: Map<K, V2>, transform: (key: K, value1: V1, value2: V2) -> W): Map<K, W> {
+    val result = LinkedHashMap<K, W>(map1.size + map2.size)
+    return mergeToBy(map1, map2, result, transform)
+}
+
+// TODO: Docs
+internal inline fun <K, V1: W, V2: W, W> mergeBy(map1: Map<K, V1>, map2: Map<K, V2>, transform: (value1: V1, value2: V2) -> W): Map<K, W> =
+    mergeBy(map1, map2) { _, value1, value2 -> transform(value1, value2) }
+
+// TODO: Docs
+internal inline fun <T, K, V, D : MutableMap<K, V>> Iterable<T>.associateTo(destination: D, transform: (T) -> Pair<K, V>, resolve: (key: K, currentValue: V, newValue: V) -> V): D {
+    for (element in this) {
+        val (key, value) = transform(element)
+        destination.putOrChange(key, value, resolve)
+    }
+    return destination
+}
+
+// TODO: Docs
+internal inline fun <T, K, V, D : MutableMap<K, V>> Iterable<T>.associateByTo(destination: D, keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (key: K, currentValue: V, newValue: V) -> V): D {
+    for (element in this) {
+        val key = keySelector(element)
+        val value = valueTransform(element)
+        destination.putOrChange(key, value, resolve)
+    }
+    return destination
+}
+
+// TODO: Docs
+internal inline fun <T, K, D : MutableMap<K, T>> Iterable<T>.associateByTo(destination: D, keySelector: (T) -> K, resolve: (key: K, currentValue: T, newValue: T) -> T): D {
+    for (element in this) {
+        val key = keySelector(element)
+        destination.putOrChange(key, element, resolve)
+    }
+    return destination
+}
+
+// TODO: Docs
+internal inline fun <T, K, V, D : MutableMap<K, V>> Iterable<T>.associateTo(destination: D, transform: (T) -> Pair<K, V>, resolve: (currentValue: V, newValue: V) -> V): D =
+    associateTo(destination, transform) { _, currentValue, newValue -> resolve(currentValue, newValue) }
+
+// TODO: Docs
+internal inline fun <T, K, V, D : MutableMap<K, V>> Iterable<T>.associateByTo(destination: D, keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (currentValue: V, newValue: V) -> V): D =
+    associateByTo(destination, keySelector, valueTransform) { _, currentValue, newValue -> resolve(currentValue, newValue) }
+
+// TODO: Docs
+internal inline fun <T, K, D : MutableMap<K, T>> Iterable<T>.associateByTo(destination: D, keySelector: (T) -> K, resolve: (currentValue: T, newValue: T) -> T): D =
+    associateByTo(destination, keySelector) { _, currentValue, newValue -> resolve(currentValue, newValue) }
+
+// TODO: Docs
+internal inline fun <T, K, V> Iterable<T>.associate(transform: (T) -> Pair<K, V>, resolve: (key: K, currentValue: V, newValue: V) -> V): Map<K, V> =
+    associateTo(LinkedHashMap(), transform, resolve)
+
+// TODO: Docs
+internal inline fun <T, K, V> Iterable<T>.associateBy(keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (key: K, currentValue: V, newValue: V) -> V): Map<K, V> =
+    associateByTo(LinkedHashMap(), keySelector, valueTransform, resolve)
+
+// TODO: Docs
+internal inline fun <T, K> Iterable<T>.associateBy(keySelector: (T) -> K, resolve: (key: K, currentValue: T, newValue: T) -> T): Map<K, T> =
+    associateByTo(LinkedHashMap(), keySelector, resolve)
+
+// TODO: Docs
+internal inline fun <T, K, V> Iterable<T>.associate(transform: (T) -> Pair<K, V>, resolve: (currentValue: V, newValue: V) -> V): Map<K, V> =
+    associateTo(LinkedHashMap(), transform, resolve)
+
+// TODO: Docs
+internal inline fun <T, K, V> Iterable<T>.associateBy(keySelector: (T) -> K, valueTransform: (T) -> V, resolve: (currentValue: V, newValue: V) -> V): Map<K, V> =
+    associateByTo(LinkedHashMap(), keySelector, valueTransform, resolve)
+
+// TODO: Docs
+internal inline fun <T, K> Iterable<T>.associateBy(keySelector: (T) -> K, resolve: (currentValue: T, newValue: T) -> T): Map<K, T> =
+    associateByTo(LinkedHashMap(), keySelector, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, W, D : MutableMap<K, W>> Map<out K, V>.mapValuesTo(destination: D, transform: (Map.Entry<K, V>) -> W, resolve: (key: K, currentValue: W, newValue: W) -> W): D =
+    entries.associateByTo(destination, { it.key }, transform, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, W, D : MutableMap<K, W>> Map<out K, V>.mapValuesTo(destination: D, transform: (key: K, value: V) -> W, resolve: (key: K, currentValue: W, newValue: W) -> W): D =
+    entries.associateByTo(destination, { it.key }, { (key, value) -> transform(key, value) }, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, W, D : MutableMap<K, W>> Map<out K, V>.mapValuesTo(destination: D, transform: (Map.Entry<K, V>) -> W, resolve: (currentValue: W, newValue: W) -> W): D =
+    entries.associateByTo(destination, { it.key }, transform, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, W, D : MutableMap<K, W>> Map<out K, V>.mapValuesTo(destination: D, transform: (key: K, value: V) -> W, resolve: (currentValue: W, newValue: W) -> W): D =
+    entries.associateByTo(destination, { it.key }, { (key, value) -> transform(key, value) }, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L, D : MutableMap<L, V>> Map<out K, V>.mapKeysTo(destination: D, transform: (Map.Entry<K, V>) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): D =
+    entries.associateByTo(destination, transform, { it.value }, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L, D : MutableMap<L, V>> Map<out K, V>.mapKeysTo(destination: D, transform: (key: K, value: V) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): D =
+    entries.associateByTo(destination, { (key, value) -> transform(key, value) }, { it.value }, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L, D : MutableMap<L, V>> Map<out K, V>.mapKeysTo(destination: D, transform: (Map.Entry<K, V>) -> L, resolve: (currentValue: V, newValue: V) -> V): D =
+    entries.associateByTo(destination, transform, { it.value }, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L, D : MutableMap<L, V>> Map<out K, V>.mapKeysTo(destination: D, transform: (key: K, value: V) -> L, resolve: (currentValue: V, newValue: V) -> V): D =
+    entries.associateByTo(destination, { (key, value) -> transform(key, value) }, { it.value }, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L> Map<out K, V>.mapKeys(transform: (Map.Entry<K, V>) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): Map<L, V> =
+    mapKeysTo(LinkedHashMap(size), transform, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L> Map<out K, V>.mapKeys(transform: (key: K, value: V) -> L, resolve: (key: L, currentValue: V, newValue: V) -> V): Map<L, V> =
+    mapKeysTo(LinkedHashMap(size), transform, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L> Map<out K, V>.mapKeys(transform: (Map.Entry<K, V>) -> L, resolve: (currentValue: V, newValue: V) -> V): Map<L, V> =
+    mapKeysTo(LinkedHashMap(size), transform, resolve)
+
+// TODO: Docs
+internal inline fun <K, V, L> Map<out K, V>.mapKeys(transform: (key: K, value: V) -> L, resolve: (currentValue: V, newValue: V) -> V): Map<L, V> =
+    mapKeysTo(LinkedHashMap(size), transform, resolve)
\ No newline at end of file
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt
index aa44660c1..43048089e 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledConstructors.kt
@@ -10,6 +10,7 @@ package space.kscience.kmath.functions
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.invoke
 
 
 /**
@@ -76,17 +77,10 @@ public inline fun <C> LabeledPolynomialWithoutCheck(vararg pairs: Pair<Map<Symbo
  *
  * @see LabeledPolynomialWithoutCheck
  */
-public fun <C> LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, add: (C, C) -> C) : LabeledPolynomial<C> {
-    val fixedCoefs = mutableMapOf<Map<Symbol, UInt>, C>()
-
-    for (entry in coefs) {
-        val key = entry.key.cleanUp()
-        val value = entry.value
-        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
-    }
-
-    return LabeledPolynomial<C>(fixedCoefs)
-}
+public fun <C> LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, add: (C, C) -> C) : LabeledPolynomial<C> =
+    LabeledPolynomialAsIs(
+        coefs.mapKeys({ key, _ -> key.cleanUp() }, add)
+    )
 
 /**
  * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
@@ -98,17 +92,10 @@ public fun <C> LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, add: (C, C) -
  *
  * @see LabeledPolynomialWithoutCheck
  */
-public fun <C> LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, add: (C, C) -> C) : LabeledPolynomial<C> {
-    val fixedCoefs = mutableMapOf<Map<Symbol, UInt>, C>()
-
-    for (entry in pairs) {
-        val key = entry.first.cleanUp()
-        val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
-    }
-
-    return LabeledPolynomial<C>(fixedCoefs)
-}
+public fun <C> LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, add: (C, C) -> C) : LabeledPolynomial<C> =
+    LabeledPolynomialAsIs(
+        pairs.associateBy({ it.first.cleanUp() }, { it.second }, add)
+    )
 
 /**
  * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
@@ -120,17 +107,10 @@ public fun <C> LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>,
  *
  * @see LabeledPolynomialWithoutCheck
  */
-public fun <C> LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, add: (C, C) -> C) : LabeledPolynomial<C> {
-    val fixedCoefs = mutableMapOf<Map<Symbol, UInt>, C>()
-
-    for (entry in pairs) {
-        val key = entry.first.cleanUp()
-        val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
-    }
-
-    return LabeledPolynomial<C>(fixedCoefs)
-}
+public fun <C> LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, add: (C, C) -> C) : LabeledPolynomial<C> =
+    LabeledPolynomialAsIs(
+        pairs.asIterable().associateBy({ it.first.cleanUp() }, { it.second }, add)
+    )
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
@@ -304,7 +284,7 @@ public class DSL1LabeledPolynomialTermSignatureBuilder {
      */
     public infix fun Symbol.inPowerOf(deg: UInt) {
         if (deg == 0u) return
-        signature[this] = signature.getOrElse(this) { 0u } + deg
+        signature.putOrChange(this, deg) { it -> it + deg }
     }
     /**
      * Declares power of [this] variable of degree [deg].
@@ -362,7 +342,7 @@ public class DSL1LabeledPolynomialBuilder<C>(
      * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
      */
     public infix fun C.with(signature: Map<Symbol, UInt>) {
-        coefficients[signature] = if (signature in coefficients) add(coefficients[signature]!!, this@with) else this@with
+        coefficients.putOrChange(signature, this@with, add)
     }
     /**
      * Declares monomial with [this] coefficient and signature constructed by [block].
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
index e3b35facc..a37a1fe39 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/labeledUtil.kt
@@ -7,10 +7,7 @@ package space.kscience.kmath.functions
 
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.Field
-import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.algebra
-import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.operations.*
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 import kotlin.jvm.JvmName
@@ -56,7 +53,7 @@ public fun LabeledPolynomial<Double>.substitute(args: Map<Symbol, Double>): Labe
                     val deg = degs.getOrElse(variable) { 0u }
                     if (deg == 0u) product else product * power(substitution, deg)
                 }
-                this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
+                putOrChange(newDegs, newC, ::add)
             }
         }
     )
@@ -75,7 +72,7 @@ public fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, args: Map<Symbol,
                     val deg = degs.getOrElse(variable) { 0u }
                     if (deg == 0u) product else product * power(substitution, deg)
                 }
-                this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
+                putOrChange(newDegs, newC, ::add)
             }
         }
     )
@@ -257,10 +254,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
         buildMap(coefficients.size) {
             coefficients
                 .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        put(variable, 1u)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
+                    val newDegs = degs.withPutOrChanged(variable, 1u) { it -> it + 1u }
                     put(
                         newDegs,
                         c / multiplyByDoubling(one, newDegs[variable]!!)
@@ -284,10 +278,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo
         buildMap(coefficients.size) {
             coefficients
                 .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        put(variable, order)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
+                    val newDegs = degs.withPutOrChanged(variable, order) { it -> it + order }
                     put(
                         newDegs,
                         newDegs[variable]!!.let { deg ->
@@ -314,10 +305,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo
         buildMap(coefficients.size) {
             coefficients
                 .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        for ((variable, order) in filteredVariablesAndOrders) put(variable, order)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
+                    val newDegs = mergeBy(degs, filteredVariablesAndOrders) { deg, order -> deg + order }
                     put(
                         newDegs,
                         filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt
index ce0db3d17..ce49088ae 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedConstructors.kt
@@ -75,17 +75,10 @@ public inline fun <C> NumberedPolynomialWithoutCheck(vararg pairs: Pair<List<UIn
  *
  * @see NumberedPolynomialWithoutCheck
  */
-public fun <C> NumberedPolynomial(coefs: Map<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> {
-    val fixedCoefs = mutableMapOf<List<UInt>, C>()
-
-    for (entry in coefs) {
-        val key = entry.key.cleanUp()
-        val value = entry.value
-        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
-    }
-
-    return NumberedPolynomial<C>(fixedCoefs)
-}
+public fun <C> NumberedPolynomial(coefs: Map<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> =
+    NumberedPolynomialAsIs(
+        coefs.mapKeys({ key, _ -> key.cleanUp() }, add)
+    )
 
 /**
  * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
@@ -97,17 +90,10 @@ public fun <C> NumberedPolynomial(coefs: Map<List<UInt>, C>, add: (C, C) -> C) :
  *
  * @see NumberedPolynomialWithoutCheck
  */
-public fun <C> NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, add: (C, C) -> C) : NumberedPolynomial<C> {
-    val fixedCoefs = mutableMapOf<List<UInt>, C>()
-
-    for (entry in pairs) {
-        val key = entry.first.cleanUp()
-        val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
-    }
-
-    return NumberedPolynomial<C>(fixedCoefs)
-}
+public fun <C> NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, add: (C, C) -> C) : NumberedPolynomial<C> =
+    NumberedPolynomialAsIs(
+        pairs.associateBy({ it.first.cleanUp() }, { it.second }, add)
+    )
 
 /**
  * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
@@ -119,17 +105,10 @@ public fun <C> NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, add: (
  *
  * @see NumberedPolynomialWithoutCheck
  */
-public fun <C> NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> {
-    val fixedCoefs = mutableMapOf<List<UInt>, C>()
-
-    for (entry in pairs) {
-        val key = entry.first.cleanUp()
-        val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
-    }
-
-    return NumberedPolynomial<C>(fixedCoefs)
-}
+public fun <C> NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> =
+    NumberedPolynomialAsIs(
+        pairs.asIterable().associateBy({ it.first.cleanUp() }, { it.second }, add)
+    )
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
@@ -349,7 +328,7 @@ public class DSL1NumberedPolynomialBuilder<C>(
      * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
      */
     public infix fun C.with(signature: List<UInt>) {
-        coefficients[signature] = if (signature in coefficients) add(coefficients[signature]!!, this@with) else this@with
+        coefficients.putOrChange(signature, this@with, add)
     }
     /**
      * Declares monomial with [this] coefficient and signature constructed by [block].
diff --git a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt
index 9d88cd648..9f29cf31a 100644
--- a/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt
+++ b/kmath-polynomial/src/commonMain/kotlin/space.kscience.kmath.functions/numberedUtil.kt
@@ -58,7 +58,7 @@ public fun NumberedPolynomial<Double>.substitute(args: Map<Int, Double>): Number
                     val deg = degs.getOrElse(variable) { 0u }
                     if (deg == 0u) product else product * substitution.pow(deg.toInt())
                 }
-                this[newDegs] = if (newDegs !in this) newC else this[newDegs]!! + newC
+                putOrChange(newDegs, newC) { it -> it + newC }
             }
         }
     )
@@ -76,7 +76,7 @@ public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>
                     val deg = degs.getOrElse(variable) { 0u }
                     if (deg == 0u) product else product * power(substitution, deg)
                 }
-                this[newDegs] = if (newDegs !in this) newC else this[newDegs]!! + newC
+                putOrChange(newDegs, newC) { it -> it + newC }
             }
         }
     )
@@ -158,8 +158,7 @@ public fun NumberedPolynomial<Double>.substitute(args: Buffer<Double>): Numbered
                     val deg = degs[variable]
                     if (deg == 0u) product else product * args[variable].pow(deg.toInt())
                 }
-                if (newDegs !in this) this[newDegs] = newC
-                else this[newDegs] = this[newDegs]!! + newC
+                putOrChange(newDegs, newC) { it -> it + newC }
             }
         }
     )
@@ -183,8 +182,7 @@ public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Buffer<C>):
                     val deg = degs[variable]
                     if (deg == 0u) product else product * power(args[variable], deg)
                 }
-                if (newDegs !in this) this[newDegs] = newC
-                else this[newDegs] = this[newDegs]!! + newC
+                putOrChange(newDegs, newC) { it -> it + newC }
             }
         }
     )
diff --git a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt
index f9a5a041b..1815749ce 100644
--- a/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt
+++ b/kmath-polynomial/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt
@@ -23,8 +23,8 @@ class NumberedConstructorsTest {
             ),
             Int.algebra.numberedPolynomialSpace {
                 NumberedPolynomialDSL1 {
-                    5 { 1 pow 2u; 3 pow 3u }
-                    (-6) { 2 pow 1u }
+                    5 { 0 pow 2u; 2 pow 3u }
+                    (-6) { 1 pow 1u }
                 }
             },
             "test 1"
@@ -47,8 +47,8 @@ class NumberedConstructorsTest {
             ),
             Int.algebra.numberedPolynomialSpace {
                 NumberedPolynomialDSL1 {
-                    5 { 1 pow 1u; 1 pow 1u }
-                    (-6) { 1 pow 2u }
+                    5 { 0 pow 1u; 0 pow 1u }
+                    (-6) { 0 pow 2u }
                 }
             },
             "test 3"
@@ -59,8 +59,8 @@ class NumberedConstructorsTest {
             ),
             Int.algebra.numberedPolynomialSpace {
                 NumberedPolynomialDSL1 {
-                    5 { 1 pow 1u; 1 pow 1u }
-                    (-6) { 1 pow 2u; 3 pow 0u }
+                    5 { 0 pow 1u; 0 pow 1u }
+                    (-6) { 0 pow 2u; 2 pow 0u }
                 }
             },
             "test 3"