From 0ac5363acf7c6717275989ec6c3376a05002b953 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sat, 16 Oct 2021 11:10:34 +0300
Subject: [PATCH 01/10] Multik wrapper prototype

---
 examples/build.gradle.kts                     |  14 +-
 .../space/kscience/kmath/tensors/multik.kt    |  21 ++
 kmath-multik/build.gradle.kts                 |  14 ++
 .../kmath/multik/MultikTensorAlgebra.kt       | 199 ++++++++++++++++++
 4 files changed, 244 insertions(+), 4 deletions(-)
 create mode 100644 examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
 create mode 100644 kmath-multik/build.gradle.kts
 create mode 100644 kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt

diff --git a/examples/build.gradle.kts b/examples/build.gradle.kts
index d06005321..7b1bce26a 100644
--- a/examples/build.gradle.kts
+++ b/examples/build.gradle.kts
@@ -29,6 +29,11 @@ dependencies {
     implementation(project(":kmath-tensors"))
     implementation(project(":kmath-symja"))
     implementation(project(":kmath-for-real"))
+    //jafama
+    implementation(project(":kmath-jafama"))
+    //multik
+    implementation(projects.kmathMultik)
+
 
     implementation("org.nd4j:nd4j-native:1.0.0-beta7")
 
@@ -42,11 +47,12 @@ dependencies {
 //    } else
     implementation("org.nd4j:nd4j-native-platform:1.0.0-beta7")
 
-    implementation("org.slf4j:slf4j-simple:1.7.31")
+    // multik implementation
+    implementation("org.jetbrains.kotlinx:multik-default:0.1.0")
+
+    implementation("org.slf4j:slf4j-simple:1.7.32")
     // plotting
-    implementation("space.kscience:plotlykt-server:0.4.2")
-    //jafama
-    implementation(project(":kmath-jafama"))
+    implementation("space.kscience:plotlykt-server:0.5.0")
 }
 
 kotlin.sourceSets.all {
diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
new file mode 100644
index 000000000..820a793ac
--- /dev/null
+++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
@@ -0,0 +1,21 @@
+/*
+ * 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 file.
+ */
+
+package space.kscience.kmath.tensors
+
+import org.jetbrains.kotlinx.multik.api.Multik
+import org.jetbrains.kotlinx.multik.api.linalg.dot
+import org.jetbrains.kotlinx.multik.api.ndarray
+import org.jetbrains.kotlinx.multik.ndarray.operations.minus
+import org.jetbrains.kotlinx.multik.ndarray.operations.plus
+import org.jetbrains.kotlinx.multik.ndarray.operations.unaryMinus
+
+fun main() {
+    val a = Multik.ndarray(intArrayOf(1, 2, 3))
+    val b = Multik.ndarray(doubleArrayOf(1.0, 2.0, 3.0))
+    2 + (-a) - 2
+
+    a dot a
+}
\ No newline at end of file
diff --git a/kmath-multik/build.gradle.kts b/kmath-multik/build.gradle.kts
new file mode 100644
index 000000000..16a7ab652
--- /dev/null
+++ b/kmath-multik/build.gradle.kts
@@ -0,0 +1,14 @@
+plugins {
+    id("ru.mipt.npm.gradle.jvm")
+}
+
+description = "JetBrains Multik connector"
+
+dependencies {
+    api(project(":kmath-tensors"))
+    api("org.jetbrains.kotlinx:multik-api:0.1.0")
+}
+
+readme {
+    maturity = ru.mipt.npm.gradle.Maturity.PROTOTYPE
+}
\ No newline at end of file
diff --git a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
new file mode 100644
index 000000000..b25d3ef56
--- /dev/null
+++ b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
@@ -0,0 +1,199 @@
+/*
+ * 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 file.
+ */
+
+package space.kscience.kmath.multik
+
+import org.jetbrains.kotlinx.multik.ndarray.data.*
+import org.jetbrains.kotlinx.multik.ndarray.operations.*
+import space.kscience.kmath.misc.PerformancePitfall
+import space.kscience.kmath.nd.mapInPlace
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.tensors.api.Tensor
+import space.kscience.kmath.tensors.api.TensorAlgebra
+
+@JvmInline
+public value class MultikTensor<T>(public val array: MutableMultiArray<T, DN>) : Tensor<T> {
+    override val shape: IntArray get() = array.shape
+
+    override fun get(index: IntArray): T = array[index]
+
+    @PerformancePitfall
+    override fun elements(): Sequence<Pair<IntArray, T>> =
+        array.multiIndices.iterator().asSequence().map { it to get(it) }
+
+    override fun set(index: IntArray, value: T) {
+        array[index] = value
+    }
+}
+
+
+public abstract class MultikTensorAlgebra<T>(
+    public val elementAlgebra: Ring<T>,
+    public val comparator: Comparator<T>
+) : TensorAlgebra<T> {
+
+    /**
+     * Convert a tensor to [MultikTensor] if necessary. If tensor is converted, changes on the resulting tensor
+     * are not reflected back onto the source
+     */
+    public fun Tensor<T>.asMultik(): MultikTensor<T> {
+        return if (this is MultikTensor) {
+            this
+        } else {
+            TODO()
+        }
+    }
+
+    public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+
+    override fun Tensor<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
+        get(intArrayOf(0))
+    } else null
+
+    override fun T.plus(other: Tensor<T>): MultikTensor<T> =
+        other.plus(this)
+
+    override fun Tensor<T>.plus(value: T): MultikTensor<T> =
+        asMultik().array.deepCopy().apply { plusAssign(value) }.wrap()
+
+    override fun Tensor<T>.plus(other: Tensor<T>): MultikTensor<T> =
+        asMultik().array.plus(other.asMultik().array).wrap()
+
+    override fun Tensor<T>.plusAssign(value: T) {
+        if (this is MultikTensor) {
+            array.plusAssign(value)
+        } else {
+            mapInPlace { _, t -> elementAlgebra.add(t, value) }
+        }
+    }
+
+    override fun Tensor<T>.plusAssign(other: Tensor<T>) {
+        if (this is MultikTensor) {
+            array.plusAssign(other.asMultik().array)
+        } else {
+            mapInPlace { index, t -> elementAlgebra.add(t, other[index]) }
+        }
+    }
+
+    //TODO avoid additional copy
+    override fun T.minus(other: Tensor<T>): MultikTensor<T> = -(other - this)
+
+    override fun Tensor<T>.minus(value: T): MultikTensor<T> =
+        asMultik().array.deepCopy().apply { minusAssign(value) }.wrap()
+
+    override fun Tensor<T>.minus(other: Tensor<T>): MultikTensor<T> =
+        asMultik().array.minus(other.asMultik().array).wrap()
+
+    override fun Tensor<T>.minusAssign(value: T) {
+        if (this is MultikTensor) {
+            array.minusAssign(value)
+        } else {
+            mapInPlace { _, t -> elementAlgebra.run { t - value } }
+        }
+    }
+
+    override fun Tensor<T>.minusAssign(other: Tensor<T>) {
+        if (this is MultikTensor) {
+            array.minusAssign(other.asMultik().array)
+        } else {
+            mapInPlace { index, t -> elementAlgebra.run { t - other[index] } }
+        }
+    }
+
+    override fun T.times(other: Tensor<T>): MultikTensor<T> =
+        other.asMultik().array.deepCopy().apply { timesAssign(this@times) }.wrap()
+
+    override fun Tensor<T>.times(value: T): Tensor<T> =
+        asMultik().array.deepCopy().apply { timesAssign(value) }.wrap()
+
+    override fun Tensor<T>.times(other: Tensor<T>): MultikTensor<T> =
+        asMultik().array.times(other.asMultik().array).wrap()
+
+    override fun Tensor<T>.timesAssign(value: T) {
+        if (this is MultikTensor) {
+            array.timesAssign(value)
+        } else {
+            mapInPlace { _, t -> elementAlgebra.multiply(t, value) }
+        }
+    }
+
+    override fun Tensor<T>.timesAssign(other: Tensor<T>) {
+        if (this is MultikTensor) {
+            array.timesAssign(other.asMultik().array)
+        } else {
+            mapInPlace { index, t -> elementAlgebra.multiply(t, other[index]) }
+        }
+    }
+
+    override fun Tensor<T>.unaryMinus(): MultikTensor<T> =
+        asMultik().array.unaryMinus().wrap()
+
+    override fun Tensor<T>.get(i: Int): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.transpose(i: Int, j: Int): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.view(shape: IntArray): MultikTensor<T> {
+        require(shape.all { it > 0 })
+        require(shape.fold(1, Int::times) == this.shape.size) {
+            "Cannot reshape array of size ${this.shape.size} into a new shape ${
+                shape.joinToString(
+                    prefix = "(",
+                    postfix = ")"
+                )
+            }"
+        }
+
+        val mt = asMultik().array
+        return if (mt.shape.contentEquals(shape)) {
+            @Suppress("UNCHECKED_CAST")
+            this as NDArray<T, DN>
+        } else {
+            NDArray(mt.data, mt.offset, shape, dim = DN(shape.size), base = mt.base ?: mt)
+        }.wrap()
+    }
+
+    override fun Tensor<T>.viewAs(other: Tensor<T>): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.dot(other: Tensor<T>): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun diagonalEmbedding(diagonalEntries: Tensor<T>, offset: Int, dim1: Int, dim2: Int): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.sum(): T = asMultik().array.reduceMultiIndexed { _: IntArray, acc: T, t: T ->
+        elementAlgebra.add(acc, t)
+    }
+
+    override fun Tensor<T>.sum(dim: Int, keepDim: Boolean): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.min(): T =
+        asMultik().array.minWith(comparator) ?: error("No elements in tensor")
+
+    override fun Tensor<T>.min(dim: Int, keepDim: Boolean): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.max(): T =
+        asMultik().array.maxWith(comparator) ?: error("No elements in tensor")
+
+
+    override fun Tensor<T>.max(dim: Int, keepDim: Boolean): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+
+    override fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): MultikTensor<T> {
+        TODO("Not yet implemented")
+    }
+}
\ No newline at end of file

From d0354da80a52e56fdb81dadd881a0ab4fa0a0d24 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 17 Oct 2021 11:12:35 +0300
Subject: [PATCH 02/10] Shapeless ND and Buffer algebras

---
 CHANGELOG.md                                  |   3 +
 .../kmath/benchmarks/NDFieldBenchmark.kt      |  32 ++-
 .../kmath/benchmarks/ViktorBenchmark.kt       |  20 +-
 .../kmath/benchmarks/ViktorLogBenchmark.kt    |  20 +-
 .../kscience/kmath/operations/complexDemo.kt  |  12 +-
 .../kscience/kmath/structures/NDField.kt      |   4 +-
 .../kmath/structures/StreamDoubleFieldND.kt   |  10 +-
 .../kscience/kmath/structures/buffers.kt      |   3 +-
 gradle/wrapper/gradle-wrapper.properties      |   2 +-
 .../kotlin/space/kscience/kmath/ast/parser.kt |  16 +-
 .../kscience/kmath/ast/rendering/features.kt  |  30 +-
 .../kscience/kmath/ast/rendering/phases.kt    |  14 +-
 .../kscience/kmath/ast/rendering/TestLatex.kt |   4 +-
 .../kmath/ast/rendering/TestMathML.kt         |   4 +-
 .../kmath/wasm/internal/WasmBuilder.kt        |  22 +-
 .../DerivativeStructureExpression.kt          |   4 +-
 .../space/kscience/kmath/complex/Complex.kt   |   3 +-
 .../kscience/kmath/complex/ComplexFieldND.kt  | 134 +++------
 .../kscience/kmath/complex/Quaternion.kt      |   2 +-
 .../FunctionalExpressionAlgebra.kt            |   8 +-
 .../kscience/kmath/expressions/MstAlgebra.kt  |  24 +-
 .../kmath/expressions/SimpleAutoDiff.kt       |   2 +-
 .../kmath/linear/BufferedLinearSpace.kt       |  29 +-
 .../kmath/linear/DoubleLinearSpace.kt         |  30 +-
 .../kscience/kmath/linear/LinearSpace.kt      |   3 +-
 .../space/kscience/kmath/nd/AlgebraND.kt      | 116 +++-----
 .../kscience/kmath/nd/BufferAlgebraND.kt      | 262 ++++++++++--------
 .../space/kscience/kmath/nd/BufferND.kt       |  24 +-
 .../space/kscience/kmath/nd/DoubleFieldND.kt  | 132 +++------
 .../space/kscience/kmath/nd/ShapeIndex.kt     | 120 ++++++++
 .../space/kscience/kmath/nd/ShortRingND.kt    |  25 +-
 .../space/kscience/kmath/nd/StructureND.kt    | 110 +-------
 .../kscience/kmath/nd/algebraNDExtentions.kt  |  34 +++
 .../kscience/kmath/operations/Algebra.kt      |  14 +-
 .../space/kscience/kmath/operations/BigInt.kt |   8 +-
 .../kmath/operations/BufferAlgebra.kt         | 179 +++++++-----
 .../kmath/operations/DoubleBufferField.kt     |  14 +-
 ...BufferOperations.kt => DoubleBufferOps.kt} |   6 +-
 .../kmath/operations/NumericAlgebra.kt        |   2 +-
 .../kscience/kmath/operations/numbers.kt      |   8 +-
 .../kscience/kmath/structures/NDFieldTest.kt  |   3 +-
 .../kmath/structures/NumberNDFieldTest.kt     |  13 +-
 .../space/kscience/kmath/chains/flowExtra.kt  |   4 +-
 .../space/kscience/kmath/real/realND.kt       |   4 +-
 .../kmath/histogram/DoubleHistogramSpace.kt   |   9 +-
 .../kmath/histogram/IndexedHistogramSpace.kt  |   9 +-
 .../histogram/MultivariateHistogramTest.kt    |   3 +-
 .../kmath/kotlingrad/scalarsAdapters.kt       |  12 +-
 .../kscience/kmath/nd4j/Nd4jArrayAlgebra.kt   | 164 +++++------
 .../kmath/nd4j/Nd4jArrayAlgebraTest.kt        |  18 +-
 .../space/kscience/kmath/symja/adapters.kt    |  12 +-
 .../kmath/tensors/core/DoubleTensorAlgebra.kt |   8 +-
 .../core/internal/TensorLinearStructure.kt    |  16 +-
 .../tensors/core/internal/tensorCastsUtils.kt |   7 +-
 .../kmath/viktor/ViktorStructureND.kt         |  20 +-
 settings.gradle.kts                           |   8 +-
 56 files changed, 893 insertions(+), 906 deletions(-)
 create mode 100644 kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt
 create mode 100644 kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
 rename kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/{DoubleBufferOperations.kt => DoubleBufferOps.kt} (97%)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 05376d425..bb267744e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -42,6 +42,9 @@
 - Use `Symbol` factory function instead of `StringSymbol`
 - New discoverability pattern: `<Type>.algebra.<nd/etc>`
 - Adjusted commons-math API for linear solvers to match conventions.
+- Buffer algebra does not require size anymore
+- Operations -> Ops
+- Default Buffer and ND algebras are now Ops and lack neutral elements (0, 1) as well as algebra-level shapes.
 
 ### Deprecated
 - Specialized `DoubleBufferAlgebra`
diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
index 76fec05d3..950a10b33 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
@@ -9,9 +9,10 @@ import kotlinx.benchmark.Benchmark
 import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
+import space.kscience.kmath.nd.BufferedFieldOpsND
 import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.autoNdAlgebra
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.one
 import space.kscience.kmath.nd4j.nd4j
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.Buffer
@@ -23,21 +24,21 @@ import space.kscience.kmath.tensors.core.tensorAlgebra
 internal class NDFieldBenchmark {
     @Benchmark
     fun autoFieldAdd(blackhole: Blackhole) = with(autoField) {
-        var res: StructureND<Double> = one
-        repeat(n) { res += one }
+        var res: StructureND<Double> = one(shape)
+        repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
 
     @Benchmark
     fun specializedFieldAdd(blackhole: Blackhole) = with(specializedField) {
-        var res: StructureND<Double> = one
+        var res: StructureND<Double> = one(shape)
         repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
 
     @Benchmark
     fun boxingFieldAdd(blackhole: Blackhole) = with(genericField) {
-        var res: StructureND<Double> = one
+        var res: StructureND<Double> = one(shape)
         repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
@@ -56,19 +57,20 @@ internal class NDFieldBenchmark {
         blackhole.consume(res)
     }
 
-//    @Benchmark
-//    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
-//        var res: StructureND<Double> = one
-//        repeat(n) { res += 1.0 }
-//        blackhole.consume(res)
-//    }
+    @Benchmark
+    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
+        var res: StructureND<Double> = one(dim, dim)
+        repeat(n) { res += 1.0 }
+        blackhole.consume(res)
+    }
 
     private companion object {
         private const val dim = 1000
         private const val n = 100
-        private val autoField = DoubleField.autoNdAlgebra(dim, dim)
-        private val specializedField = DoubleField.ndAlgebra(dim, dim)
-        private val genericField = DoubleField.ndAlgebra(Buffer.Companion::boxing, dim, dim)
-        private val nd4jField = DoubleField.nd4j(dim, dim)
+        private val shape = intArrayOf(dim, dim)
+        private val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
+        private val specializedField = DoubleField.ndAlgebra
+        private val genericField = BufferedFieldOpsND(DoubleField, Buffer.Companion::boxing)
+        private val nd4jField = DoubleField.nd4j
     }
 }
diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt
index b97a05a52..6b4d5759b 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt
@@ -10,18 +10,17 @@ import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
 import org.jetbrains.bio.viktor.F64Array
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.autoNdAlgebra
-import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.viktor.ViktorNDField
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.viktor.ViktorFieldND
 
 @State(Scope.Benchmark)
 internal class ViktorBenchmark {
     @Benchmark
     fun automaticFieldAddition(blackhole: Blackhole) {
         with(autoField) {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
             blackhole.consume(res)
         }
@@ -30,7 +29,7 @@ internal class ViktorBenchmark {
     @Benchmark
     fun realFieldAddition(blackhole: Blackhole) {
         with(realField) {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
             blackhole.consume(res)
         }
@@ -39,7 +38,7 @@ internal class ViktorBenchmark {
     @Benchmark
     fun viktorFieldAddition(blackhole: Blackhole) {
         with(viktorField) {
-            var res = one
+            var res = one(shape)
             repeat(n) { res += 1.0 }
             blackhole.consume(res)
         }
@@ -56,10 +55,11 @@ internal class ViktorBenchmark {
     private companion object {
         private const val dim = 1000
         private const val n = 100
+        private val shape = Shape(dim, dim)
 
         // automatically build context most suited for given type.
-        private val autoField = DoubleField.autoNdAlgebra(dim, dim)
-        private val realField = DoubleField.ndAlgebra(dim, dim)
-        private val viktorField = ViktorNDField(dim, dim)
+        private val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
+        private val realField = DoubleField.ndAlgebra
+        private val viktorField = ViktorFieldND(dim, dim)
     }
 }
diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
index 91e9dcd76..ef2adaad8 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
@@ -10,18 +10,21 @@ import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
 import org.jetbrains.bio.viktor.F64Array
-import space.kscience.kmath.nd.autoNdAlgebra
+import space.kscience.kmath.nd.BufferedFieldOpsND
+import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.one
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.viktor.ViktorFieldND
 
 @State(Scope.Benchmark)
 internal class ViktorLogBenchmark {
     @Benchmark
     fun realFieldLog(blackhole: Blackhole) {
-        with(realNdField) {
-            val fortyTwo = produce { 42.0 }
-            var res = one
+        with(realField) {
+            val fortyTwo = produce(shape) { 42.0 }
+            var res = one(shape)
             repeat(n) { res = ln(fortyTwo) }
             blackhole.consume(res)
         }
@@ -30,7 +33,7 @@ internal class ViktorLogBenchmark {
     @Benchmark
     fun viktorFieldLog(blackhole: Blackhole) {
         with(viktorField) {
-            val fortyTwo = produce { 42.0 }
+            val fortyTwo = produce(shape) { 42.0 }
             var res = one
             repeat(n) { res = ln(fortyTwo) }
             blackhole.consume(res)
@@ -48,10 +51,11 @@ internal class ViktorLogBenchmark {
     private companion object {
         private const val dim = 1000
         private const val n = 100
+        private val shape = Shape(dim, dim)
 
         // automatically build context most suited for given type.
-        private val autoField = DoubleField.autoNdAlgebra(dim, dim)
-        private val realNdField = DoubleField.ndAlgebra(dim, dim)
-        private val viktorField = ViktorFieldND(intArrayOf(dim, dim))
+        private val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
+        private val realField = DoubleField.ndAlgebra
+        private val viktorField = ViktorFieldND(dim, dim)
     }
 }
diff --git a/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt b/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
index 319221bcc..67d83d77c 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
@@ -11,27 +11,27 @@ import space.kscience.kmath.complex.bufferAlgebra
 import space.kscience.kmath.complex.ndAlgebra
 import space.kscience.kmath.nd.BufferND
 import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.produce
 
 fun main() = Complex.algebra {
     val complex = 2 + 2 * i
     println(complex * 8 - 5 * i)
 
     //flat buffer
-    val buffer = bufferAlgebra(8).run {
-        buffer { Complex(it, -it) }.map { Complex(it.im, it.re) }
+    val buffer = with(bufferAlgebra){
+        buffer(8) { Complex(it, -it) }.map { Complex(it.im, it.re) }
     }
     println(buffer)
 
-
     // 2d element
-    val element: BufferND<Complex> = ndAlgebra(2, 2).produce { (i, j) ->
+    val element: BufferND<Complex> = ndAlgebra.produce(2, 2) { (i, j) ->
         Complex(i - j, i + j)
     }
     println(element)
 
     // 1d element operation
-    val result: StructureND<Complex> = ndAlgebra(8).run {
-        val a = produce { (it) -> i * it - it.toDouble() }
+    val result: StructureND<Complex> = ndAlgebra{
+        val a = produce(8) { (it) -> i * it - it.toDouble() }
         val b = 3
         val c = Complex(1.0, 1.0)
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
index 5b0e2eb30..7359f3bf6 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
@@ -14,7 +14,7 @@ import space.kscience.kmath.nd.ndAlgebra
 import space.kscience.kmath.nd4j.Nd4jArrayField
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.viktor.ViktorNDField
+import space.kscience.kmath.viktor.ViktorFieldND
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 import kotlin.system.measureTimeMillis
@@ -41,7 +41,7 @@ fun main() {
     // Nd4j specialized field.
     val nd4jField = Nd4jArrayField.real(dim, dim)
     //viktor field
-    val viktorField = ViktorNDField(dim, dim)
+    val viktorField = ViktorFieldND(dim, dim)
     //parallel processing based on Java Streams
     val parallelField = DoubleField.ndStreaming(dim, dim)
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
index b1248bd0f..f1f5f2e84 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
@@ -8,7 +8,7 @@ package space.kscience.kmath.structures
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 import java.util.*
 import java.util.stream.IntStream
 
@@ -17,11 +17,11 @@ import java.util.stream.IntStream
  * execution.
  */
 class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, DoubleField>,
-    NumbersAddOperations<StructureND<Double>>,
+    NumbersAddOps<StructureND<Double>>,
     ExtendedField<StructureND<Double>> {
 
     private val strides = DefaultStrides(shape)
-    override val elementContext: DoubleField get() = DoubleField
+    override val elementAlgebra: DoubleField get() = DoubleField
     override val zero: BufferND<Double> by lazy { produce { zero } }
     override val one: BufferND<Double> by lazy { produce { one } }
 
@@ -36,7 +36,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
                 this@StreamDoubleFieldND.shape,
                 shape
             )
-            this is BufferND && this.strides == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer
+            this is BufferND && this.indexes == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer
             else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
         }
 
@@ -69,7 +69,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
         return BufferND(strides, array.asBuffer())
     }
 
-    override fun combine(
+    override fun zip(
         a: StructureND<Double>,
         b: StructureND<Double>,
         transform: DoubleField.(Double, Double) -> Double,
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/buffers.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/buffers.kt
index d78141507..889ea99bd 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/buffers.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/buffers.kt
@@ -8,6 +8,7 @@ package space.kscience.kmath.structures
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.buffer
 import space.kscience.kmath.operations.bufferAlgebra
+import space.kscience.kmath.operations.withSize
 
 inline fun <reified R : Any> MutableBuffer.Companion.same(
     n: Int,
@@ -16,7 +17,7 @@ inline fun <reified R : Any> MutableBuffer.Companion.same(
 
 
 fun main() {
-    with(DoubleField.bufferAlgebra(5)) {
+    with(DoubleField.bufferAlgebra.withSize(5)) {
         println(number(2.0) + buffer(1, 2, 3, 4, 5))
     }
 }
diff --git a/gradle/wrapper/gradle-wrapper.properties b/gradle/wrapper/gradle-wrapper.properties
index 05679dc3c..ffed3a254 100644
--- a/gradle/wrapper/gradle-wrapper.properties
+++ b/gradle/wrapper/gradle-wrapper.properties
@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-7.1.1-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-7.2-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists
diff --git a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt
index ef6d51c7b..7f2780548 100644
--- a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt
+++ b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt
@@ -18,10 +18,10 @@ import com.github.h0tk3y.betterParse.parser.ParseResult
 import com.github.h0tk3y.betterParse.parser.Parser
 import space.kscience.kmath.expressions.MST
 import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.operations.FieldOperations
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.FieldOps
+import space.kscience.kmath.operations.GroupOps
 import space.kscience.kmath.operations.PowerOperations
-import space.kscience.kmath.operations.RingOperations
+import space.kscience.kmath.operations.RingOps
 
 /**
  * better-parse implementation of grammar defined in the ArithmeticsEvaluator.g4.
@@ -60,7 +60,7 @@ public object ArithmeticsEvaluator : Grammar<MST>() {
         .or(binaryFunction)
         .or(unaryFunction)
         .or(singular)
-        .or(-minus and parser(ArithmeticsEvaluator::term) map { MST.Unary(GroupOperations.MINUS_OPERATION, it) })
+        .or(-minus and parser(ArithmeticsEvaluator::term) map { MST.Unary(GroupOps.MINUS_OPERATION, it) })
         .or(-lpar and parser(ArithmeticsEvaluator::subSumChain) and -rpar)
 
     private val powChain: Parser<MST> by leftAssociative(term = term, operator = pow) { a, _, b ->
@@ -72,9 +72,9 @@ public object ArithmeticsEvaluator : Grammar<MST>() {
         operator = div or mul use TokenMatch::type
     ) { a, op, b ->
         if (op == div)
-            MST.Binary(FieldOperations.DIV_OPERATION, a, b)
+            MST.Binary(FieldOps.DIV_OPERATION, a, b)
         else
-            MST.Binary(RingOperations.TIMES_OPERATION, a, b)
+            MST.Binary(RingOps.TIMES_OPERATION, a, b)
     }
 
     private val subSumChain: Parser<MST> by leftAssociative(
@@ -82,9 +82,9 @@ public object ArithmeticsEvaluator : Grammar<MST>() {
         operator = plus or minus use TokenMatch::type
     ) { a, op, b ->
         if (op == plus)
-            MST.Binary(GroupOperations.PLUS_OPERATION, a, b)
+            MST.Binary(GroupOps.PLUS_OPERATION, a, b)
         else
-            MST.Binary(GroupOperations.MINUS_OPERATION, a, b)
+            MST.Binary(GroupOps.MINUS_OPERATION, a, b)
     }
 
     override val rootParser: Parser<MST> by subSumChain
diff --git a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/features.kt b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/features.kt
index a7a28d87f..8b76b6f19 100644
--- a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/features.kt
+++ b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/features.kt
@@ -39,7 +39,7 @@ public val PrintNumeric: RenderFeature = RenderFeature { _, node ->
 @UnstableKMathAPI
 private fun printSignedNumberString(s: String): MathSyntax = if (s.startsWith('-'))
     UnaryMinusSyntax(
-        operation = GroupOperations.MINUS_OPERATION,
+        operation = GroupOps.MINUS_OPERATION,
         operand = OperandSyntax(
             operand = NumberSyntax(string = s.removePrefix("-")),
             parentheses = true,
@@ -72,7 +72,7 @@ public class PrettyPrintFloats(public val types: Set<KClass<out Number>>) : Rend
             val exponent = afterE.toDouble().toString().removeSuffix(".0")
 
             return MultiplicationSyntax(
-                operation = RingOperations.TIMES_OPERATION,
+                operation = RingOps.TIMES_OPERATION,
                 left = OperandSyntax(operand = NumberSyntax(significand), parentheses = true),
                 right = OperandSyntax(
                     operand = SuperscriptSyntax(
@@ -91,7 +91,7 @@ public class PrettyPrintFloats(public val types: Set<KClass<out Number>>) : Rend
 
             if (toString.startsWith('-'))
                 return UnaryMinusSyntax(
-                    operation = GroupOperations.MINUS_OPERATION,
+                    operation = GroupOps.MINUS_OPERATION,
                     operand = OperandSyntax(operand = infty, parentheses = true),
                 )
 
@@ -211,9 +211,9 @@ public class BinaryPlus(operations: Collection<String>?) : Binary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.PLUS_OPERATION].
+         * The default instance configured with [GroupOps.PLUS_OPERATION].
          */
-        public val Default: BinaryPlus = BinaryPlus(setOf(GroupOperations.PLUS_OPERATION))
+        public val Default: BinaryPlus = BinaryPlus(setOf(GroupOps.PLUS_OPERATION))
     }
 }
 
@@ -233,9 +233,9 @@ public class BinaryMinus(operations: Collection<String>?) : Binary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.MINUS_OPERATION].
+         * The default instance configured with [GroupOps.MINUS_OPERATION].
          */
-        public val Default: BinaryMinus = BinaryMinus(setOf(GroupOperations.MINUS_OPERATION))
+        public val Default: BinaryMinus = BinaryMinus(setOf(GroupOps.MINUS_OPERATION))
     }
 }
 
@@ -253,9 +253,9 @@ public class UnaryPlus(operations: Collection<String>?) : Unary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.PLUS_OPERATION].
+         * The default instance configured with [GroupOps.PLUS_OPERATION].
          */
-        public val Default: UnaryPlus = UnaryPlus(setOf(GroupOperations.PLUS_OPERATION))
+        public val Default: UnaryPlus = UnaryPlus(setOf(GroupOps.PLUS_OPERATION))
     }
 }
 
@@ -273,9 +273,9 @@ public class UnaryMinus(operations: Collection<String>?) : Unary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.MINUS_OPERATION].
+         * The default instance configured with [GroupOps.MINUS_OPERATION].
          */
-        public val Default: UnaryMinus = UnaryMinus(setOf(GroupOperations.MINUS_OPERATION))
+        public val Default: UnaryMinus = UnaryMinus(setOf(GroupOps.MINUS_OPERATION))
     }
 }
 
@@ -295,9 +295,9 @@ public class Fraction(operations: Collection<String>?) : Binary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [FieldOperations.DIV_OPERATION].
+         * The default instance configured with [FieldOps.DIV_OPERATION].
          */
-        public val Default: Fraction = Fraction(setOf(FieldOperations.DIV_OPERATION))
+        public val Default: Fraction = Fraction(setOf(FieldOps.DIV_OPERATION))
     }
 }
 
@@ -422,9 +422,9 @@ public class Multiplication(operations: Collection<String>?) : Binary(operations
 
     public companion object {
         /**
-         * The default instance configured with [RingOperations.TIMES_OPERATION].
+         * The default instance configured with [RingOps.TIMES_OPERATION].
          */
-        public val Default: Multiplication = Multiplication(setOf(RingOperations.TIMES_OPERATION))
+        public val Default: Multiplication = Multiplication(setOf(RingOps.TIMES_OPERATION))
     }
 }
 
diff --git a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/phases.kt b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/phases.kt
index 3d05e03d6..ecea2d104 100644
--- a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/phases.kt
+++ b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/phases.kt
@@ -7,10 +7,10 @@ package space.kscience.kmath.ast.rendering
 
 import space.kscience.kmath.ast.rendering.FeaturedMathRendererWithPostProcess.PostProcessPhase
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.FieldOperations
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.FieldOps
+import space.kscience.kmath.operations.GroupOps
 import space.kscience.kmath.operations.PowerOperations
-import space.kscience.kmath.operations.RingOperations
+import space.kscience.kmath.operations.RingOps
 
 /**
  * Removes unnecessary times (&times;) symbols from [MultiplicationSyntax].
@@ -306,10 +306,10 @@ public class SimplifyParentheses(public val precedenceFunction: (MathSyntax) ->
 
                 is BinarySyntax -> when (it.operation) {
                     PowerOperations.POW_OPERATION -> 1
-                    RingOperations.TIMES_OPERATION -> 3
-                    FieldOperations.DIV_OPERATION -> 3
-                    GroupOperations.MINUS_OPERATION -> 4
-                    GroupOperations.PLUS_OPERATION -> 4
+                    RingOps.TIMES_OPERATION -> 3
+                    FieldOps.DIV_OPERATION -> 3
+                    GroupOps.MINUS_OPERATION -> 4
+                    GroupOps.PLUS_OPERATION -> 4
                     else -> 0
                 }
 
diff --git a/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestLatex.kt b/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestLatex.kt
index d8e432230..aba713c43 100644
--- a/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestLatex.kt
+++ b/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestLatex.kt
@@ -7,7 +7,7 @@ package space.kscience.kmath.ast.rendering
 
 import space.kscience.kmath.ast.rendering.TestUtils.testLatex
 import space.kscience.kmath.expressions.MST
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import kotlin.test.Test
 
 internal class TestLatex {
@@ -36,7 +36,7 @@ internal class TestLatex {
     fun unaryOperator() = testLatex("sin(1)", "\\operatorname{sin}\\,\\left(1\\right)")
 
     @Test
-    fun unaryPlus() = testLatex(MST.Unary(GroupOperations.PLUS_OPERATION, MST.Numeric(1)), "+1")
+    fun unaryPlus() = testLatex(MST.Unary(GroupOps.PLUS_OPERATION, MST.Numeric(1)), "+1")
 
     @Test
     fun unaryMinus() = testLatex("-x", "-x")
diff --git a/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestMathML.kt b/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestMathML.kt
index a7fcbc75b..658ecd47a 100644
--- a/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestMathML.kt
+++ b/kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestMathML.kt
@@ -7,7 +7,7 @@ package space.kscience.kmath.ast.rendering
 
 import space.kscience.kmath.ast.rendering.TestUtils.testMathML
 import space.kscience.kmath.expressions.MST
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import kotlin.test.Test
 
 internal class TestMathML {
@@ -47,7 +47,7 @@ internal class TestMathML {
 
     @Test
     fun unaryPlus() =
-        testMathML(MST.Unary(GroupOperations.PLUS_OPERATION, MST.Numeric(1)), "<mo>+</mo><mn>1</mn>")
+        testMathML(MST.Unary(GroupOps.PLUS_OPERATION, MST.Numeric(1)), "<mo>+</mo><mn>1</mn>")
 
     @Test
     fun unaryMinus() = testMathML("-x", "<mo>-</mo><mi>x</mi>")
diff --git a/kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/internal/WasmBuilder.kt b/kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/internal/WasmBuilder.kt
index 5b6cf65db..b04c4d48f 100644
--- a/kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/internal/WasmBuilder.kt
+++ b/kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/internal/WasmBuilder.kt
@@ -108,8 +108,8 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double>(f64, DoubleF
     override fun visitNumeric(mst: Numeric): ExpressionRef = ctx.f64.const(mst.value)
 
     override fun visitUnary(mst: Unary): ExpressionRef = when (mst.operation) {
-        GroupOperations.MINUS_OPERATION -> ctx.f64.neg(visit(mst.value))
-        GroupOperations.PLUS_OPERATION -> visit(mst.value)
+        GroupOps.MINUS_OPERATION -> ctx.f64.neg(visit(mst.value))
+        GroupOps.PLUS_OPERATION -> visit(mst.value)
         PowerOperations.SQRT_OPERATION -> ctx.f64.sqrt(visit(mst.value))
         TrigonometricOperations.SIN_OPERATION -> ctx.call("sin", arrayOf(visit(mst.value)), f64)
         TrigonometricOperations.COS_OPERATION -> ctx.call("cos", arrayOf(visit(mst.value)), f64)
@@ -129,10 +129,10 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double>(f64, DoubleF
     }
 
     override fun visitBinary(mst: Binary): ExpressionRef = when (mst.operation) {
-        GroupOperations.PLUS_OPERATION -> ctx.f64.add(visit(mst.left), visit(mst.right))
-        GroupOperations.MINUS_OPERATION -> ctx.f64.sub(visit(mst.left), visit(mst.right))
-        RingOperations.TIMES_OPERATION -> ctx.f64.mul(visit(mst.left), visit(mst.right))
-        FieldOperations.DIV_OPERATION -> ctx.f64.div(visit(mst.left), visit(mst.right))
+        GroupOps.PLUS_OPERATION -> ctx.f64.add(visit(mst.left), visit(mst.right))
+        GroupOps.MINUS_OPERATION -> ctx.f64.sub(visit(mst.left), visit(mst.right))
+        RingOps.TIMES_OPERATION -> ctx.f64.mul(visit(mst.left), visit(mst.right))
+        FieldOps.DIV_OPERATION -> ctx.f64.div(visit(mst.left), visit(mst.right))
         PowerOperations.POW_OPERATION -> ctx.call("pow", arrayOf(visit(mst.left), visit(mst.right)), f64)
         else -> super.visitBinary(mst)
     }
@@ -142,15 +142,15 @@ internal class IntWasmBuilder(target: MST) : WasmBuilder<Int>(i32, IntRing, targ
     override fun visitNumeric(mst: Numeric): ExpressionRef = ctx.i32.const(mst.value)
 
     override fun visitUnary(mst: Unary): ExpressionRef = when (mst.operation) {
-        GroupOperations.MINUS_OPERATION -> ctx.i32.sub(ctx.i32.const(0), visit(mst.value))
-        GroupOperations.PLUS_OPERATION -> visit(mst.value)
+        GroupOps.MINUS_OPERATION -> ctx.i32.sub(ctx.i32.const(0), visit(mst.value))
+        GroupOps.PLUS_OPERATION -> visit(mst.value)
         else -> super.visitUnary(mst)
     }
 
     override fun visitBinary(mst: Binary): ExpressionRef = when (mst.operation) {
-        GroupOperations.PLUS_OPERATION -> ctx.i32.add(visit(mst.left), visit(mst.right))
-        GroupOperations.MINUS_OPERATION -> ctx.i32.sub(visit(mst.left), visit(mst.right))
-        RingOperations.TIMES_OPERATION -> ctx.i32.mul(visit(mst.left), visit(mst.right))
+        GroupOps.PLUS_OPERATION -> ctx.i32.add(visit(mst.left), visit(mst.right))
+        GroupOps.MINUS_OPERATION -> ctx.i32.sub(visit(mst.left), visit(mst.right))
+        RingOps.TIMES_OPERATION -> ctx.i32.mul(visit(mst.left), visit(mst.right))
         else -> super.visitBinary(mst)
     }
 }
diff --git a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
index bc0119ca2..a178e8dd7 100644
--- a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
+++ b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
@@ -9,7 +9,7 @@ import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 import space.kscience.kmath.expressions.*
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 
 /**
  * A field over commons-math [DerivativeStructure].
@@ -22,7 +22,7 @@ public class DerivativeStructureField(
     public val order: Int,
     bindings: Map<Symbol, Double>,
 ) : ExtendedField<DerivativeStructure>, ExpressionAlgebra<Double, DerivativeStructure>,
-    NumbersAddOperations<DerivativeStructure> {
+    NumbersAddOps<DerivativeStructure> {
     public val numberOfVariables: Int = bindings.size
 
     override val zero: DerivativeStructure by lazy { DerivativeStructure(numberOfVariables, order) }
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
index 7d948cb61..e61a7bccc 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
@@ -52,7 +52,7 @@ private val PI_DIV_2 = Complex(PI / 2, 0)
 public object ComplexField :
     ExtendedField<Complex>,
     Norm<Complex, Complex>,
-    NumbersAddOperations<Complex>,
+    NumbersAddOps<Complex>,
     ScaleOperations<Complex> {
 
     override val zero: Complex = 0.0.toComplex()
@@ -216,7 +216,6 @@ public data class Complex(val re: Double, val im: Double) {
 
 public val Complex.Companion.algebra: ComplexField get() = ComplexField
 
-
 /**
  * Creates a complex number with real part equal to this real.
  *
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
index 29e790d16..3951b5de0 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
@@ -6,13 +6,8 @@
 package space.kscience.kmath.complex
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.BufferND
-import space.kscience.kmath.nd.BufferedFieldND
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.operations.BufferField
-import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
-import space.kscience.kmath.operations.bufferAlgebra
+import space.kscience.kmath.nd.*
+import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.Buffer
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
@@ -22,100 +17,61 @@ import kotlin.contracts.contract
  * An optimized nd-field for complex numbers
  */
 @OptIn(UnstableKMathAPI::class)
-public class ComplexFieldND(
-    shape: IntArray,
-) : BufferedFieldND<Complex, ComplexField>(shape, ComplexField, Buffer.Companion::complex),
-    NumbersAddOperations<StructureND<Complex>>,
-    ExtendedField<StructureND<Complex>> {
+public sealed class ComplexFieldOpsND : BufferedFieldOpsND<Complex, ComplexField>(ComplexField.bufferAlgebra),
+    ScaleOperations<StructureND<Complex>>, ExtendedFieldOps<StructureND<Complex>> {
 
-    override val zero: BufferND<Complex> by lazy { produce { zero } }
-    override val one: BufferND<Complex> by lazy { produce { one } }
-
-    override fun number(value: Number): BufferND<Complex> {
-        val d = value.toComplex() // minimize conversions
-        return produce { d }
+    override fun StructureND<Complex>.toBufferND(): BufferND<Complex> = when (this) {
+        is BufferND -> this
+        else -> {
+            val indexer = indexerBuilder(shape)
+            BufferND(indexer, Buffer.complex(indexer.linearSize) { offset -> get(indexer.index(offset)) })
+        }
     }
 
-//
-//    @Suppress("OVERRIDE_BY_INLINE")
-//    override inline fun map(
-//        arg: AbstractNDBuffer<Double>,
-//        transform: DoubleField.(Double) -> Double,
-//    ): RealNDElement {
-//        check(arg)
-//        val array = RealBuffer(arg.strides.linearSize) { offset -> DoubleField.transform(arg.buffer[offset]) }
-//        return BufferedNDFieldElement(this, array)
-//    }
-//
-//    @Suppress("OVERRIDE_BY_INLINE")
-//    override inline fun produce(initializer: DoubleField.(IntArray) -> Double): RealNDElement {
-//        val array = RealBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
-//        return BufferedNDFieldElement(this, array)
-//    }
-//
-//    @Suppress("OVERRIDE_BY_INLINE")
-//    override inline fun mapIndexed(
-//        arg: AbstractNDBuffer<Double>,
-//        transform: DoubleField.(index: IntArray, Double) -> Double,
-//    ): RealNDElement {
-//        check(arg)
-//        return BufferedNDFieldElement(
-//            this,
-//            RealBuffer(arg.strides.linearSize) { offset ->
-//                elementContext.transform(
-//                    arg.strides.index(offset),
-//                    arg.buffer[offset]
-//                )
-//            })
-//    }
-//
-//    @Suppress("OVERRIDE_BY_INLINE")
-//    override inline fun combine(
-//        a: AbstractNDBuffer<Double>,
-//        b: AbstractNDBuffer<Double>,
-//        transform: DoubleField.(Double, Double) -> Double,
-//    ): RealNDElement {
-//        check(a, b)
-//        val buffer = RealBuffer(strides.linearSize) { offset ->
-//            elementContext.transform(a.buffer[offset], b.buffer[offset])
-//        }
-//        return BufferedNDFieldElement(this, buffer)
-//    }
+    //TODO do specialization
 
-    override fun power(arg: StructureND<Complex>, pow: Number): BufferND<Complex> = arg.map { power(it, pow) }
+    override fun scale(a: StructureND<Complex>, value: Double): BufferND<Complex> =
+        mapInline(a.toBufferND()) { it * value }
 
-    override fun exp(arg: StructureND<Complex>): BufferND<Complex> = arg.map { exp(it) }
+    override fun power(arg: StructureND<Complex>, pow: Number): BufferND<Complex> =
+        mapInline(arg.toBufferND()) { power(it, pow) }
 
-    override fun ln(arg: StructureND<Complex>): BufferND<Complex> = arg.map { ln(it) }
+    override fun exp(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { exp(it) }
+    override fun ln(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { ln(it) }
 
-    override fun sin(arg: StructureND<Complex>): BufferND<Complex> = arg.map { sin(it) }
-    override fun cos(arg: StructureND<Complex>): BufferND<Complex> = arg.map { cos(it) }
-    override fun tan(arg: StructureND<Complex>): BufferND<Complex> = arg.map { tan(it) }
-    override fun asin(arg: StructureND<Complex>): BufferND<Complex> = arg.map { asin(it) }
-    override fun acos(arg: StructureND<Complex>): BufferND<Complex> = arg.map { acos(it) }
-    override fun atan(arg: StructureND<Complex>): BufferND<Complex> = arg.map { atan(it) }
+    override fun sin(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { sin(it) }
+    override fun cos(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { cos(it) }
+    override fun tan(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { tan(it) }
+    override fun asin(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { asin(it) }
+    override fun acos(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { acos(it) }
+    override fun atan(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { atan(it) }
 
-    override fun sinh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { sinh(it) }
-    override fun cosh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { cosh(it) }
-    override fun tanh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { tanh(it) }
-    override fun asinh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { asinh(it) }
-    override fun acosh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { acosh(it) }
-    override fun atanh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { atanh(it) }
-}
+    override fun sinh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { sinh(it) }
+    override fun cosh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { cosh(it) }
+    override fun tanh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { tanh(it) }
+    override fun asinh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { asinh(it) }
+    override fun acosh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { acosh(it) }
+    override fun atanh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { atanh(it) }
 
-
-/**
- * Fast element production using function inlining
- */
-public inline fun BufferedFieldND<Complex, ComplexField>.produceInline(initializer: ComplexField.(Int) -> Complex): BufferND<Complex> {
-    contract { callsInPlace(initializer, InvocationKind.EXACTLY_ONCE) }
-    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.initializer(offset) }
-    return BufferND(strides, buffer)
+    public companion object : ComplexFieldOpsND()
 }
 
 @UnstableKMathAPI
-public fun ComplexField.bufferAlgebra(size: Int): BufferField<Complex, ComplexField> =
-    bufferAlgebra(Buffer.Companion::complex, size)
+public val ComplexField.bufferAlgebra: BufferFieldOps<Complex, ComplexField>
+    get() = bufferAlgebra(Buffer.Companion::complex)
+
+
+@OptIn(UnstableKMathAPI::class)
+public class ComplexFieldND(override val shape: Shape) :
+    ComplexFieldOpsND(), FieldND<Complex, ComplexField>, NumbersAddOps<StructureND<Complex>> {
+
+    override fun number(value: Number): BufferND<Complex> {
+        val d = value.toDouble() // minimize conversions
+        return produce(shape) { d.toComplex() }
+    }
+}
+
+public val ComplexField.ndAlgebra: ComplexFieldOpsND get() = ComplexFieldOpsND
 
 public fun ComplexField.ndAlgebra(vararg shape: Int): ComplexFieldND = ComplexFieldND(shape)
 
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
index e5d7ebd1e..b0ec10c35 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
@@ -44,7 +44,7 @@ public val Quaternion.r: Double
  */
 @OptIn(UnstableKMathAPI::class)
 public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>, PowerOperations<Quaternion>,
-    ExponentialOperations<Quaternion>, NumbersAddOperations<Quaternion>, ScaleOperations<Quaternion> {
+    ExponentialOperations<Quaternion>, NumbersAddOps<Quaternion>, ScaleOperations<Quaternion> {
     override val zero: Quaternion = 0.toQuaternion()
     override val one: Quaternion = 1.toQuaternion()
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt
index 36ccb96f7..1baca0f55 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt
@@ -52,13 +52,13 @@ public open class FunctionalExpressionGroup<T, out A : Group<T>>(
     override val zero: Expression<T> get() = const(algebra.zero)
 
     override fun Expression<T>.unaryMinus(): Expression<T> =
-        unaryOperation(GroupOperations.MINUS_OPERATION, this)
+        unaryOperation(GroupOps.MINUS_OPERATION, this)
 
     /**
      * Builds an Expression of addition of two another expressions.
      */
     override fun add(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperation(GroupOperations.PLUS_OPERATION, a, b)
+        binaryOperation(GroupOps.PLUS_OPERATION, a, b)
 
 //    /**
 //     * Builds an Expression of multiplication of expression by number.
@@ -89,7 +89,7 @@ public open class FunctionalExpressionRing<T, out A : Ring<T>>(
      * Builds an Expression of multiplication of two expressions.
      */
     override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, b)
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, b)
 
     public operator fun Expression<T>.times(arg: T): Expression<T> = this * const(arg)
     public operator fun T.times(arg: Expression<T>): Expression<T> = arg * this
@@ -108,7 +108,7 @@ public open class FunctionalExpressionField<T, out A : Field<T>>(
      * Builds an Expression of division an expression by another one.
      */
     override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperationFunction(FieldOperations.DIV_OPERATION)(a, b)
+        binaryOperationFunction(FieldOps.DIV_OPERATION)(a, b)
 
     public operator fun Expression<T>.div(arg: T): Expression<T> = this / const(arg)
     public operator fun T.div(arg: Expression<T>): Expression<T> = arg / this
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt
index bbc74005c..360715408 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt
@@ -31,18 +31,18 @@ public object MstGroup : Group<MST>, NumericAlgebra<MST>, ScaleOperations<MST> {
 
     override fun number(value: Number): MST.Numeric = MstNumericAlgebra.number(value)
     override fun bindSymbolOrNull(value: String): Symbol = MstNumericAlgebra.bindSymbolOrNull(value)
-    override fun add(a: MST, b: MST): MST.Binary = binaryOperationFunction(GroupOperations.PLUS_OPERATION)(a, b)
+    override fun add(a: MST, b: MST): MST.Binary = binaryOperationFunction(GroupOps.PLUS_OPERATION)(a, b)
     override operator fun MST.unaryPlus(): MST.Unary =
-        unaryOperationFunction(GroupOperations.PLUS_OPERATION)(this)
+        unaryOperationFunction(GroupOps.PLUS_OPERATION)(this)
 
     override operator fun MST.unaryMinus(): MST.Unary =
-        unaryOperationFunction(GroupOperations.MINUS_OPERATION)(this)
+        unaryOperationFunction(GroupOps.MINUS_OPERATION)(this)
 
     override operator fun MST.minus(b: MST): MST.Binary =
-        binaryOperationFunction(GroupOperations.MINUS_OPERATION)(this, b)
+        binaryOperationFunction(GroupOps.MINUS_OPERATION)(this, b)
 
     override fun scale(a: MST, value: Double): MST.Binary =
-        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, number(value))
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, number(value))
 
     override fun binaryOperationFunction(operation: String): (left: MST, right: MST) -> MST.Binary =
         MstNumericAlgebra.binaryOperationFunction(operation)
@@ -56,7 +56,7 @@ public object MstGroup : Group<MST>, NumericAlgebra<MST>, ScaleOperations<MST> {
  */
 @Suppress("OVERRIDE_BY_INLINE")
 @OptIn(UnstableKMathAPI::class)
-public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MST> {
+public object MstRing : Ring<MST>, NumbersAddOps<MST>, ScaleOperations<MST> {
     override inline val zero: MST.Numeric get() = MstGroup.zero
     override val one: MST.Numeric = number(1.0)
 
@@ -65,10 +65,10 @@ public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MS
     override fun add(a: MST, b: MST): MST.Binary = MstGroup.add(a, b)
 
     override fun scale(a: MST, value: Double): MST.Binary =
-        MstGroup.binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, MstGroup.number(value))
+        MstGroup.binaryOperationFunction(RingOps.TIMES_OPERATION)(a, MstGroup.number(value))
 
     override fun multiply(a: MST, b: MST): MST.Binary =
-        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, b)
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, b)
 
     override operator fun MST.unaryPlus(): MST.Unary = MstGroup { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstGroup { -this@unaryMinus }
@@ -86,7 +86,7 @@ public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MS
  */
 @Suppress("OVERRIDE_BY_INLINE")
 @OptIn(UnstableKMathAPI::class)
-public object MstField : Field<MST>, NumbersAddOperations<MST>, ScaleOperations<MST> {
+public object MstField : Field<MST>, NumbersAddOps<MST>, ScaleOperations<MST> {
     override inline val zero: MST.Numeric get() = MstRing.zero
     override inline val one: MST.Numeric get() = MstRing.one
 
@@ -95,11 +95,11 @@ public object MstField : Field<MST>, NumbersAddOperations<MST>, ScaleOperations<
     override fun add(a: MST, b: MST): MST.Binary = MstRing.add(a, b)
 
     override fun scale(a: MST, value: Double): MST.Binary =
-        MstGroup.binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, MstGroup.number(value))
+        MstGroup.binaryOperationFunction(RingOps.TIMES_OPERATION)(a, MstGroup.number(value))
 
     override fun multiply(a: MST, b: MST): MST.Binary = MstRing.multiply(a, b)
     override fun divide(a: MST, b: MST): MST.Binary =
-        binaryOperationFunction(FieldOperations.DIV_OPERATION)(a, b)
+        binaryOperationFunction(FieldOps.DIV_OPERATION)(a, b)
 
     override operator fun MST.unaryPlus(): MST.Unary = MstRing { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstRing { -this@unaryMinus }
@@ -138,7 +138,7 @@ public object MstExtendedField : ExtendedField<MST>, NumericAlgebra<MST> {
     override fun sqrt(arg: MST): MST = unaryOperationFunction(PowerOperations.SQRT_OPERATION)(arg)
 
     override fun scale(a: MST, value: Double): MST =
-        binaryOperation(GroupOperations.PLUS_OPERATION, a, number(value))
+        binaryOperation(GroupOps.PLUS_OPERATION, a, number(value))
 
     override fun multiply(a: MST, b: MST): MST.Binary = MstField.multiply(a, b)
     override fun divide(a: MST, b: MST): MST.Binary = MstField.divide(a, b)
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt
index d5b80da2c..089503dc8 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt
@@ -59,7 +59,7 @@ public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T
 public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
     public val context: F,
     bindings: Map<Symbol, T>,
-) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>>, NumbersAddOperations<AutoDiffValue<T>> {
+) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>>, NumbersAddOps<AutoDiffValue<T>> {
     override val zero: AutoDiffValue<T> get() = const(context.zero)
     override val one: AutoDiffValue<T> get() = const(context.one)
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
index 3d562f26f..39dbe3a81 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
@@ -6,12 +6,10 @@
 package space.kscience.kmath.linear
 
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.BufferedRingND
+import space.kscience.kmath.nd.BufferedRingOpsND
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.nd.asND
-import space.kscience.kmath.nd.ndAlgebra
-import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.VirtualBuffer
@@ -19,31 +17,28 @@ import space.kscience.kmath.structures.indices
 
 
 public class BufferedLinearSpace<T, out A : Ring<T>>(
-    override val elementAlgebra: A,
-    private val bufferFactory: BufferFactory<T>,
+    private val bufferAlgebra: BufferAlgebra<T, A>
 ) : LinearSpace<T, A> {
+    override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
 
-    private fun ndRing(
-        rows: Int,
-        cols: Int,
-    ): BufferedRingND<T, A> = elementAlgebra.ndAlgebra(bufferFactory, rows, cols)
+    private val ndAlgebra = BufferedRingOpsND(bufferAlgebra)
 
     override fun buildMatrix(rows: Int, columns: Int, initializer: A.(i: Int, j: Int) -> T): Matrix<T> =
-        ndRing(rows, columns).produce { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
+        ndAlgebra.produce(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
 
     override fun buildVector(size: Int, initializer: A.(Int) -> T): Point<T> =
-        bufferFactory(size) { elementAlgebra.initializer(it) }
+        bufferAlgebra.buffer(size) { elementAlgebra.initializer(it) }
 
-    override fun Matrix<T>.unaryMinus(): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.unaryMinus(): Matrix<T> = ndAlgebra {
         asND().map { -it }.as2D()
     }
 
-    override fun Matrix<T>.plus(other: Matrix<T>): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.plus(other: Matrix<T>): Matrix<T> = ndAlgebra {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::plus. Expected $shape but found ${other.shape}" }
         asND().plus(other.asND()).as2D()
     }
 
-    override fun Matrix<T>.minus(other: Matrix<T>): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.minus(other: Matrix<T>): Matrix<T> = ndAlgebra {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::minus. Expected $shape but found ${other.shape}" }
         asND().minus(other.asND()).as2D()
     }
@@ -88,11 +83,11 @@ public class BufferedLinearSpace<T, out A : Ring<T>>(
         }
     }
 
-    override fun Matrix<T>.times(value: T): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.times(value: T): Matrix<T> = ndAlgebra {
         asND().map { it * value }.as2D()
     }
 }
 
 
 public fun <T, A : Ring<T>> A.linearSpace(bufferFactory: BufferFactory<T>): BufferedLinearSpace<T, A> =
-    BufferedLinearSpace(this, bufferFactory)
+    BufferedLinearSpace(BufferRingOps(this, bufferFactory))
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
index c2f53939f..ec6040af0 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
@@ -6,11 +6,12 @@
 package space.kscience.kmath.linear
 
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.DoubleFieldND
+import space.kscience.kmath.nd.DoubleFieldOpsND
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.nd.asND
-import space.kscience.kmath.operations.DoubleBufferOperations
+import space.kscience.kmath.operations.DoubleBufferOps
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
 
@@ -18,30 +19,27 @@ public object DoubleLinearSpace : LinearSpace<Double, DoubleField> {
 
     override val elementAlgebra: DoubleField get() = DoubleField
 
-    private fun ndRing(
-        rows: Int,
-        cols: Int,
-    ): DoubleFieldND = DoubleFieldND(intArrayOf(rows, cols))
-
     override fun buildMatrix(
         rows: Int,
         columns: Int,
         initializer: DoubleField.(i: Int, j: Int) -> Double
-    ): Matrix<Double> = ndRing(rows, columns).produce { (i, j) -> DoubleField.initializer(i, j) }.as2D()
+    ): Matrix<Double> = DoubleFieldOpsND.produce(intArrayOf(rows, columns)) { (i, j) ->
+        DoubleField.initializer(i, j)
+    }.as2D()
 
     override fun buildVector(size: Int, initializer: DoubleField.(Int) -> Double): DoubleBuffer =
         DoubleBuffer(size) { DoubleField.initializer(it) }
 
-    override fun Matrix<Double>.unaryMinus(): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.unaryMinus(): Matrix<Double> = DoubleFieldOpsND {
         asND().map { -it }.as2D()
     }
 
-    override fun Matrix<Double>.plus(other: Matrix<Double>): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.plus(other: Matrix<Double>): Matrix<Double> = DoubleFieldOpsND {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::plus. Expected $shape but found ${other.shape}" }
         asND().plus(other.asND()).as2D()
     }
 
-    override fun Matrix<Double>.minus(other: Matrix<Double>): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.minus(other: Matrix<Double>): Matrix<Double> = DoubleFieldOpsND {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::minus. Expected $shape but found ${other.shape}" }
         asND().minus(other.asND()).as2D()
     }
@@ -84,23 +82,23 @@ public object DoubleLinearSpace : LinearSpace<Double, DoubleField> {
 
     }
 
-    override fun Matrix<Double>.times(value: Double): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.times(value: Double): Matrix<Double> = DoubleFieldOpsND {
         asND().map { it * value }.as2D()
     }
 
-    public override fun Point<Double>.plus(other: Point<Double>): DoubleBuffer = DoubleBufferOperations.run {
+    public override fun Point<Double>.plus(other: Point<Double>): DoubleBuffer = DoubleBufferOps.run {
         this@plus + other
     }
 
-    public override fun Point<Double>.minus(other: Point<Double>): DoubleBuffer = DoubleBufferOperations.run {
+    public override fun Point<Double>.minus(other: Point<Double>): DoubleBuffer = DoubleBufferOps.run {
         this@minus - other
     }
 
-    public override fun Point<Double>.times(value: Double): DoubleBuffer = DoubleBufferOperations.run {
+    public override fun Point<Double>.times(value: Double): DoubleBuffer = DoubleBufferOps.run {
         scale(this@times, value)
     }
 
-    public operator fun Point<Double>.div(value: Double): DoubleBuffer = DoubleBufferOperations.run {
+    public operator fun Point<Double>.div(value: Double): DoubleBuffer = DoubleBufferOps.run {
         scale(this@div, 1.0 / value)
     }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
index 1d8985b59..5349ad864 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
@@ -10,6 +10,7 @@ import space.kscience.kmath.nd.MutableStructure2D
 import space.kscience.kmath.nd.Structure2D
 import space.kscience.kmath.nd.StructureFeature
 import space.kscience.kmath.nd.as1D
+import space.kscience.kmath.operations.BufferRingOps
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.invoke
@@ -188,7 +189,7 @@ public interface LinearSpace<T, out A : Ring<T>> {
         public fun <T : Any, A : Ring<T>> buffered(
             algebra: A,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
-        ): LinearSpace<T, A> = BufferedLinearSpace(algebra, bufferFactory)
+        ): LinearSpace<T, A> = BufferedLinearSpace(BufferRingOps(algebra, bufferFactory))
 
         @Deprecated("use DoubleField.linearSpace")
         public val double: LinearSpace<Double, DoubleField> = buffered(DoubleField, ::DoubleBuffer)
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
index b925c2642..dde04a97a 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
@@ -7,7 +7,6 @@ package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
-import space.kscience.kmath.structures.*
 import kotlin.reflect.KClass
 
 /**
@@ -19,6 +18,14 @@ import kotlin.reflect.KClass
 public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) :
     RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.")
 
+public typealias Shape = IntArray
+
+public fun Shape(shapeFirst: Int, vararg shapeRest: Int): Shape = intArrayOf(shapeFirst, *shapeRest)
+
+public interface WithShape {
+    public val shape: Shape
+}
+
 /**
  * The base interface for all ND-algebra implementations.
  *
@@ -26,20 +33,15 @@ public class ShapeMismatchException(public val expected: IntArray, public val ac
  * @param C the type of the element context.
  */
 public interface AlgebraND<T, out C : Algebra<T>> {
-    /**
-     * The shape of ND-structures this algebra operates on.
-     */
-    public val shape: IntArray
-
     /**
      * The algebra over elements of ND structure.
      */
-    public val elementContext: C
+    public val elementAlgebra: C
 
     /**
      * Produces a new NDStructure using given initializer function.
      */
-    public fun produce(initializer: C.(IntArray) -> T): StructureND<T>
+    public fun produce(shape: Shape, initializer: C.(IntArray) -> T): StructureND<T>
 
     /**
      * Maps elements from one structure to another one by applying [transform] to them.
@@ -54,7 +56,7 @@ public interface AlgebraND<T, out C : Algebra<T>> {
     /**
      * Combines two structures into one.
      */
-    public fun combine(a: StructureND<T>, b: StructureND<T>, transform: C.(T, T) -> T): StructureND<T>
+    public fun zip(left: StructureND<T>, right: StructureND<T>, transform: C.(T, T) -> T): StructureND<T>
 
     /**
      * Element-wise invocation of function working on [T] on a [StructureND].
@@ -77,7 +79,6 @@ public interface AlgebraND<T, out C : Algebra<T>> {
     public companion object
 }
 
-
 /**
  * Get a feature of the structure in this scope. Structure features take precedence other context features.
  *
@@ -89,37 +90,13 @@ public interface AlgebraND<T, out C : Algebra<T>> {
 public inline fun <T : Any, reified F : StructureFeature> AlgebraND<T, *>.getFeature(structure: StructureND<T>): F? =
     getFeature(structure, F::class)
 
-/**
- * Checks if given elements are consistent with this context.
- *
- * @param structures the structures to check.
- * @return the array of valid structures.
- */
-internal fun <T, C : Algebra<T>> AlgebraND<T, C>.checkShape(vararg structures: StructureND<T>): Array<out StructureND<T>> =
-    structures
-        .map(StructureND<T>::shape)
-        .singleOrNull { !shape.contentEquals(it) }
-        ?.let<IntArray, Array<out StructureND<T>>> { throw ShapeMismatchException(shape, it) }
-        ?: structures
-
-/**
- * Checks if given element is consistent with this context.
- *
- * @param element the structure to check.
- * @return the valid structure.
- */
-internal fun <T, C : Algebra<T>> AlgebraND<T, C>.checkShape(element: StructureND<T>): StructureND<T> {
-    if (!element.shape.contentEquals(shape)) throw ShapeMismatchException(shape, element.shape)
-    return element
-}
-
 /**
  * Space of [StructureND].
  *
  * @param T the type of the element contained in ND structure.
- * @param S the type of group over structure elements.
+ * @param A the type of group over structure elements.
  */
-public interface GroupND<T, out S : Group<T>> : Group<StructureND<T>>, AlgebraND<T, S> {
+public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>, AlgebraND<T, A> {
     /**
      * Element-wise addition.
      *
@@ -128,7 +105,7 @@ public interface GroupND<T, out S : Group<T>> : Group<StructureND<T>>, AlgebraND
      * @return the sum.
      */
     override fun add(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        combine(a, b) { aValue, bValue -> add(aValue, bValue) }
+        zip(a, b) { aValue, bValue -> add(aValue, bValue) }
 
     // TODO move to extensions after KEEP-176
 
@@ -171,13 +148,17 @@ public interface GroupND<T, out S : Group<T>> : Group<StructureND<T>>, AlgebraND
     public companion object
 }
 
+public interface GroupND<T, out A : Group<T>> : Group<StructureND<T>>, GroupOpsND<T, A>, WithShape {
+    override val zero: StructureND<T> get() = produce(shape) { elementAlgebra.zero }
+}
+
 /**
  * Ring of [StructureND].
  *
  * @param T the type of the element contained in ND structure.
- * @param R the type of ring over structure elements.
+ * @param A the type of ring over structure elements.
  */
-public interface RingND<T, out R : Ring<T>> : Ring<StructureND<T>>, GroupND<T, R> {
+public interface RingOpsND<T, out A : RingOps<T>> : RingOps<StructureND<T>>, GroupOpsND<T, A> {
     /**
      * Element-wise multiplication.
      *
@@ -186,7 +167,7 @@ public interface RingND<T, out R : Ring<T>> : Ring<StructureND<T>>, GroupND<T, R
      * @return the product.
      */
     override fun multiply(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
+        zip(a, b) { aValue, bValue -> multiply(aValue, bValue) }
 
     //TODO move to extensions after KEEP-176
 
@@ -211,13 +192,19 @@ public interface RingND<T, out R : Ring<T>> : Ring<StructureND<T>>, GroupND<T, R
     public companion object
 }
 
+public interface RingND<T, out A : Ring<T>> : Ring<StructureND<T>>, RingOpsND<T, A>, GroupND<T, A>, WithShape {
+    override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
+}
+
+
 /**
  * Field of [StructureND].
  *
  * @param T the type of the element contained in ND structure.
- * @param F the type field over structure elements.
+ * @param A the type field over structure elements.
  */
-public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T, F> {
+public interface FieldOpsND<T, out A : Field<T>> : FieldOps<StructureND<T>>, RingOpsND<T, A>,
+    ScaleOperations<StructureND<T>> {
     /**
      * Element-wise division.
      *
@@ -226,9 +213,9 @@ public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T,
      * @return the quotient.
      */
     override fun divide(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
+        zip(a, b) { aValue, bValue -> divide(aValue, bValue) }
 
-    //TODO move to extensions after KEEP-176
+    //TODO move to extensions after https://github.com/Kotlin/KEEP/blob/master/proposals/context-receivers.md
     /**
      * Divides an ND structure by an element of it.
      *
@@ -247,42 +234,9 @@ public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T,
      */
     public operator fun T.div(arg: StructureND<T>): StructureND<T> = arg.map { divide(it, this@div) }
 
-    /**
-     * Element-wise scaling.
-     *
-     * @param a the multiplicand.
-     * @param value the multiplier.
-     * @return the product.
-     */
     override fun scale(a: StructureND<T>, value: Double): StructureND<T> = a.map { scale(it, value) }
-
-//    @ThreadLocal
-//    public companion object {
-//        private val realNDFieldCache: MutableMap<IntArray, RealNDField> = hashMapOf()
-//
-//        /**
-//         * Create a nd-field for [Double] values or pull it from cache if it was created previously.
-//         */
-//        public fun real(vararg shape: Int): RealNDField = realNDFieldCache.getOrPut(shape) { RealNDField(shape) }
-//
-//        /**
-//         * Create an ND field with boxing generic buffer.
-//         */
-//        public fun <T : Any, F : Field<T>> boxing(
-//            field: F,
-//            vararg shape: Int,
-//            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
-//        ): BufferedNDField<T, F> = BufferedNDField(shape, field, bufferFactory)
-//
-//        /**
-//         * Create a most suitable implementation for nd-field using reified class.
-//         */
-//        @Suppress("UNCHECKED_CAST")
-//        public inline fun <reified T : Any, F : Field<T>> auto(field: F, vararg shape: Int): NDField<T, F> =
-//            when {
-//                T::class == Double::class -> real(*shape) as NDField<T, F>
-//                T::class == Complex::class -> complex(*shape) as BufferedNDField<T, F>
-//                else -> BoxingNDField(shape, field, Buffer.Companion::auto)
-//            }
-//    }
 }
+
+public interface FieldND<T, out A : Field<T>> : Field<StructureND<T>>, FieldOpsND<T, A>, RingND<T, A>, WithShape {
+    override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
index ae72f3689..06534c5e5 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
@@ -3,145 +3,173 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
+@file:OptIn(UnstableKMathAPI::class)
+
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
-import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-import kotlin.jvm.JvmName
 
 public interface BufferAlgebraND<T, out A : Algebra<T>> : AlgebraND<T, A> {
-    public val strides: Strides
-    public val bufferFactory: BufferFactory<T>
+    public val indexerBuilder: (IntArray) -> ShapeIndex
+    public val bufferAlgebra: BufferAlgebra<T, A>
+    override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
 
-    override fun produce(initializer: A.(IntArray) -> T): BufferND<T> = BufferND(
-        strides,
-        bufferFactory(strides.linearSize) { offset ->
-            elementContext.initializer(strides.index(offset))
+    override fun produce(shape: Shape, initializer: A.(IntArray) -> T): BufferND<T> {
+        val indexer = indexerBuilder(shape)
+        return BufferND(
+            indexer,
+            bufferAlgebra.buffer(indexer.linearSize) { offset ->
+                elementAlgebra.initializer(indexer.index(offset))
+            }
+        )
+    }
+
+    public fun StructureND<T>.toBufferND(): BufferND<T> = when (this) {
+        is BufferND -> this
+        else -> {
+            val indexer = indexerBuilder(shape)
+            BufferND(indexer, bufferAlgebra.buffer(indexer.linearSize) { offset -> get(indexer.index(offset)) })
+        }
+    }
+
+    override fun StructureND<T>.map(transform: A.(T) -> T): BufferND<T> = mapInline(toBufferND(), transform)
+
+    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): BufferND<T> =
+        mapIndexedInline(toBufferND(), transform)
+
+    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): BufferND<T> =
+        zipInline(left.toBufferND(), right.toBufferND(), transform)
+
+    public companion object {
+        public val defaultIndexerBuilder: (IntArray) -> ShapeIndex = DefaultStrides.Companion::invoke
+    }
+}
+
+public inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.mapInline(
+    arg: BufferND<T>,
+    crossinline transform: A.(T) -> T
+): BufferND<T> {
+    val indexes = arg.indexes
+    return BufferND(indexes, bufferAlgebra.mapInline(arg.buffer, transform))
+}
+
+internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.mapIndexedInline(
+    arg: BufferND<T>,
+    crossinline transform: A.(index: IntArray, arg: T) -> T
+): BufferND<T> {
+    val indexes = arg.indexes
+    return BufferND(
+        indexes,
+        bufferAlgebra.mapIndexedInline(arg.buffer) { offset, value ->
+            transform(indexes.index(offset), value)
         }
     )
-
-    public val StructureND<T>.buffer: Buffer<T>
-        get() = when {
-            !shape.contentEquals(this@BufferAlgebraND.shape) -> throw ShapeMismatchException(
-                this@BufferAlgebraND.shape,
-                shape
-            )
-            this is BufferND && this.strides == this@BufferAlgebraND.strides -> this.buffer
-            else -> bufferFactory(strides.linearSize) { offset -> get(strides.index(offset)) }
-        }
-
-    override fun StructureND<T>.map(transform: A.(T) -> T): BufferND<T> {
-        val buffer = bufferFactory(strides.linearSize) { offset ->
-            elementContext.transform(buffer[offset])
-        }
-        return BufferND(strides, buffer)
-    }
-
-    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): BufferND<T> {
-        val buffer = bufferFactory(strides.linearSize) { offset ->
-            elementContext.transform(
-                strides.index(offset),
-                buffer[offset]
-            )
-        }
-        return BufferND(strides, buffer)
-    }
-
-    override fun combine(a: StructureND<T>, b: StructureND<T>, transform: A.(T, T) -> T): BufferND<T> {
-        val buffer = bufferFactory(strides.linearSize) { offset ->
-            elementContext.transform(a.buffer[offset], b.buffer[offset])
-        }
-        return BufferND(strides, buffer)
-    }
 }
 
-public open class BufferedGroupND<T, out A : Group<T>>(
-    final override val shape: IntArray,
-    final override val elementContext: A,
-    final override val bufferFactory: BufferFactory<T>,
-) : GroupND<T, A>, BufferAlgebraND<T, A> {
-    override val strides: Strides = DefaultStrides(shape)
-    override val zero: BufferND<T> by lazy { produce { zero } }
-    override fun StructureND<T>.unaryMinus(): StructureND<T> = produce { -get(it) }
+internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.zipInline(
+    l: BufferND<T>,
+    r: BufferND<T>,
+    crossinline block: A.(l: T, r: T) -> T
+): BufferND<T> {
+    require(l.indexes == r.indexes)
+    val indexes = l.indexes
+    return BufferND(indexes, bufferAlgebra.zipInline(l.buffer, r.buffer, block))
 }
 
-public open class BufferedRingND<T, out R : Ring<T>>(
-    shape: IntArray,
-    elementContext: R,
-    bufferFactory: BufferFactory<T>,
-) : BufferedGroupND<T, R>(shape, elementContext, bufferFactory), RingND<T, R> {
-    override val one: BufferND<T> by lazy { produce { one } }
+public open class BufferedGroupNDOps<T, out A : Group<T>>(
+    override val bufferAlgebra: BufferAlgebra<T, A>,
+    override val indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+) : GroupOpsND<T, A>, BufferAlgebraND<T, A> {
+    override fun StructureND<T>.unaryMinus(): StructureND<T> = map { -it }
 }
 
-public open class BufferedFieldND<T, out R : Field<T>>(
-    shape: IntArray,
-    elementContext: R,
-    bufferFactory: BufferFactory<T>,
-) : BufferedRingND<T, R>(shape, elementContext, bufferFactory), FieldND<T, R> {
+public open class BufferedRingOpsND<T, out A : Ring<T>>(
+    bufferAlgebra: BufferAlgebra<T, A>,
+    indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+) : BufferedGroupNDOps<T, A>(bufferAlgebra, indexerBuilder), RingOpsND<T, A>
+
+public open class BufferedFieldOpsND<T, out A : Field<T>>(
+    bufferAlgebra: BufferAlgebra<T, A>,
+    indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+) : BufferedRingOpsND<T, A>(bufferAlgebra, indexerBuilder), FieldOpsND<T, A> {
+
+    public constructor(
+        elementAlgebra: A,
+        bufferFactory: BufferFactory<T>,
+        indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+    ) : this(BufferFieldOps(elementAlgebra, bufferFactory), indexerBuilder)
 
     override fun scale(a: StructureND<T>, value: Double): StructureND<T> = a.map { it * value }
 }
 
-// group factories
-public fun <T, A : Group<T>> A.ndAlgebra(
-    bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-): BufferedGroupND<T, A> = BufferedGroupND(shape, this, bufferFactory)
+public val <T, A : Group<T>> BufferAlgebra<T, A>.nd: BufferedGroupNDOps<T, A> get() = BufferedGroupNDOps(this)
+public val <T, A : Ring<T>> BufferAlgebra<T, A>.nd: BufferedRingOpsND<T, A> get() = BufferedRingOpsND(this)
+public val <T, A : Field<T>> BufferAlgebra<T, A>.nd: BufferedFieldOpsND<T, A> get() = BufferedFieldOpsND(this)
 
-@JvmName("withNdGroup")
-public inline fun <T, A : Group<T>, R> A.withNdAlgebra(
-    noinline bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-    action: BufferedGroupND<T, A>.() -> R,
-): R {
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-    return ndAlgebra(bufferFactory, *shape).run(action)
-}
 
-//ring factories
-public fun <T, A : Ring<T>> A.ndAlgebra(
-    bufferFactory: BufferFactory<T>,
+public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.produce(
     vararg shape: Int,
-): BufferedRingND<T, A> = BufferedRingND(shape, this, bufferFactory)
+    initializer: A.(IntArray) -> T
+): BufferND<T> = produce(shape, initializer)
 
-@JvmName("withNdRing")
-public inline fun <T, A : Ring<T>, R> A.withNdAlgebra(
-    noinline bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-    action: BufferedRingND<T, A>.() -> R,
-): R {
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-    return ndAlgebra(bufferFactory, *shape).run(action)
-}
+//// group factories
+//public fun <T, A : Group<T>> A.ndAlgebra(
+//    bufferAlgebra: BufferAlgebra<T, A>,
+//    vararg shape: Int,
+//): BufferedGroupNDOps<T, A> = BufferedGroupNDOps(bufferAlgebra)
+//
+//@JvmName("withNdGroup")
+//public inline fun <T, A : Group<T>, R> A.withNdAlgebra(
+//    noinline bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//    action: BufferedGroupNDOps<T, A>.() -> R,
+//): R {
+//    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+//    return ndAlgebra(bufferFactory, *shape).run(action)
+//}
 
-//field factories
-public fun <T, A : Field<T>> A.ndAlgebra(
-    bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-): BufferedFieldND<T, A> = BufferedFieldND(shape, this, bufferFactory)
-
-/**
- * Create a [FieldND] for this [Field] inferring proper buffer factory from the type
- */
-@UnstableKMathAPI
-@Suppress("UNCHECKED_CAST")
-public inline fun <reified T : Any, A : Field<T>> A.autoNdAlgebra(
-    vararg shape: Int,
-): FieldND<T, A> = when (this) {
-    DoubleField -> DoubleFieldND(shape) as FieldND<T, A>
-    else -> BufferedFieldND(shape, this, Buffer.Companion::auto)
-}
-
-@JvmName("withNdField")
-public inline fun <T, A : Field<T>, R> A.withNdAlgebra(
-    noinline bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-    action: BufferedFieldND<T, A>.() -> R,
-): R {
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-    return ndAlgebra(bufferFactory, *shape).run(action)
-}
\ No newline at end of file
+////ring factories
+//public fun <T, A : Ring<T>> A.ndAlgebra(
+//    bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//): BufferedRingNDOps<T, A> = BufferedRingNDOps(shape, this, bufferFactory)
+//
+//@JvmName("withNdRing")
+//public inline fun <T, A : Ring<T>, R> A.withNdAlgebra(
+//    noinline bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//    action: BufferedRingNDOps<T, A>.() -> R,
+//): R {
+//    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+//    return ndAlgebra(bufferFactory, *shape).run(action)
+//}
+//
+////field factories
+//public fun <T, A : Field<T>> A.ndAlgebra(
+//    bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//): BufferedFieldNDOps<T, A> = BufferedFieldNDOps(shape, this, bufferFactory)
+//
+///**
+// * Create a [FieldND] for this [Field] inferring proper buffer factory from the type
+// */
+//@UnstableKMathAPI
+//@Suppress("UNCHECKED_CAST")
+//public inline fun <reified T : Any, A : Field<T>> A.autoNdAlgebra(
+//    vararg shape: Int,
+//): FieldND<T, A> = when (this) {
+//    DoubleField -> DoubleFieldND(shape) as FieldND<T, A>
+//    else -> BufferedFieldNDOps(shape, this, Buffer.Companion::auto)
+//}
+//
+//@JvmName("withNdField")
+//public inline fun <T, A : Field<T>, R> A.withNdAlgebra(
+//    noinline bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//    action: BufferedFieldNDOps<T, A>.() -> R,
+//): R {
+//    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+//    return ndAlgebra(bufferFactory, *shape).run(action)
+//}
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt
index 694e0ceae..9eba401ab 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt
@@ -15,26 +15,20 @@ import space.kscience.kmath.structures.MutableBufferFactory
  * Represents [StructureND] over [Buffer].
  *
  * @param T the type of items.
- * @param strides The strides to access elements of [Buffer] by linear indices.
+ * @param indexes The strides to access elements of [Buffer] by linear indices.
  * @param buffer The underlying buffer.
  */
 public open class BufferND<out T>(
-    public val strides: Strides,
+    public val indexes: ShapeIndex,
     public val buffer: Buffer<T>,
 ) : StructureND<T> {
 
-    init {
-        if (strides.linearSize != buffer.size) {
-            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
-        }
-    }
+    override operator fun get(index: IntArray): T = buffer[indexes.offset(index)]
 
-    override operator fun get(index: IntArray): T = buffer[strides.offset(index)]
-
-    override val shape: IntArray get() = strides.shape
+    override val shape: IntArray get() = indexes.shape
 
     @PerformancePitfall
-    override fun elements(): Sequence<Pair<IntArray, T>> = strides.indices().map {
+    override fun elements(): Sequence<Pair<IntArray, T>> = indexes.indices().map {
         it to this[it]
     }
 
@@ -49,7 +43,7 @@ public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
     crossinline transform: (T) -> R,
 ): BufferND<R> {
     return if (this is BufferND<T>)
-        BufferND(this.strides, factory.invoke(strides.linearSize) { transform(buffer[it]) })
+        BufferND(this.indexes, factory.invoke(indexes.linearSize) { transform(buffer[it]) })
     else {
         val strides = DefaultStrides(shape)
         BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
@@ -64,11 +58,11 @@ public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
  * @param mutableBuffer The underlying buffer.
  */
 public class MutableBufferND<T>(
-    strides: Strides,
+    strides: ShapeIndex,
     public val mutableBuffer: MutableBuffer<T>,
 ) : MutableStructureND<T>, BufferND<T>(strides, mutableBuffer) {
     override fun set(index: IntArray, value: T) {
-        mutableBuffer[strides.offset(index)] = value
+        mutableBuffer[indexes.offset(index)] = value
     }
 }
 
@@ -80,7 +74,7 @@ public inline fun <T, reified R : Any> MutableStructureND<T>.mapToMutableBuffer(
     crossinline transform: (T) -> R,
 ): MutableBufferND<R> {
     return if (this is MutableBufferND<T>)
-        MutableBufferND(this.strides, factory.invoke(strides.linearSize) { transform(mutableBuffer[it]) })
+        MutableBufferND(this.indexes, factory.invoke(indexes.linearSize) { transform(mutableBuffer[it]) })
     else {
         val strides = DefaultStrides(shape)
         MutableBufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
index 0c7d4d5d1..294c44ec4 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
@@ -6,108 +6,68 @@
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
-import space.kscience.kmath.operations.ScaleOperations
+import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.DoubleBuffer
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
-@OptIn(UnstableKMathAPI::class)
-public class DoubleFieldND(
-    shape: IntArray,
-) : BufferedFieldND<Double, DoubleField>(shape, DoubleField, ::DoubleBuffer),
-    NumbersAddOperations<StructureND<Double>>,
-    ScaleOperations<StructureND<Double>>,
-    ExtendedField<StructureND<Double>> {
+public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(DoubleField.bufferAlgebra),
+    ScaleOperations<StructureND<Double>>, ExtendedFieldOps<StructureND<Double>> {
 
-    override val zero: BufferND<Double> by lazy { produce { zero } }
-    override val one: BufferND<Double> by lazy { produce { one } }
+    override fun StructureND<Double>.toBufferND(): BufferND<Double> = when (this) {
+        is BufferND -> this
+        else -> {
+            val indexer = indexerBuilder(shape)
+            BufferND(indexer, DoubleBuffer(indexer.linearSize) { offset -> get(indexer.index(offset)) })
+        }
+    }
+
+    //TODO do specialization
+
+    override fun scale(a: StructureND<Double>, value: Double): BufferND<Double> =
+        mapInline(a.toBufferND()) { it * value }
+
+    override fun power(arg: StructureND<Double>, pow: Number): BufferND<Double> =
+        mapInline(arg.toBufferND()) { power(it, pow) }
+
+    override fun exp(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { exp(it) }
+    override fun ln(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { ln(it) }
+
+    override fun sin(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { sin(it) }
+    override fun cos(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { cos(it) }
+    override fun tan(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { tan(it) }
+    override fun asin(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { asin(it) }
+    override fun acos(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { acos(it) }
+    override fun atan(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { atan(it) }
+
+    override fun sinh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { sinh(it) }
+    override fun cosh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { cosh(it) }
+    override fun tanh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { tanh(it) }
+    override fun asinh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { asinh(it) }
+    override fun acosh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { acosh(it) }
+    override fun atanh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { atanh(it) }
+
+    public companion object : DoubleFieldOpsND()
+}
+
+@OptIn(UnstableKMathAPI::class)
+public class DoubleFieldND(override val shape: Shape) :
+    DoubleFieldOpsND(), FieldND<Double, DoubleField>, NumbersAddOps<StructureND<Double>> {
 
     override fun number(value: Number): BufferND<Double> {
         val d = value.toDouble() // minimize conversions
-        return produce { d }
+        return produce(shape) { d }
     }
-
-    override val StructureND<Double>.buffer: DoubleBuffer
-        get() = when {
-            !shape.contentEquals(this@DoubleFieldND.shape) -> throw ShapeMismatchException(
-                this@DoubleFieldND.shape,
-                shape
-            )
-            this is BufferND && this.strides == this@DoubleFieldND.strides -> this.buffer as DoubleBuffer
-            else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
-        }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun StructureND<Double>.map(
-        transform: DoubleField.(Double) -> Double,
-    ): BufferND<Double> {
-        val buffer = DoubleBuffer(strides.linearSize) { offset -> DoubleField.transform(buffer.array[offset]) }
-        return BufferND(strides, buffer)
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun produce(initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
-        val array = DoubleArray(strides.linearSize) { offset ->
-            val index = strides.index(offset)
-            DoubleField.initializer(index)
-        }
-        return BufferND(strides, DoubleBuffer(array))
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun StructureND<Double>.mapIndexed(
-        transform: DoubleField.(index: IntArray, Double) -> Double,
-    ): BufferND<Double> = BufferND(
-        strides,
-        buffer = DoubleBuffer(strides.linearSize) { offset ->
-            DoubleField.transform(
-                strides.index(offset),
-                buffer.array[offset]
-            )
-        })
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun combine(
-        a: StructureND<Double>,
-        b: StructureND<Double>,
-        transform: DoubleField.(Double, Double) -> Double,
-    ): BufferND<Double> {
-        val buffer = DoubleBuffer(strides.linearSize) { offset ->
-            DoubleField.transform(a.buffer.array[offset], b.buffer.array[offset])
-        }
-        return BufferND(strides, buffer)
-    }
-
-    override fun scale(a: StructureND<Double>, value: Double): StructureND<Double> = a.map { it * value }
-
-    override fun power(arg: StructureND<Double>, pow: Number): BufferND<Double> = arg.map { power(it, pow) }
-
-    override fun exp(arg: StructureND<Double>): BufferND<Double> = arg.map { exp(it) }
-    override fun ln(arg: StructureND<Double>): BufferND<Double> = arg.map { ln(it) }
-
-    override fun sin(arg: StructureND<Double>): BufferND<Double> = arg.map { sin(it) }
-    override fun cos(arg: StructureND<Double>): BufferND<Double> = arg.map { cos(it) }
-    override fun tan(arg: StructureND<Double>): BufferND<Double> = arg.map { tan(it) }
-    override fun asin(arg: StructureND<Double>): BufferND<Double> = arg.map { asin(it) }
-    override fun acos(arg: StructureND<Double>): BufferND<Double> = arg.map { acos(it) }
-    override fun atan(arg: StructureND<Double>): BufferND<Double> = arg.map { atan(it) }
-
-    override fun sinh(arg: StructureND<Double>): BufferND<Double> = arg.map { sinh(it) }
-    override fun cosh(arg: StructureND<Double>): BufferND<Double> = arg.map { cosh(it) }
-    override fun tanh(arg: StructureND<Double>): BufferND<Double> = arg.map { tanh(it) }
-    override fun asinh(arg: StructureND<Double>): BufferND<Double> = arg.map { asinh(it) }
-    override fun acosh(arg: StructureND<Double>): BufferND<Double> = arg.map { acosh(it) }
-    override fun atanh(arg: StructureND<Double>): BufferND<Double> = arg.map { atanh(it) }
 }
 
+public val DoubleField.ndAlgebra: DoubleFieldOpsND get() = DoubleFieldOpsND
+
 public fun DoubleField.ndAlgebra(vararg shape: Int): DoubleFieldND = DoubleFieldND(shape)
 
 /**
  * Produce a context for n-dimensional operations inside this real field
  */
+@UnstableKMathAPI
 public inline fun <R> DoubleField.withNdAlgebra(vararg shape: Int, action: DoubleFieldND.() -> R): R {
     contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
     return DoubleFieldND(shape).run(action)
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt
new file mode 100644
index 000000000..bdbae70c2
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt
@@ -0,0 +1,120 @@
+/*
+ * 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 file.
+ */
+
+package space.kscience.kmath.nd
+
+import kotlin.native.concurrent.ThreadLocal
+
+/**
+ * A converter from linear index to multivariate index
+ */
+public interface ShapeIndex{
+    public val shape: Shape
+
+    /**
+     * Get linear index from multidimensional index
+     */
+    public fun offset(index: IntArray): Int
+
+    /**
+     * Get multidimensional from linear
+     */
+    public fun index(offset: Int): IntArray
+
+    /**
+     * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides
+     */
+    public val linearSize: Int
+
+    // TODO introduce a fast way to calculate index of the next element?
+
+    /**
+     * Iterate over ND indices in a natural order
+     */
+    public fun indices(): Sequence<IntArray>
+
+    override fun equals(other: Any?): Boolean
+    override fun hashCode(): Int
+}
+
+/**
+ * Linear transformation of indexes
+ */
+public abstract class Strides: ShapeIndex {
+    /**
+     * Array strides
+     */
+    public abstract val strides: IntArray
+
+    public override fun offset(index: IntArray): Int = index.mapIndexed { i, value ->
+        if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
+        value * strides[i]
+    }.sum()
+
+    // TODO introduce a fast way to calculate index of the next element?
+
+    /**
+     * Iterate over ND indices in a natural order
+     */
+    public override fun indices(): Sequence<IntArray> = (0 until linearSize).asSequence().map(::index)
+}
+
+/**
+ * Simple implementation of [Strides].
+ */
+public class DefaultStrides private constructor(override val shape: IntArray) : Strides() {
+    override val linearSize: Int get() = strides[shape.size]
+
+    /**
+     * Strides for memory access
+     */
+    override val strides: IntArray by lazy {
+        sequence {
+            var current = 1
+            yield(1)
+
+            shape.forEach {
+                current *= it
+                yield(current)
+            }
+        }.toList().toIntArray()
+    }
+
+    override fun index(offset: Int): IntArray {
+        val res = IntArray(shape.size)
+        var current = offset
+        var strideIndex = strides.size - 2
+
+        while (strideIndex >= 0) {
+            res[strideIndex] = (current / strides[strideIndex])
+            current %= strides[strideIndex]
+            strideIndex--
+        }
+
+        return res
+    }
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other !is DefaultStrides) return false
+        if (!shape.contentEquals(other.shape)) return false
+        return true
+    }
+
+    override fun hashCode(): Int = shape.contentHashCode()
+
+    @ThreadLocal
+    public companion object {
+        //private val defaultStridesCache = HashMap<IntArray, Strides>()
+
+        /**
+         * Cached builder for default strides
+         */
+        public operator fun invoke(shape: IntArray): Strides = DefaultStrides(shape)
+            //defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
+
+        //TODO fix cache
+    }
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
index b56bef230..65c1f71b4 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
@@ -6,34 +6,27 @@
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 import space.kscience.kmath.operations.ShortRing
-import space.kscience.kmath.structures.Buffer
-import space.kscience.kmath.structures.ShortBuffer
+import space.kscience.kmath.operations.bufferAlgebra
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
+public sealed class ShortRingOpsND : BufferedRingOpsND<Short, ShortRing>(ShortRing.bufferAlgebra) {
+    public companion object : ShortRingOpsND()
+}
+
 @OptIn(UnstableKMathAPI::class)
 public class ShortRingND(
-    shape: IntArray,
-) : BufferedRingND<Short, ShortRing>(shape, ShortRing, Buffer.Companion::auto),
-    NumbersAddOperations<StructureND<Short>> {
-
-    override val zero: BufferND<Short> by lazy { produce { zero } }
-    override val one: BufferND<Short> by lazy { produce { one } }
+    override val shape: Shape
+) : ShortRingOpsND(), RingND<Short, ShortRing>, NumbersAddOps<StructureND<Short>> {
 
     override fun number(value: Number): BufferND<Short> {
         val d = value.toShort() // minimize conversions
-        return produce { d }
+        return produce(shape) { d }
     }
 }
 
-/**
- * Fast element production using function inlining.
- */
-public inline fun BufferedRingND<Short, ShortRing>.produceInline(crossinline initializer: ShortRing.(Int) -> Short): BufferND<Short> =
-    BufferND(strides, ShortBuffer(ShortArray(strides.linearSize) { offset -> ShortRing.initializer(offset) }))
-
 public inline fun <R> ShortRing.withNdAlgebra(vararg shape: Int, action: ShortRingND.() -> R): R {
     contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
     return ShortRingND(shape).run(action)
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt
index 6123336ba..611d2724f 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt
@@ -15,7 +15,6 @@ import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import kotlin.jvm.JvmName
 import kotlin.math.abs
-import kotlin.native.concurrent.ThreadLocal
 import kotlin.reflect.KClass
 
 public interface StructureFeature : Feature<StructureFeature>
@@ -72,7 +71,7 @@ public interface StructureND<out T> : Featured<StructureFeature> {
             if (st1 === st2) return true
 
             // fast comparison of buffers if possible
-            if (st1 is BufferND && st2 is BufferND && st1.strides == st2.strides)
+            if (st1 is BufferND && st2 is BufferND && st1.indexes == st2.indexes)
                 return Buffer.contentEquals(st1.buffer, st2.buffer)
 
             //element by element comparison if it could not be avoided
@@ -88,7 +87,7 @@ public interface StructureND<out T> : Featured<StructureFeature> {
             if (st1 === st2) return true
 
             // fast comparison of buffers if possible
-            if (st1 is BufferND && st2 is BufferND && st1.strides == st2.strides)
+            if (st1 is BufferND && st2 is BufferND && st1.indexes == st2.indexes)
                 return Buffer.contentEquals(st1.buffer, st2.buffer)
 
             //element by element comparison if it could not be avoided
@@ -187,11 +186,11 @@ public fun <T : Comparable<T>> LinearSpace<T, Ring<T>>.contentEquals(
  * Indicates whether some [StructureND] is equal to another one with [absoluteTolerance].
  */
 @PerformancePitfall
-public fun <T : Comparable<T>> GroupND<T, Ring<T>>.contentEquals(
+public fun <T : Comparable<T>> GroupOpsND<T, Ring<T>>.contentEquals(
     st1: StructureND<T>,
     st2: StructureND<T>,
     absoluteTolerance: T,
-): Boolean = st1.elements().all { (index, value) -> elementContext { (value - st2[index]) } < absoluteTolerance }
+): Boolean = st1.elements().all { (index, value) -> elementAlgebra { (value - st2[index]) } < absoluteTolerance }
 
 /**
  * Indicates whether some [StructureND] is equal to another one with [absoluteTolerance].
@@ -231,107 +230,10 @@ public interface MutableStructureND<T> : StructureND<T> {
  * Transform a structure element-by element in place.
  */
 @OptIn(PerformancePitfall::class)
-public inline fun <T> MutableStructureND<T>.mapInPlace(action: (IntArray, T) -> T): Unit =
+public inline fun <T> MutableStructureND<T>.mapInPlace(action: (index: IntArray, t: T) -> T): Unit =
     elements().forEach { (index, oldValue) -> this[index] = action(index, oldValue) }
 
-/**
- * A way to convert ND indices to linear one and back.
- */
-public interface Strides {
-    /**
-     * Shape of NDStructure
-     */
-    public val shape: IntArray
-
-    /**
-     * Array strides
-     */
-    public val strides: IntArray
-
-    /**
-     * Get linear index from multidimensional index
-     */
-    public fun offset(index: IntArray): Int = index.mapIndexed { i, value ->
-        if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
-        value * strides[i]
-    }.sum()
-
-    /**
-     * Get multidimensional from linear
-     */
-    public fun index(offset: Int): IntArray
-
-    /**
-     * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides
-     */
-    public val linearSize: Int
-
-    // TODO introduce a fast way to calculate index of the next element?
-
-    /**
-     * Iterate over ND indices in a natural order
-     */
-    public fun indices(): Sequence<IntArray> = (0 until linearSize).asSequence().map(::index)
-}
-
-/**
- * Simple implementation of [Strides].
- */
-public class DefaultStrides private constructor(override val shape: IntArray) : Strides {
-    override val linearSize: Int
-        get() = strides[shape.size]
-
-    /**
-     * Strides for memory access
-     */
-    override val strides: IntArray by lazy {
-        sequence {
-            var current = 1
-            yield(1)
-
-            shape.forEach {
-                current *= it
-                yield(current)
-            }
-        }.toList().toIntArray()
-    }
-
-    override fun index(offset: Int): IntArray {
-        val res = IntArray(shape.size)
-        var current = offset
-        var strideIndex = strides.size - 2
-
-        while (strideIndex >= 0) {
-            res[strideIndex] = (current / strides[strideIndex])
-            current %= strides[strideIndex]
-            strideIndex--
-        }
-
-        return res
-    }
-
-    override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-        if (other !is DefaultStrides) return false
-        if (!shape.contentEquals(other.shape)) return false
-        return true
-    }
-
-    override fun hashCode(): Int = shape.contentHashCode()
-
-    @ThreadLocal
-    public companion object {
-        private val defaultStridesCache = HashMap<IntArray, Strides>()
-
-        /**
-         * Cached builder for default strides
-         */
-        public operator fun invoke(shape: IntArray): Strides =
-            defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
-    }
-}
-
-public inline fun <reified T : Any> StructureND<T>.combine(
+public inline fun <reified T : Any> StructureND<T>.zip(
     struct: StructureND<T>,
     crossinline block: (T, T) -> T,
 ): StructureND<T> {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
new file mode 100644
index 000000000..7bc18a4dd
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
@@ -0,0 +1,34 @@
+/*
+ * 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 file.
+ */
+
+package space.kscience.kmath.nd
+
+import space.kscience.kmath.operations.Algebra
+import space.kscience.kmath.operations.Group
+import space.kscience.kmath.operations.Ring
+import kotlin.jvm.JvmName
+
+
+public fun <T, A : Algebra<T>> AlgebraND<T, A>.produce(
+    shapeFirst: Int,
+    vararg shapeRest: Int,
+    initializer: A.(IntArray) -> T
+): StructureND<T> = produce(Shape(shapeFirst, *shapeRest), initializer)
+
+public fun <T, A : Group<T>> AlgebraND<T, A>.zero(shape: Shape): StructureND<T> = produce(shape) { zero }
+
+@JvmName("zeroVarArg")
+public fun <T, A : Group<T>> AlgebraND<T, A>.zero(
+    shapeFirst: Int,
+    vararg shapeRest: Int,
+): StructureND<T> = produce(shapeFirst, *shapeRest) { zero }
+
+public fun <T, A : Ring<T>> AlgebraND<T, A>.one(shape: Shape): StructureND<T> = produce(shape) { one }
+
+@JvmName("oneVarArg")
+public fun <T, A : Ring<T>> AlgebraND<T, A>.one(
+    shapeFirst: Int,
+    vararg shapeRest: Int,
+): StructureND<T> = produce(shapeFirst, *shapeRest) { one }
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index daff58d9a..d731ee4ee 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -117,7 +117,7 @@ public inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = r
  *
  * @param T the type of element of this semispace.
  */
-public interface GroupOperations<T> : Algebra<T> {
+public interface GroupOps<T> : Algebra<T> {
     /**
      * Addition of two elements.
      *
@@ -162,7 +162,7 @@ public interface GroupOperations<T> : Algebra<T> {
      * @return the difference.
      */
     public operator fun T.minus(b: T): T = add(this, -b)
-
+    // Dynamic dispatch of operations
     override fun unaryOperationFunction(operation: String): (arg: T) -> T = when (operation) {
         PLUS_OPERATION -> { arg -> +arg }
         MINUS_OPERATION -> { arg -> -arg }
@@ -193,7 +193,7 @@ public interface GroupOperations<T> : Algebra<T> {
  *
  * @param T the type of element of this semispace.
  */
-public interface Group<T> : GroupOperations<T> {
+public interface Group<T> : GroupOps<T> {
     /**
      * The neutral element of addition.
      */
@@ -206,7 +206,7 @@ public interface Group<T> : GroupOperations<T> {
  *
  * @param T the type of element of this semiring.
  */
-public interface RingOperations<T> : GroupOperations<T> {
+public interface RingOps<T> : GroupOps<T> {
     /**
      * Multiplies two elements.
      *
@@ -242,7 +242,7 @@ public interface RingOperations<T> : GroupOperations<T> {
  *
  * @param T the type of element of this ring.
  */
-public interface Ring<T> : Group<T>, RingOperations<T> {
+public interface Ring<T> : Group<T>, RingOps<T> {
     /**
      * The neutral element of multiplication
      */
@@ -256,7 +256,7 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
  *
  * @param T the type of element of this semifield.
  */
-public interface FieldOperations<T> : RingOperations<T> {
+public interface FieldOps<T> : RingOps<T> {
     /**
      * Division of two elements.
      *
@@ -295,6 +295,6 @@ public interface FieldOperations<T> : RingOperations<T> {
  *
  * @param T the type of element of this field.
  */
-public interface Field<T> : Ring<T>, FieldOperations<T>, ScaleOperations<T>, NumericAlgebra<T> {
+public interface Field<T> : Ring<T>, FieldOps<T>, ScaleOperations<T>, NumericAlgebra<T> {
     override fun number(value: Number): T = scale(one, value.toDouble())
 }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 82754e43d..97e35e4b0 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -6,7 +6,7 @@
 package space.kscience.kmath.operations
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.BufferedRingND
+import space.kscience.kmath.nd.BufferedRingOpsND
 import space.kscience.kmath.operations.BigInt.Companion.BASE
 import space.kscience.kmath.operations.BigInt.Companion.BASE_SIZE
 import space.kscience.kmath.structures.Buffer
@@ -26,7 +26,7 @@ private typealias TBase = ULong
  * @author Peter Klimai
  */
 @OptIn(UnstableKMathAPI::class)
-public object BigIntField : Field<BigInt>, NumbersAddOperations<BigInt>, ScaleOperations<BigInt> {
+public object BigIntField : Field<BigInt>, NumbersAddOps<BigInt>, ScaleOperations<BigInt> {
     override val zero: BigInt = BigInt.ZERO
     override val one: BigInt = BigInt.ONE
 
@@ -542,5 +542,5 @@ public inline fun MutableBuffer.Companion.bigInt(size: Int, initializer: (Int) -
 public inline fun BigInt.mutableBuffer(size: Int, initializer: (Int) -> BigInt): Buffer<BigInt> =
     Buffer.boxing(size, initializer)
 
-public fun BigIntField.nd(vararg shape: Int): BufferedRingND<BigInt, BigIntField> =
-    BufferedRingND(shape, BigIntField, BigInt::buffer)
+public val BigIntField.nd: BufferedRingOpsND<BigInt, BigIntField>
+    get() = BufferedRingOpsND(BufferRingOps(BigIntField, BigInt::buffer))
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt
index e82b62c1b..5a14e7734 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt
@@ -5,32 +5,34 @@
 
 package space.kscience.kmath.operations
 
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.ShortBuffer
+
+public interface WithSize {
+    public val size: Int
+}
 
 /**
  * An algebra over [Buffer]
  */
-@UnstableKMathAPI
-public interface BufferAlgebra<T, A : Algebra<T>> : Algebra<Buffer<T>> {
-    public val bufferFactory: BufferFactory<T>
+public interface BufferAlgebra<T, out A : Algebra<T>> : Algebra<Buffer<T>> {
     public val elementAlgebra: A
-    public val size: Int
+    public val bufferFactory: BufferFactory<T>
 
-    public fun buffer(vararg elements: T): Buffer<T> {
+    public fun buffer(size: Int, vararg elements: T): Buffer<T> {
         require(elements.size == size) { "Expected $size elements but found ${elements.size}" }
         return bufferFactory(size) { elements[it] }
     }
 
     //TODO move to multi-receiver inline extension
-    public fun Buffer<T>.map(block: (T) -> T): Buffer<T> = bufferFactory(size) { block(get(it)) }
+    public fun Buffer<T>.map(block: A.(T) -> T): Buffer<T> = mapInline(this, block)
 
-    public fun Buffer<T>.zip(other: Buffer<T>, block: (left: T, right: T) -> T): Buffer<T> {
-        require(size == other.size) { "Incompatible buffer sizes. left: $size, right: ${other.size}" }
-        return bufferFactory(size) { block(this[it], other[it]) }
-    }
+    public fun Buffer<T>.mapIndexed(block: A.(index: Int, arg: T) -> T): Buffer<T> = mapIndexedInline(this, block)
+
+    public fun Buffer<T>.zip(other: Buffer<T>, block: A.(left: T, right: T) -> T): Buffer<T> =
+        zipInline(this, other, block)
 
     override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> {
         val operationFunction = elementAlgebra.unaryOperationFunction(operation)
@@ -45,112 +47,149 @@ public interface BufferAlgebra<T, A : Algebra<T>> : Algebra<Buffer<T>> {
     }
 }
 
-@UnstableKMathAPI
-public fun <T> BufferField<T, *>.buffer(initializer: (Int) -> T): Buffer<T> {
+/**
+ * Inline map
+ */
+public inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapInline(
+    buffer: Buffer<T>,
+    crossinline block: A.(T) -> T
+): Buffer<T> = bufferFactory(buffer.size) { elementAlgebra.block(buffer[it]) }
+
+/**
+ * Inline map
+ */
+public inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapIndexedInline(
+    buffer: Buffer<T>,
+    crossinline block: A.(index: Int, arg: T) -> T
+): Buffer<T> = bufferFactory(buffer.size) { elementAlgebra.block(it, buffer[it]) }
+
+/**
+ * Inline zip
+ */
+public inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.zipInline(
+    l: Buffer<T>,
+    r: Buffer<T>,
+    crossinline block: A.(l: T, r: T) -> T
+): Buffer<T> {
+    require(l.size == r.size) { "Incompatible buffer sizes. left: ${l.size}, right: ${r.size}" }
+    return bufferFactory(l.size) { elementAlgebra.block(l[it], r[it]) }
+}
+
+public fun <T> BufferAlgebra<T, *>.buffer(size: Int, initializer: (Int) -> T): Buffer<T> {
+    return bufferFactory(size, initializer)
+}
+
+public fun <T, A> A.buffer(initializer: (Int) -> T): Buffer<T> where A : BufferAlgebra<T, *>, A : WithSize {
     return bufferFactory(size, initializer)
 }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.sin(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::sin)
+    mapInline(arg) { sin(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.cos(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::cos)
+    mapInline(arg) { cos(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.tan(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::tan)
+    mapInline(arg) { tan(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.asin(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::asin)
+    mapInline(arg) { asin(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.acos(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::acos)
+    mapInline(arg) { acos(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.atan(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::atan)
+    mapInline(arg) { atan(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.exp(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::exp)
+    mapInline(arg) { exp(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.ln(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::ln)
+    mapInline(arg) { ln(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.sinh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::sinh)
+    mapInline(arg) { sinh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.cosh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::cosh)
+    mapInline(arg) { cosh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.tanh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::tanh)
+    mapInline(arg) { tanh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.asinh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::asinh)
+    mapInline(arg) { asinh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.acosh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::acosh)
+    mapInline(arg) { acosh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.atanh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::atanh)
+    mapInline(arg) { atanh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : PowerOperations<T>> BufferAlgebra<T, A>.pow(arg: Buffer<T>, pow: Number): Buffer<T> =
-    with(elementAlgebra) { arg.map { power(it, pow) } }
+    mapInline(arg) { power(it, pow) }
 
 
-@UnstableKMathAPI
-public class BufferField<T, A : Field<T>>(
-    override val bufferFactory: BufferFactory<T>,
+public open class BufferRingOps<T, A: Ring<T>>(
     override val elementAlgebra: A,
+    override val bufferFactory: BufferFactory<T>,
+) : BufferAlgebra<T, A>, RingOps<Buffer<T>>{
+
+    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l + r }
+    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l * r }
+    override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
+
+    override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> =
+        super<BufferAlgebra>.unaryOperationFunction(operation)
+
+    override fun binaryOperationFunction(operation: String): (left: Buffer<T>, right: Buffer<T>) -> Buffer<T> =
+        super<BufferAlgebra>.binaryOperationFunction(operation)
+}
+
+public val ShortRing.bufferAlgebra: BufferRingOps<Short, ShortRing>
+    get() = BufferRingOps(ShortRing, ::ShortBuffer)
+
+public open class BufferFieldOps<T, A : Field<T>>(
+    elementAlgebra: A,
+    bufferFactory: BufferFactory<T>,
+) : BufferRingOps<T, A>(elementAlgebra, bufferFactory), BufferAlgebra<T, A>, FieldOps<Buffer<T>>, ScaleOperations<Buffer<T>> {
+
+    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l + r }
+    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l * r }
+    override fun divide(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l / r }
+
+    override fun scale(a: Buffer<T>, value: Double): Buffer<T> = a.map { scale(it, value) }
+    override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
+
+    override fun binaryOperationFunction(operation: String): (left: Buffer<T>, right: Buffer<T>) -> Buffer<T> =
+        super<BufferRingOps>.binaryOperationFunction(operation)
+}
+
+public class BufferField<T, A : Field<T>>(
+    elementAlgebra: A,
+    bufferFactory: BufferFactory<T>,
     override val size: Int
-) : BufferAlgebra<T, A>, Field<Buffer<T>> {
+) : BufferFieldOps<T, A>(elementAlgebra, bufferFactory), Field<Buffer<T>>, WithSize {
 
     override val zero: Buffer<T> = bufferFactory(size) { elementAlgebra.zero }
     override val one: Buffer<T> = bufferFactory(size) { elementAlgebra.one }
-
-
-    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = a.zip(b, elementAlgebra::add)
-    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = a.zip(b, elementAlgebra::multiply)
-    override fun divide(a: Buffer<T>, b: Buffer<T>): Buffer<T> = a.zip(b, elementAlgebra::divide)
-
-    override fun scale(a: Buffer<T>, value: Double): Buffer<T> = with(elementAlgebra) { a.map { scale(it, value) } }
-    override fun Buffer<T>.unaryMinus(): Buffer<T> = with(elementAlgebra) { map { -it } }
-
-    override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> {
-        return super<BufferAlgebra>.unaryOperationFunction(operation)
-    }
-
-    override fun binaryOperationFunction(operation: String): (left: Buffer<T>, right: Buffer<T>) -> Buffer<T> {
-        return super<BufferAlgebra>.binaryOperationFunction(operation)
-    }
 }
 
+/**
+ * Generate full buffer field from given buffer operations
+ */
+public fun <T, A : Field<T>> BufferFieldOps<T, A>.withSize(size: Int): BufferField<T, A> =
+    BufferField(elementAlgebra, bufferFactory, size)
+
 //Double buffer specialization
 
-@UnstableKMathAPI
 public fun BufferField<Double, *>.buffer(vararg elements: Number): Buffer<Double> {
     require(elements.size == size) { "Expected $size elements but found ${elements.size}" }
     return bufferFactory(size) { elements[it].toDouble() }
 }
 
-@UnstableKMathAPI
-public fun <T, A : Field<T>> A.bufferAlgebra(bufferFactory: BufferFactory<T>, size: Int): BufferField<T, A> =
-    BufferField(bufferFactory, this, size)
+public fun <T, A : Field<T>> A.bufferAlgebra(bufferFactory: BufferFactory<T>): BufferFieldOps<T, A> =
+    BufferFieldOps(this, bufferFactory)
 
-@UnstableKMathAPI
-public fun DoubleField.bufferAlgebra(size: Int): BufferField<Double, DoubleField> =
-    BufferField(::DoubleBuffer, DoubleField, size)
+public val DoubleField.bufferAlgebra: BufferFieldOps<Double, DoubleField>
+    get() = BufferFieldOps(DoubleField, ::DoubleBuffer)
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt
index acc2c2dc0..060ea5a7e 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt
@@ -13,21 +13,21 @@ import space.kscience.kmath.structures.DoubleBuffer
  *
  * @property size the size of buffers to operate on.
  */
-public class DoubleBufferField(public val size: Int) : ExtendedField<Buffer<Double>>, DoubleBufferOperations() {
+public class DoubleBufferField(public val size: Int) : ExtendedField<Buffer<Double>>, DoubleBufferOps() {
     override val zero: Buffer<Double> by lazy { DoubleBuffer(size) { 0.0 } }
     override val one: Buffer<Double> by lazy { DoubleBuffer(size) { 1.0 } }
 
-    override fun sinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.sinh(arg)
+    override fun sinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.sinh(arg)
 
-    override fun cosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.cosh(arg)
+    override fun cosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.cosh(arg)
 
-    override fun tanh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.tanh(arg)
+    override fun tanh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.tanh(arg)
 
-    override fun asinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.asinh(arg)
+    override fun asinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.asinh(arg)
 
-    override fun acosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.acosh(arg)
+    override fun acosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.acosh(arg)
 
-    override fun atanh(arg: Buffer<Double>): DoubleBuffer= super<DoubleBufferOperations>.atanh(arg)
+    override fun atanh(arg: Buffer<Double>): DoubleBuffer= super<DoubleBufferOps>.atanh(arg)
 
     //    override fun number(value: Number): Buffer<Double> = DoubleBuffer(size) { value.toDouble() }
 //
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOperations.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt
similarity index 97%
rename from kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOperations.kt
rename to kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt
index 50b821962..2580cd6f8 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOperations.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt
@@ -12,9 +12,9 @@ import space.kscience.kmath.structures.DoubleBuffer
 import kotlin.math.*
 
 /**
- * [ExtendedFieldOperations] over [DoubleBuffer].
+ * [ExtendedFieldOps] over [DoubleBuffer].
  */
-public abstract class DoubleBufferOperations : ExtendedFieldOperations<Buffer<Double>>, Norm<Buffer<Double>, Double> {
+public abstract class DoubleBufferOps : ExtendedFieldOps<Buffer<Double>>, Norm<Buffer<Double>, Double> {
     override fun Buffer<Double>.unaryMinus(): DoubleBuffer = if (this is DoubleBuffer) {
         DoubleBuffer(size) { -array[it] }
     } else {
@@ -185,7 +185,7 @@ public abstract class DoubleBufferOperations : ExtendedFieldOperations<Buffer<Do
         DoubleBuffer(DoubleArray(a.size) { aArray[it] * value })
     } else DoubleBuffer(DoubleArray(a.size) { a[it] * value })
 
-    public companion object : DoubleBufferOperations()
+    public companion object : DoubleBufferOps()
 }
 
 public object DoubleL2Norm : Norm<Point<Double>, Double> {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
index a3d8f5ffe..ca88ad42d 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
@@ -150,7 +150,7 @@ public interface ScaleOperations<T> : Algebra<T> {
  * TODO to be removed and replaced by extensions after multiple receivers are there
  */
 @UnstableKMathAPI
-public interface NumbersAddOperations<T> : Ring<T>, NumericAlgebra<T> {
+public interface NumbersAddOps<T> : Ring<T>, NumericAlgebra<T> {
     /**
      * Addition of element and scalar.
      *
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt
index 4c0010bf9..c1775296c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt
@@ -10,8 +10,8 @@ import kotlin.math.pow as kpow
 /**
  * Advanced Number-like semifield that implements basic operations.
  */
-public interface ExtendedFieldOperations<T> :
-    FieldOperations<T>,
+public interface ExtendedFieldOps<T> :
+    FieldOps<T>,
     TrigonometricOperations<T>,
     PowerOperations<T>,
     ExponentialOperations<T>,
@@ -35,14 +35,14 @@ public interface ExtendedFieldOperations<T> :
         ExponentialOperations.ACOSH_OPERATION -> ::acosh
         ExponentialOperations.ASINH_OPERATION -> ::asinh
         ExponentialOperations.ATANH_OPERATION -> ::atanh
-        else -> super<FieldOperations>.unaryOperationFunction(operation)
+        else -> super<FieldOps>.unaryOperationFunction(operation)
     }
 }
 
 /**
  * Advanced Number-like field that implements basic operations.
  */
-public interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T>, NumericAlgebra<T>{
+public interface ExtendedField<T> : ExtendedFieldOps<T>, Field<T>, NumericAlgebra<T>{
     override fun sinh(arg: T): T = (exp(arg) - exp(-arg)) / 2.0
     override fun cosh(arg: T): T = (exp(arg) + exp(-arg)) / 2.0
     override fun tanh(arg: T): T = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
index 05a67ab09..2009eb64f 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
@@ -7,6 +7,7 @@ package space.kscience.kmath.structures
 
 import space.kscience.kmath.nd.get
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.produce
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.testutils.FieldVerifier
@@ -21,7 +22,7 @@ internal class NDFieldTest {
 
     @Test
     fun testStrides() {
-        val ndArray = DoubleField.ndAlgebra(10, 10).produce { (it[0] + it[1]).toDouble() }
+        val ndArray = DoubleField.ndAlgebra.produce(10, 10) { (it[0] + it[1]).toDouble() }
         assertEquals(ndArray[5, 5], 10.0)
     }
 }
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
index e58976f4a..907301a53 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
@@ -7,10 +7,7 @@ package space.kscience.kmath.structures
 
 import space.kscience.kmath.linear.linearSpace
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.combine
-import space.kscience.kmath.nd.get
-import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.Norm
 import space.kscience.kmath.operations.algebra
@@ -22,9 +19,9 @@ import kotlin.test.assertEquals
 
 @Suppress("UNUSED_VARIABLE")
 class NumberNDFieldTest {
-    val algebra = DoubleField.ndAlgebra(3, 3)
-    val array1 = algebra.produce { (i, j) -> (i + j).toDouble() }
-    val array2 = algebra.produce { (i, j) -> (i - j).toDouble() }
+    val algebra = DoubleField.ndAlgebra
+    val array1 = algebra.produce(3, 3) { (i, j) -> (i + j).toDouble() }
+    val array2 = algebra.produce(3, 3) { (i, j) -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
@@ -77,7 +74,7 @@ class NumberNDFieldTest {
 
     @Test
     fun combineTest() {
-        val division = array1.combine(array2, Double::div)
+        val division = array1.zip(array2, Double::div)
     }
 
     object L2Norm : Norm<StructureND<Number>, Double> {
diff --git a/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/chains/flowExtra.kt b/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/chains/flowExtra.kt
index 1821daac9..1620f029c 100644
--- a/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/chains/flowExtra.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/chains/flowExtra.kt
@@ -10,12 +10,12 @@ import kotlinx.coroutines.flow.Flow
 import kotlinx.coroutines.flow.map
 import kotlinx.coroutines.flow.runningReduce
 import kotlinx.coroutines.flow.scan
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.operations.invoke
 
-public fun <T> Flow<T>.cumulativeSum(group: GroupOperations<T>): Flow<T> =
+public fun <T> Flow<T>.cumulativeSum(group: GroupOps<T>): Flow<T> =
     group { runningReduce { sum, element -> sum + element } }
 
 @ExperimentalCoroutinesApi
diff --git a/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/realND.kt b/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/realND.kt
index b2c3209c2..0edd51be2 100644
--- a/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/realND.kt
+++ b/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/realND.kt
@@ -13,8 +13,8 @@ import space.kscience.kmath.structures.DoubleBuffer
  * Map one [BufferND] using function without indices.
  */
 public inline fun BufferND<Double>.mapInline(crossinline transform: DoubleField.(Double) -> Double): BufferND<Double> {
-    val array = DoubleArray(strides.linearSize) { offset -> DoubleField.transform(buffer[offset]) }
-    return BufferND(strides, DoubleBuffer(array))
+    val array = DoubleArray(indexes.linearSize) { offset -> DoubleField.transform(buffer[offset]) }
+    return BufferND(indexes, DoubleBuffer(array))
 }
 
 /**
diff --git a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/DoubleHistogramSpace.kt b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/DoubleHistogramSpace.kt
index 5446f05f8..c452edc9c 100644
--- a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/DoubleHistogramSpace.kt
+++ b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/DoubleHistogramSpace.kt
@@ -28,10 +28,9 @@ public class DoubleHistogramSpace(
 
     public val dimension: Int get() = lower.size
 
-    private val shape = IntArray(binNums.size) { binNums[it] + 2 }
+    override val shape: IntArray = IntArray(binNums.size) { binNums[it] + 2 }
     override val histogramValueSpace: DoubleFieldND = DoubleField.ndAlgebra(*shape)
 
-    override val strides: Strides get() = histogramValueSpace.strides
     private val binSize = DoubleBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] }
 
     /**
@@ -52,7 +51,7 @@ public class DoubleHistogramSpace(
         val lowerBoundary = index.mapIndexed { axis, i ->
             when (i) {
                 0 -> Double.NEGATIVE_INFINITY
-                strides.shape[axis] - 1 -> upper[axis]
+                shape[axis] - 1 -> upper[axis]
                 else -> lower[axis] + (i.toDouble()) * binSize[axis]
             }
         }.asBuffer()
@@ -60,7 +59,7 @@ public class DoubleHistogramSpace(
         val upperBoundary = index.mapIndexed { axis, i ->
             when (i) {
                 0 -> lower[axis]
-                strides.shape[axis] - 1 -> Double.POSITIVE_INFINITY
+                shape[axis] - 1 -> Double.POSITIVE_INFINITY
                 else -> lower[axis] + (i.toDouble() + 1) * binSize[axis]
             }
         }.asBuffer()
@@ -75,7 +74,7 @@ public class DoubleHistogramSpace(
     }
 
     override fun produce(builder: HistogramBuilder<Double>.() -> Unit): IndexedHistogram<Double, Double> {
-        val ndCounter = StructureND.auto(strides) { Counter.real() }
+        val ndCounter = StructureND.auto(shape) { Counter.real() }
         val hBuilder = HistogramBuilder<Double> { point, value ->
             val index = getIndex(point)
             ndCounter[index].add(value.toDouble())
diff --git a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt
index 44f3072d2..7c719ccd7 100644
--- a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt
+++ b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt
@@ -8,8 +8,9 @@ package space.kscience.kmath.histogram
 import space.kscience.kmath.domains.Domain
 import space.kscience.kmath.linear.Point
 import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.nd.DefaultStrides
 import space.kscience.kmath.nd.FieldND
-import space.kscience.kmath.nd.Strides
+import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.Group
 import space.kscience.kmath.operations.ScaleOperations
@@ -34,10 +35,10 @@ public class IndexedHistogram<T : Comparable<T>, V : Any>(
         return context.produceBin(index, values[index])
     }
 
-    override val dimension: Int get() = context.strides.shape.size
+    override val dimension: Int get() = context.shape.size
 
     override val bins: Iterable<Bin<T>>
-        get() = context.strides.indices().map {
+        get() = DefaultStrides(context.shape).indices().map {
             context.produceBin(it, values[it])
         }.asIterable()
 
@@ -49,7 +50,7 @@ public class IndexedHistogram<T : Comparable<T>, V : Any>(
 public interface IndexedHistogramSpace<T : Comparable<T>, V : Any>
     : Group<IndexedHistogram<T, V>>, ScaleOperations<IndexedHistogram<T, V>> {
     //public val valueSpace: Space<V>
-    public val strides: Strides
+    public val shape: Shape
     public val histogramValueSpace: FieldND<V, *> //= NDAlgebra.space(valueSpace, Buffer.Companion::boxing, *shape),
 
     /**
diff --git a/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt b/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt
index c797eb65a..23dd076e1 100644
--- a/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt
+++ b/kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt
@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.histogram
 
+import space.kscience.kmath.nd.DefaultStrides
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.real.DoubleVector
 import kotlin.random.Random
@@ -69,7 +70,7 @@ internal class MultivariateHistogramTest {
             }
             val res = histogram1 - histogram2
             assertTrue {
-                strides.indices().all { index ->
+                DefaultStrides(shape).indices().all { index ->
                     res.values[index] <= histogram1.values[index]
                 }
             }
diff --git a/kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/scalarsAdapters.kt b/kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/scalarsAdapters.kt
index 857824275..11e5853a8 100644
--- a/kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/scalarsAdapters.kt
+++ b/kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/scalarsAdapters.kt
@@ -106,8 +106,8 @@ public fun <X : SFun<X>> MST.toSFun(): SFun<X> = when (this) {
     is Symbol -> toSVar()
 
     is MST.Unary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> +value.toSFun<X>()
-        GroupOperations.MINUS_OPERATION -> -value.toSFun<X>()
+        GroupOps.PLUS_OPERATION -> +value.toSFun<X>()
+        GroupOps.MINUS_OPERATION -> -value.toSFun<X>()
         TrigonometricOperations.SIN_OPERATION -> sin(value.toSFun())
         TrigonometricOperations.COS_OPERATION -> cos(value.toSFun())
         TrigonometricOperations.TAN_OPERATION -> tan(value.toSFun())
@@ -124,10 +124,10 @@ public fun <X : SFun<X>> MST.toSFun(): SFun<X> = when (this) {
     }
 
     is MST.Binary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> left.toSFun<X>() + right.toSFun()
-        GroupOperations.MINUS_OPERATION -> left.toSFun<X>() - right.toSFun()
-        RingOperations.TIMES_OPERATION -> left.toSFun<X>() * right.toSFun()
-        FieldOperations.DIV_OPERATION -> left.toSFun<X>() / right.toSFun()
+        GroupOps.PLUS_OPERATION -> left.toSFun<X>() + right.toSFun()
+        GroupOps.MINUS_OPERATION -> left.toSFun<X>() - right.toSFun()
+        RingOps.TIMES_OPERATION -> left.toSFun<X>() * right.toSFun()
+        FieldOps.DIV_OPERATION -> left.toSFun<X>() / right.toSFun()
         PowerOperations.POW_OPERATION -> left.toSFun<X>() pow (right as MST.Numeric).toSConst()
         else -> error("Binary operation $operation not defined in $this")
     }
diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
index b604bf5f2..d65ad0dc9 100644
--- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
+++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
@@ -15,13 +15,6 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.*
 
-internal fun AlgebraND<*, *>.checkShape(array: INDArray): INDArray {
-    val arrayShape = array.shape().toIntArray()
-    if (!shape.contentEquals(arrayShape)) throw ShapeMismatchException(shape, arrayShape)
-    return array
-}
-
-
 /**
  * Represents [AlgebraND] over [Nd4jArrayAlgebra].
  *
@@ -39,33 +32,34 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
      */
     public val StructureND<T>.ndArray: INDArray
 
-    override fun produce(initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
+    override fun produce(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
         val struct = Nd4j.create(*shape)!!.wrap()
-        struct.indicesIterator().forEach { struct[it] = elementContext.initializer(it) }
+        struct.indicesIterator().forEach { struct[it] = elementAlgebra.initializer(it) }
         return struct
     }
 
     override fun StructureND<T>.map(transform: C.(T) -> T): Nd4jArrayStructure<T> {
         val newStruct = ndArray.dup().wrap()
-        newStruct.elements().forEach { (idx, value) -> newStruct[idx] = elementContext.transform(value) }
+        newStruct.elements().forEach { (idx, value) -> newStruct[idx] = elementAlgebra.transform(value) }
         return newStruct
     }
 
     override fun StructureND<T>.mapIndexed(
         transform: C.(index: IntArray, T) -> T,
     ): Nd4jArrayStructure<T> {
-        val new = Nd4j.create(*this@Nd4jArrayAlgebra.shape).wrap()
-        new.indicesIterator().forEach { idx -> new[idx] = elementContext.transform(idx, this[idx]) }
+        val new = Nd4j.create(*shape).wrap()
+        new.indicesIterator().forEach { idx -> new[idx] = elementAlgebra.transform(idx, this[idx]) }
         return new
     }
 
-    override fun combine(
-        a: StructureND<T>,
-        b: StructureND<T>,
+    override fun zip(
+        left: StructureND<T>,
+        right: StructureND<T>,
         transform: C.(T, T) -> T,
     ): Nd4jArrayStructure<T> {
-        val new = Nd4j.create(*shape).wrap()
-        new.indicesIterator().forEach { idx -> new[idx] = elementContext.transform(a[idx], b[idx]) }
+        require(left.shape.contentEquals(right.shape)) { "Can't zip tow structures of shape ${left.shape} and ${right.shape}" }
+        val new = Nd4j.create(*left.shape).wrap()
+        new.indicesIterator().forEach { idx -> new[idx] = elementAlgebra.transform(left[idx], right[idx]) }
         return new
     }
 }
@@ -76,10 +70,7 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
  * @param T the type of the element contained in ND structure.
  * @param S the type of space of structure elements.
  */
-public sealed interface Nd4jArrayGroup<T, out S : Ring<T>> : GroupND<T, S>, Nd4jArrayAlgebra<T, S> {
-
-    override val zero: Nd4jArrayStructure<T>
-        get() = Nd4j.zeros(*shape).wrap()
+public sealed interface Nd4jArrayGroupOps<T, out S : Ring<T>> : GroupOpsND<T, S>, Nd4jArrayAlgebra<T, S> {
 
     override fun add(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
         a.ndArray.add(b.ndArray).wrap()
@@ -101,10 +92,7 @@ public sealed interface Nd4jArrayGroup<T, out S : Ring<T>> : GroupND<T, S>, Nd4j
  * @param R the type of ring of structure elements.
  */
 @OptIn(UnstableKMathAPI::class)
-public sealed interface Nd4jArrayRing<T, out R : Ring<T>> : RingND<T, R>, Nd4jArrayGroup<T, R> {
-
-    override val one: Nd4jArrayStructure<T>
-        get() = Nd4j.ones(*shape).wrap()
+public sealed interface Nd4jArrayRingOps<T, out R : Ring<T>> : RingOpsND<T, R>, Nd4jArrayGroupOps<T, R> {
 
     override fun multiply(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
         a.ndArray.mul(b.ndArray).wrap()
@@ -125,21 +113,12 @@ public sealed interface Nd4jArrayRing<T, out R : Ring<T>> : RingND<T, R>, Nd4jAr
 //    }
 
     public companion object {
-        private val intNd4jArrayRingCache: ThreadLocal<MutableMap<IntArray, IntNd4jArrayRing>> =
-            ThreadLocal.withInitial(::HashMap)
-
-        /**
-         * Creates an [RingND] for [Int] values or pull it from cache if it was created previously.
-         */
-        public fun int(vararg shape: Int): Nd4jArrayRing<Int, IntRing> =
-            intNd4jArrayRingCache.get().getOrPut(shape) { IntNd4jArrayRing(shape) }
-
         /**
          * Creates a most suitable implementation of [RingND] using reified class.
          */
         @Suppress("UNCHECKED_CAST")
-        public inline fun <reified T : Number> auto(vararg shape: Int): Nd4jArrayRing<T, Ring<T>> = when {
-            T::class == Int::class -> int(*shape) as Nd4jArrayRing<T, Ring<T>>
+        public inline fun <reified T : Number> auto(vararg shape: Int): Nd4jArrayRingOps<T, Ring<T>> = when {
+            T::class == Int::class -> IntRing.nd4j as Nd4jArrayRingOps<T, Ring<T>>
             else -> throw UnsupportedOperationException("This factory method only supports Long type.")
         }
     }
@@ -151,38 +130,21 @@ public sealed interface Nd4jArrayRing<T, out R : Ring<T>> : RingND<T, R>, Nd4jAr
  * @param T the type of the element contained in ND structure.
  * @param F the type field of structure elements.
  */
-public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldND<T, F>, Nd4jArrayRing<T, F> {
+public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldOpsND<T, F>, Nd4jArrayRingOps<T, F> {
+
     override fun divide(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
         a.ndArray.div(b.ndArray).wrap()
 
     public operator fun Number.div(b: StructureND<T>): Nd4jArrayStructure<T> = b.ndArray.rdiv(this).wrap()
 
     public companion object {
-        private val floatNd4jArrayFieldCache: ThreadLocal<MutableMap<IntArray, FloatNd4jArrayField>> =
-            ThreadLocal.withInitial(::HashMap)
-
-        private val doubleNd4JArrayFieldCache: ThreadLocal<MutableMap<IntArray, DoubleNd4jArrayField>> =
-            ThreadLocal.withInitial(::HashMap)
-
-        /**
-         * Creates an [FieldND] for [Float] values or pull it from cache if it was created previously.
-         */
-        public fun float(vararg shape: Int): Nd4jArrayRing<Float, FloatField> =
-            floatNd4jArrayFieldCache.get().getOrPut(shape) { FloatNd4jArrayField(shape) }
-
-        /**
-         * Creates an [FieldND] for [Double] values or pull it from cache if it was created previously.
-         */
-        public fun real(vararg shape: Int): Nd4jArrayRing<Double, DoubleField> =
-            doubleNd4JArrayFieldCache.get().getOrPut(shape) { DoubleNd4jArrayField(shape) }
-
         /**
          * Creates a most suitable implementation of [FieldND] using reified class.
          */
         @Suppress("UNCHECKED_CAST")
         public inline fun <reified T : Any> auto(vararg shape: Int): Nd4jArrayField<T, Field<T>> = when {
-            T::class == Float::class -> float(*shape) as Nd4jArrayField<T, Field<T>>
-            T::class == Double::class -> real(*shape) as Nd4jArrayField<T, Field<T>>
+            T::class == Float::class -> FloatField.nd4j as Nd4jArrayField<T, Field<T>>
+            T::class == Double::class -> DoubleField.nd4j as Nd4jArrayField<T, Field<T>>
             else -> throw UnsupportedOperationException("This factory method only supports Float and Double types.")
         }
     }
@@ -191,8 +153,9 @@ public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldND<T, F>, Nd4
 /**
  * Represents intersection of [ExtendedField] and [Field] over [Nd4jArrayStructure].
  */
-public sealed interface Nd4jArrayExtendedField<T, out F : ExtendedField<T>> : ExtendedField<StructureND<T>>,
-    Nd4jArrayField<T, F> {
+public sealed interface Nd4jArrayExtendedFieldOps<T, out F : ExtendedField<T>> :
+    ExtendedFieldOps<StructureND<T>>, Nd4jArrayField<T, F> {
+
     override fun sin(arg: StructureND<T>): StructureND<T> = Transforms.sin(arg.ndArray).wrap()
     override fun cos(arg: StructureND<T>): StructureND<T> = Transforms.cos(arg.ndArray).wrap()
     override fun asin(arg: StructureND<T>): StructureND<T> = Transforms.asin(arg.ndArray).wrap()
@@ -221,63 +184,59 @@ public sealed interface Nd4jArrayExtendedField<T, out F : ExtendedField<T>> : Ex
 /**
  * Represents [FieldND] over [Nd4jArrayDoubleStructure].
  */
-public class DoubleNd4jArrayField(override val shape: IntArray) : Nd4jArrayExtendedField<Double, DoubleField> {
-    override val elementContext: DoubleField get() = DoubleField
+public open class DoubleNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps<Double, DoubleField> {
+    override val elementAlgebra: DoubleField get() = DoubleField
 
-    override fun INDArray.wrap(): Nd4jArrayStructure<Double> = checkShape(this).asDoubleStructure()
+    override fun INDArray.wrap(): Nd4jArrayStructure<Double> = asDoubleStructure()
 
     @OptIn(PerformancePitfall::class)
     override val StructureND<Double>.ndArray: INDArray
         get() = when (this) {
-            is Nd4jArrayStructure<Double> -> checkShape(ndArray)
+            is Nd4jArrayStructure<Double> -> ndArray
             else -> Nd4j.zeros(*shape).also {
                 elements().forEach { (idx, value) -> it.putScalar(idx, value) }
             }
         }
 
-    override fun scale(a: StructureND<Double>, value: Double): Nd4jArrayStructure<Double> {
-        return a.ndArray.mul(value).wrap()
-    }
+    override fun scale(a: StructureND<Double>, value: Double): Nd4jArrayStructure<Double> = a.ndArray.mul(value).wrap()
 
-    override operator fun StructureND<Double>.div(arg: Double): Nd4jArrayStructure<Double> {
-        return ndArray.div(arg).wrap()
-    }
+    override operator fun StructureND<Double>.div(arg: Double): Nd4jArrayStructure<Double> = ndArray.div(arg).wrap()
 
-    override operator fun StructureND<Double>.plus(arg: Double): Nd4jArrayStructure<Double> {
-        return ndArray.add(arg).wrap()
-    }
+    override operator fun StructureND<Double>.plus(arg: Double): Nd4jArrayStructure<Double> = ndArray.add(arg).wrap()
 
-    override operator fun StructureND<Double>.minus(arg: Double): Nd4jArrayStructure<Double> {
-        return ndArray.sub(arg).wrap()
-    }
+    override operator fun StructureND<Double>.minus(arg: Double): Nd4jArrayStructure<Double> = ndArray.sub(arg).wrap()
 
-    override operator fun StructureND<Double>.times(arg: Double): Nd4jArrayStructure<Double> {
-        return ndArray.mul(arg).wrap()
-    }
+    override operator fun StructureND<Double>.times(arg: Double): Nd4jArrayStructure<Double> = ndArray.mul(arg).wrap()
 
-    override operator fun Double.div(arg: StructureND<Double>): Nd4jArrayStructure<Double> {
-        return arg.ndArray.rdiv(this).wrap()
-    }
+    override operator fun Double.div(arg: StructureND<Double>): Nd4jArrayStructure<Double> =
+        arg.ndArray.rdiv(this).wrap()
 
-    override operator fun Double.minus(arg: StructureND<Double>): Nd4jArrayStructure<Double> {
-        return arg.ndArray.rsub(this).wrap()
-    }
+    override operator fun Double.minus(arg: StructureND<Double>): Nd4jArrayStructure<Double> =
+        arg.ndArray.rsub(this).wrap()
+
+    public companion object : DoubleNd4jArrayFieldOps()
 }
 
-public fun DoubleField.nd4j(vararg shape: Int): DoubleNd4jArrayField = DoubleNd4jArrayField(intArrayOf(*shape))
+public val DoubleField.nd4j: DoubleNd4jArrayFieldOps get() = DoubleNd4jArrayFieldOps
+
+public class DoubleNd4jArrayField(override val shape: Shape) : DoubleNd4jArrayFieldOps(), FieldND<Double, DoubleField>
+
+public fun DoubleField.nd4j(shapeFirst: Int, vararg shapeRest: Int): DoubleNd4jArrayField =
+    DoubleNd4jArrayField(intArrayOf(shapeFirst, * shapeRest))
+
 
 /**
  * Represents [FieldND] over [Nd4jArrayStructure] of [Float].
  */
-public class FloatNd4jArrayField(override val shape: IntArray) : Nd4jArrayExtendedField<Float, FloatField> {
-    override val elementContext: FloatField get() = FloatField
+public open class FloatNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps<Float, FloatField> {
+    override val elementAlgebra: FloatField get() = FloatField
 
-    override fun INDArray.wrap(): Nd4jArrayStructure<Float> = checkShape(this).asFloatStructure()
+    override fun INDArray.wrap(): Nd4jArrayStructure<Float> = asFloatStructure()
 
     @OptIn(PerformancePitfall::class)
     override val StructureND<Float>.ndArray: INDArray
         get() = when (this) {
-            is Nd4jArrayStructure<Float> -> checkShape(ndArray)
+            is Nd4jArrayStructure<Float> -> ndArray
             else -> Nd4j.zeros(*shape).also {
                 elements().forEach { (idx, value) -> it.putScalar(idx, value) }
             }
@@ -303,21 +262,29 @@ public class FloatNd4jArrayField(override val shape: IntArray) : Nd4jArrayExtend
 
     override operator fun Float.minus(arg: StructureND<Float>): Nd4jArrayStructure<Float> =
         arg.ndArray.rsub(this).wrap()
+
+    public companion object : FloatNd4jArrayFieldOps()
 }
 
+public class FloatNd4jArrayField(override val shape: Shape) : FloatNd4jArrayFieldOps(), RingND<Float, FloatField>
+
+public val FloatField.nd4j: FloatNd4jArrayFieldOps get() = FloatNd4jArrayFieldOps
+
+public fun FloatField.nd4j(shapeFirst: Int, vararg shapeRest: Int): FloatNd4jArrayField =
+    FloatNd4jArrayField(intArrayOf(shapeFirst, * shapeRest))
+
 /**
  * Represents [RingND] over [Nd4jArrayIntStructure].
  */
-public class IntNd4jArrayRing(override val shape: IntArray) : Nd4jArrayRing<Int, IntRing> {
-    override val elementContext: IntRing
-        get() = IntRing
+public open class IntNd4jArrayRingOps : Nd4jArrayRingOps<Int, IntRing> {
+    override val elementAlgebra: IntRing get() = IntRing
 
-    override fun INDArray.wrap(): Nd4jArrayStructure<Int> = checkShape(this).asIntStructure()
+    override fun INDArray.wrap(): Nd4jArrayStructure<Int> = asIntStructure()
 
     @OptIn(PerformancePitfall::class)
     override val StructureND<Int>.ndArray: INDArray
         get() = when (this) {
-            is Nd4jArrayStructure<Int> -> checkShape(ndArray)
+            is Nd4jArrayStructure<Int> -> ndArray
             else -> Nd4j.zeros(*shape).also {
                 elements().forEach { (idx, value) -> it.putScalar(idx, value) }
             }
@@ -334,4 +301,13 @@ public class IntNd4jArrayRing(override val shape: IntArray) : Nd4jArrayRing<Int,
 
     override operator fun Int.minus(arg: StructureND<Int>): Nd4jArrayStructure<Int> =
         arg.ndArray.rsub(this).wrap()
+
+    public companion object : IntNd4jArrayRingOps()
 }
+
+public val IntRing.nd4j: IntNd4jArrayRingOps get() = IntNd4jArrayRingOps
+
+public class IntNd4jArrayRing(override val shape: Shape) : IntNd4jArrayRingOps(), RingND<Int, IntRing>
+
+public fun IntRing.nd4j(shapeFirst: Int, vararg shapeRest: Int): IntNd4jArrayRing =
+    IntNd4jArrayRing(intArrayOf(shapeFirst, * shapeRest))
\ No newline at end of file
diff --git a/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt b/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
index a03a7269e..465937fa9 100644
--- a/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
+++ b/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
@@ -8,6 +8,10 @@ package space.kscience.kmath.nd4j
 import org.nd4j.linalg.factory.Nd4j
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.one
+import space.kscience.kmath.nd.produce
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.IntRing
 import space.kscience.kmath.operations.invoke
 import kotlin.math.PI
 import kotlin.test.Test
@@ -19,7 +23,7 @@ import kotlin.test.fail
 internal class Nd4jArrayAlgebraTest {
     @Test
     fun testProduce() {
-        val res = with(DoubleNd4jArrayField(intArrayOf(2, 2))) { produce { it.sum().toDouble() } }
+        val res = DoubleField.nd4j.produce(2, 2) { it.sum().toDouble() }
         val expected = (Nd4j.create(2, 2) ?: fail()).asDoubleStructure()
         expected[intArrayOf(0, 0)] = 0.0
         expected[intArrayOf(0, 1)] = 1.0
@@ -30,7 +34,9 @@ internal class Nd4jArrayAlgebraTest {
 
     @Test
     fun testMap() {
-        val res = with(IntNd4jArrayRing(intArrayOf(2, 2))) { one.map { it + it * 2 } }
+        val res = IntRing.nd4j {
+            one(2, 2).map { it + it * 2 }
+        }
         val expected = (Nd4j.create(2, 2) ?: fail()).asIntStructure()
         expected[intArrayOf(0, 0)] = 3
         expected[intArrayOf(0, 1)] = 3
@@ -41,7 +47,7 @@ internal class Nd4jArrayAlgebraTest {
 
     @Test
     fun testAdd() {
-        val res = with(IntNd4jArrayRing(intArrayOf(2, 2))) { one + 25 }
+        val res = IntRing.nd4j { one(2, 2) + 25 }
         val expected = (Nd4j.create(2, 2) ?: fail()).asIntStructure()
         expected[intArrayOf(0, 0)] = 26
         expected[intArrayOf(0, 1)] = 26
@@ -51,10 +57,10 @@ internal class Nd4jArrayAlgebraTest {
     }
 
     @Test
-    fun testSin() = DoubleNd4jArrayField(intArrayOf(2, 2)).invoke {
-        val initial = produce { (i, j) -> if (i == j) PI / 2 else 0.0 }
+    fun testSin() = DoubleField.nd4j{
+        val initial = produce(2, 2) { (i, j) -> if (i == j) PI / 2 else 0.0 }
         val transformed = sin(initial)
-        val expected = produce { (i, j) -> if (i == j) 1.0 else 0.0 }
+        val expected = produce(2, 2) { (i, j) -> if (i == j) 1.0 else 0.0 }
 
         println(transformed)
         assertTrue { StructureND.contentEquals(transformed, expected) }
diff --git a/kmath-symja/src/main/kotlin/space/kscience/kmath/symja/adapters.kt b/kmath-symja/src/main/kotlin/space/kscience/kmath/symja/adapters.kt
index 8def1ae83..a7ca298a9 100644
--- a/kmath-symja/src/main/kotlin/space/kscience/kmath/symja/adapters.kt
+++ b/kmath-symja/src/main/kotlin/space/kscience/kmath/symja/adapters.kt
@@ -64,8 +64,8 @@ public fun MST.toIExpr(): IExpr = when (this) {
     }
 
     is MST.Unary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> value.toIExpr()
-        GroupOperations.MINUS_OPERATION -> F.Negate(value.toIExpr())
+        GroupOps.PLUS_OPERATION -> value.toIExpr()
+        GroupOps.MINUS_OPERATION -> F.Negate(value.toIExpr())
         TrigonometricOperations.SIN_OPERATION -> F.Sin(value.toIExpr())
         TrigonometricOperations.COS_OPERATION -> F.Cos(value.toIExpr())
         TrigonometricOperations.TAN_OPERATION -> F.Tan(value.toIExpr())
@@ -85,10 +85,10 @@ public fun MST.toIExpr(): IExpr = when (this) {
     }
 
     is MST.Binary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> left.toIExpr() + right.toIExpr()
-        GroupOperations.MINUS_OPERATION -> left.toIExpr() - right.toIExpr()
-        RingOperations.TIMES_OPERATION -> left.toIExpr() * right.toIExpr()
-        FieldOperations.DIV_OPERATION -> F.Divide(left.toIExpr(), right.toIExpr())
+        GroupOps.PLUS_OPERATION -> left.toIExpr() + right.toIExpr()
+        GroupOps.MINUS_OPERATION -> left.toIExpr() - right.toIExpr()
+        RingOps.TIMES_OPERATION -> left.toIExpr() * right.toIExpr()
+        FieldOps.DIV_OPERATION -> F.Divide(left.toIExpr(), right.toIExpr())
         PowerOperations.POW_OPERATION -> F.Power(left.toIExpr(), F.symjify((right as MST.Numeric).value))
         else -> error("Binary operation $operation not defined in $this")
     }
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
index 8e39e6cdd..594070cd2 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
@@ -373,8 +373,12 @@ public open class DoubleTensorAlgebra :
         return resTensor
     }
 
-    override fun diagonalEmbedding(diagonalEntries: Tensor<Double>, offset: Int, dim1: Int, dim2: Int):
-            DoubleTensor {
+    override fun diagonalEmbedding(
+        diagonalEntries: Tensor<Double>,
+        offset: Int,
+        dim1: Int,
+        dim2: Int
+    ): DoubleTensor {
         val n = diagonalEntries.shape.size
         val d1 = minusIndexFrom(n + 1, dim1)
         val d2 = minusIndexFrom(n + 1, dim2)
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/TensorLinearStructure.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/TensorLinearStructure.kt
index 817ed60d8..57668722a 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/TensorLinearStructure.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/TensorLinearStructure.kt
@@ -44,7 +44,7 @@ internal fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArra
  *
  * @param shape the shape of the tensor.
  */
-internal class TensorLinearStructure(override val shape: IntArray) : Strides {
+internal class TensorLinearStructure(override val shape: IntArray) : Strides() {
     override val strides: IntArray
         get() = stridesFromShape(shape)
 
@@ -54,4 +54,18 @@ internal class TensorLinearStructure(override val shape: IntArray) : Strides {
     override val linearSize: Int
         get() = shape.reduce(Int::times)
 
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other == null || this::class != other::class) return false
+
+        other as TensorLinearStructure
+
+        if (!shape.contentEquals(other.shape)) return false
+
+        return true
+    }
+
+    override fun hashCode(): Int {
+        return shape.contentHashCode()
+    }
 }
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt
index 29aa02931..e0451c2eb 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt
@@ -26,8 +26,11 @@ internal fun <T> Tensor<T>.copyToBufferedTensor(): BufferedTensor<T> =
 
 internal fun <T> Tensor<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
     is BufferedTensor<T> -> this
-    is MutableBufferND<T> -> if (this.strides.strides contentEquals TensorLinearStructure(this.shape).strides)
-        BufferedTensor(this.shape, this.mutableBuffer, 0) else this.copyToBufferedTensor()
+    is MutableBufferND<T> -> if (this.indexes == TensorLinearStructure(this.shape)) {
+        BufferedTensor(this.shape, this.mutableBuffer, 0)
+    } else {
+        this.copyToBufferedTensor()
+    }
     else -> this.copyToBufferedTensor()
 }
 
diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
index 682123ddd..fca23bc16 100644
--- a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
+++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
@@ -11,7 +11,7 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 import space.kscience.kmath.operations.ScaleOperations
 
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
@@ -34,7 +34,7 @@ public fun F64Array.asStructure(): ViktorStructureND = ViktorStructureND(this)
 @OptIn(UnstableKMathAPI::class)
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, DoubleField>,
-    NumbersAddOperations<StructureND<Double>>, ExtendedField<StructureND<Double>>,
+    NumbersAddOps<StructureND<Double>>, ExtendedField<StructureND<Double>>,
     ScaleOperations<StructureND<Double>> {
 
     public val StructureND<Double>.f64Buffer: F64Array
@@ -44,7 +44,7 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
                 shape
             )
             this is ViktorStructureND && this.f64Buffer.shape.contentEquals(this@ViktorFieldND.shape) -> this.f64Buffer
-            else -> produce { this@f64Buffer[it] }.f64Buffer
+            else -> produce(shape) { this@f64Buffer[it] }.f64Buffer
         }
 
     override val zero: ViktorStructureND by lazy { F64Array.full(init = 0.0, shape = shape).asStructure() }
@@ -52,9 +52,9 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
 
     private val strides: Strides = DefaultStrides(shape)
 
-    override val elementContext: DoubleField get() = DoubleField
+    override val elementAlgebra: DoubleField get() = DoubleField
 
-    override fun produce(initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
+    override fun produce(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
         F64Array(*shape).apply {
             this@ViktorFieldND.strides.indices().forEach { index ->
                 set(value = DoubleField.initializer(index), indices = index)
@@ -78,13 +78,13 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
         }
     }.asStructure()
 
-    override fun combine(
-        a: StructureND<Double>,
-        b: StructureND<Double>,
+    override fun zip(
+        left: StructureND<Double>,
+        right: StructureND<Double>,
         transform: DoubleField.(Double, Double) -> Double,
     ): ViktorStructureND = F64Array(*shape).apply {
         this@ViktorFieldND.strides.indices().forEach { index ->
-            set(value = DoubleField.transform(a[index], b[index]), indices = index)
+            set(value = DoubleField.transform(left[index], right[index]), indices = index)
         }
     }.asStructure()
 
@@ -123,4 +123,4 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
     override fun ln(arg: StructureND<Double>): ViktorStructureND = arg.f64Buffer.log().asStructure()
 }
 
-public fun ViktorNDField(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)
+public fun ViktorFieldND(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)
diff --git a/settings.gradle.kts b/settings.gradle.kts
index 528adb336..dc70cbb9e 100644
--- a/settings.gradle.kts
+++ b/settings.gradle.kts
@@ -1,16 +1,18 @@
 pluginManagement {
     repositories {
-        mavenLocal()
         maven("https://repo.kotlin.link")
         mavenCentral()
         gradlePluginPortal()
     }
 
-    val kotlinVersion = "1.6.0-M1"
+    val kotlinVersion = "1.6.0-RC"
+    val toolsVersion = "0.10.5"
 
     plugins {
         id("org.jetbrains.kotlinx.benchmark") version "0.3.1"
-        id("ru.mipt.npm.gradle.project") version "0.10.5"
+        id("ru.mipt.npm.gradle.project") version toolsVersion
+        id("ru.mipt.npm.gradle.jvm") version toolsVersion
+        id("ru.mipt.npm.gradle.mpp") version toolsVersion
         kotlin("multiplatform") version kotlinVersion
         kotlin("plugin.allopen") version kotlinVersion
     }

From 688382eed6e514cf61d00047b75a8669c7599ce8 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 17 Oct 2021 12:42:35 +0300
Subject: [PATCH 03/10] Shapeless ND and Buffer algebras

---
 .../kmath/benchmarks/NDFieldBenchmark.kt      |  12 +-
 .../kmath/functions/matrixIntegration.kt      |   3 +-
 .../kscience/kmath/structures/ComplexND.kt    |   1 +
 .../kscience/kmath/structures/NDField.kt      |  26 ++--
 .../kmath/structures/StreamDoubleFieldND.kt   |  14 +-
 .../DerivativeStructureExpression.kt          |   6 +-
 .../space/kscience/kmath/complex/Complex.kt   |  24 ++--
 .../kscience/kmath/complex/Quaternion.kt      |  26 ++--
 .../FunctionalExpressionAlgebra.kt            |  12 +-
 .../kscience/kmath/expressions/MstAlgebra.kt  |  32 ++---
 .../kmath/expressions/SimpleAutoDiff.kt       |  24 ++--
 .../space/kscience/kmath/nd/AlgebraND.kt      |  26 ++--
 .../kscience/kmath/nd/BufferAlgebraND.kt      |   6 +-
 .../space/kscience/kmath/nd/BufferND.kt       |  12 +-
 .../space/kscience/kmath/nd/DoubleFieldND.kt  | 134 +++++++++++++++---
 .../kscience/kmath/operations/Algebra.kt      |  34 ++---
 .../space/kscience/kmath/operations/BigInt.kt |   6 +-
 .../kmath/operations/BufferAlgebra.kt         |  10 +-
 .../kmath/operations/DoubleBufferOps.kt       |  63 ++++----
 .../kscience/kmath/operations/numbers.kt      |  68 ++++-----
 .../kscience/kmath/operations/BigNumbers.kt   |  14 +-
 .../kscience/kmath/functions/Polynomial.kt    |   6 +-
 .../kmath/geometry/Euclidean2DSpace.kt        |   2 +-
 .../kmath/geometry/Euclidean3DSpace.kt        |   4 +-
 .../kmath/histogram/IndexedHistogramSpace.kt  |   8 +-
 .../kmath/histogram/TreeHistogramSpace.kt     |  12 +-
 .../kscience/kmath/jafama/KMathJafama.kt      |  28 ++--
 .../kscience/kmath/nd4j/Nd4jArrayAlgebra.kt   |  16 +--
 .../kscience/kmath/stat/SamplerAlgebra.kt     |   4 +-
 .../kmath/tensors/api/TensorAlgebra.kt        |  16 ++-
 .../tensors/core/internal/tensorCastsUtils.kt |   2 +-
 .../kmath/viktor/ViktorStructureND.kt         |  12 +-
 32 files changed, 382 insertions(+), 281 deletions(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
index 950a10b33..7f7c03412 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
@@ -57,12 +57,12 @@ internal class NDFieldBenchmark {
         blackhole.consume(res)
     }
 
-    @Benchmark
-    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
-        var res: StructureND<Double> = one(dim, dim)
-        repeat(n) { res += 1.0 }
-        blackhole.consume(res)
-    }
+//    @Benchmark
+//    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
+//        var res: StructureND<Double> = one(dim, dim)
+//        repeat(n) { res += 1.0 }
+//        blackhole.consume(res)
+//    }
 
     private companion object {
         private const val dim = 1000
diff --git a/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt b/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
index 93b5671fe..609afb47e 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
@@ -9,6 +9,7 @@ import space.kscience.kmath.integration.gaussIntegrator
 import space.kscience.kmath.integration.integrate
 import space.kscience.kmath.integration.value
 import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.produce
 import space.kscience.kmath.nd.withNdAlgebra
 import space.kscience.kmath.operations.algebra
 import space.kscience.kmath.operations.invoke
@@ -17,7 +18,7 @@ fun main(): Unit = Double.algebra {
     withNdAlgebra(2, 2) {
 
         //Produce a diagonal StructureND
-        fun diagonal(v: Double) = produce { (i, j) ->
+        fun diagonal(v: Double) = produce {  (i, j) ->
             if (i == j) v else 0.0
         }
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
index d4554b3ba..42636fafb 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
@@ -12,6 +12,7 @@ import space.kscience.kmath.linear.transpose
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.produce
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
 import kotlin.system.measureTimeMillis
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
index 7359f3bf6..cf0721ce7 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
@@ -8,10 +8,8 @@ package space.kscience.kmath.structures
 import kotlinx.coroutines.DelicateCoroutinesApi
 import kotlinx.coroutines.GlobalScope
 import org.nd4j.linalg.factory.Nd4j
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.autoNdAlgebra
-import space.kscience.kmath.nd.ndAlgebra
-import space.kscience.kmath.nd4j.Nd4jArrayField
+import space.kscience.kmath.nd.*
+import space.kscience.kmath.nd4j.nd4j
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.viktor.ViktorFieldND
@@ -31,15 +29,17 @@ fun main() {
     Nd4j.zeros(0)
     val dim = 1000
     val n = 1000
+    val shape = Shape(dim, dim)
+
 
     // automatically build context most suited for given type.
-    val autoField = DoubleField.autoNdAlgebra(dim, dim)
+    val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
     // specialized nd-field for Double. It works as generic Double field as well.
-    val realField = DoubleField.ndAlgebra(dim, dim)
+    val realField = DoubleField.ndAlgebra
     //A generic boxing field. It should be used for objects, not primitives.
-    val boxingField = DoubleField.ndAlgebra(Buffer.Companion::boxing, dim, dim)
+    val boxingField = BufferedFieldOpsND(DoubleField, Buffer.Companion::boxing)
     // Nd4j specialized field.
-    val nd4jField = Nd4jArrayField.real(dim, dim)
+    val nd4jField = DoubleField.nd4j
     //viktor field
     val viktorField = ViktorFieldND(dim, dim)
     //parallel processing based on Java Streams
@@ -47,21 +47,21 @@ fun main() {
 
     measureAndPrint("Boxing addition") {
         boxingField {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
         }
     }
 
     measureAndPrint("Specialized addition") {
         realField {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
         }
     }
 
     measureAndPrint("Nd4j specialized addition") {
         nd4jField {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
         }
     }
@@ -82,13 +82,13 @@ fun main() {
 
     measureAndPrint("Automatic field addition") {
         autoField {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
         }
     }
 
     measureAndPrint("Lazy addition") {
-        val res = realField.one.mapAsync(GlobalScope) {
+        val res = realField.one(shape).mapAsync(GlobalScope) {
             var c = 0.0
             repeat(n) {
                 c += 1.0
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
index f1f5f2e84..dfd06973e 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
@@ -22,12 +22,12 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
 
     private val strides = DefaultStrides(shape)
     override val elementAlgebra: DoubleField get() = DoubleField
-    override val zero: BufferND<Double> by lazy { produce { zero } }
-    override val one: BufferND<Double> by lazy { produce { one } }
+    override val zero: BufferND<Double> by lazy { produce(shape) { zero } }
+    override val one: BufferND<Double> by lazy { produce(shape) { one } }
 
     override fun number(value: Number): BufferND<Double> {
         val d = value.toDouble() // minimize conversions
-        return produce { d }
+        return produce(shape) { d }
     }
 
     private val StructureND<Double>.buffer: DoubleBuffer
@@ -40,7 +40,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
             else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
         }
 
-    override fun produce(initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
+    override fun produce(shape: Shape, initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
         val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
             val index = strides.index(offset)
             DoubleField.initializer(index)
@@ -70,12 +70,12 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
     }
 
     override fun zip(
-        a: StructureND<Double>,
-        b: StructureND<Double>,
+        left: StructureND<Double>,
+        right: StructureND<Double>,
         transform: DoubleField.(Double, Double) -> Double,
     ): BufferND<Double> {
         val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
-            DoubleField.transform(a.buffer.array[offset], b.buffer.array[offset])
+            DoubleField.transform(left.buffer.array[offset], right.buffer.array[offset])
         }.toArray()
         return BufferND(strides, array.asBuffer())
     }
diff --git a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
index a178e8dd7..d42e40d1e 100644
--- a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
+++ b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
@@ -70,12 +70,12 @@ public class DerivativeStructureField(
 
     override fun DerivativeStructure.unaryMinus(): DerivativeStructure = negate()
 
-    override fun add(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.add(b)
+    override fun add(left: DerivativeStructure, right: DerivativeStructure): DerivativeStructure = left.add(right)
 
     override fun scale(a: DerivativeStructure, value: Double): DerivativeStructure = a.multiply(value)
 
-    override fun multiply(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.multiply(b)
-    override fun divide(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.divide(b)
+    override fun multiply(left: DerivativeStructure, right: DerivativeStructure): DerivativeStructure = left.multiply(right)
+    override fun divide(left: DerivativeStructure, right: DerivativeStructure): DerivativeStructure = left.divide(right)
     override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
     override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
     override fun tan(arg: DerivativeStructure): DerivativeStructure = arg.tan()
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
index e61a7bccc..879cfe94e 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
@@ -77,33 +77,33 @@ public object ComplexField :
 
     override fun scale(a: Complex, value: Double): Complex = Complex(a.re * value, a.im * value)
 
-    override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
+    override fun add(left: Complex, right: Complex): Complex = Complex(left.re + right.re, left.im + right.im)
 //    override fun multiply(a: Complex, k: Number): Complex = Complex(a.re * k.toDouble(), a.im * k.toDouble())
 
-    override fun multiply(a: Complex, b: Complex): Complex =
-        Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
+    override fun multiply(left: Complex, right: Complex): Complex =
+        Complex(left.re * right.re - left.im * right.im, left.re * right.im + left.im * right.re)
 
-    override fun divide(a: Complex, b: Complex): Complex = when {
-        abs(b.im) < abs(b.re) -> {
-            val wr = b.im / b.re
-            val wd = b.re + wr * b.im
+    override fun divide(left: Complex, right: Complex): Complex = when {
+        abs(right.im) < abs(right.re) -> {
+            val wr = right.im / right.re
+            val wd = right.re + wr * right.im
 
             if (wd.isNaN() || wd == 0.0)
                 throw ArithmeticException("Division by zero or infinity")
             else
-                Complex((a.re + a.im * wr) / wd, (a.im - a.re * wr) / wd)
+                Complex((left.re + left.im * wr) / wd, (left.im - left.re * wr) / wd)
         }
 
-        b.im == 0.0 -> throw ArithmeticException("Division by zero")
+        right.im == 0.0 -> throw ArithmeticException("Division by zero")
 
         else -> {
-            val wr = b.re / b.im
-            val wd = b.im + wr * b.re
+            val wr = right.re / right.im
+            val wd = right.im + wr * right.re
 
             if (wd.isNaN() || wd == 0.0)
                 throw ArithmeticException("Division by zero or infinity")
             else
-                Complex((a.re * wr + a.im) / wd, (a.im * wr - a.re) / wd)
+                Complex((left.re * wr + left.im) / wd, (left.im * wr - left.re) / wd)
         }
     }
 
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
index b0ec10c35..9fdd60e1f 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
@@ -63,27 +63,27 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
      */
     public val k: Quaternion = Quaternion(0, 0, 0, 1)
 
-    override fun add(a: Quaternion, b: Quaternion): Quaternion =
-        Quaternion(a.w + b.w, a.x + b.x, a.y + b.y, a.z + b.z)
+    override fun add(left: Quaternion, right: Quaternion): Quaternion =
+        Quaternion(left.w + right.w, left.x + right.x, left.y + right.y, left.z + right.z)
 
     override fun scale(a: Quaternion, value: Double): Quaternion =
         Quaternion(a.w * value, a.x * value, a.y * value, a.z * value)
 
-    override fun multiply(a: Quaternion, b: Quaternion): Quaternion = Quaternion(
-        a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z,
-        a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
-        a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x,
-        a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w,
+    override fun multiply(left: Quaternion, right: Quaternion): Quaternion = Quaternion(
+        left.w * right.w - left.x * right.x - left.y * right.y - left.z * right.z,
+        left.w * right.x + left.x * right.w + left.y * right.z - left.z * right.y,
+        left.w * right.y - left.x * right.z + left.y * right.w + left.z * right.x,
+        left.w * right.z + left.x * right.y - left.y * right.x + left.z * right.w,
     )
 
-    override fun divide(a: Quaternion, b: Quaternion): Quaternion {
-        val s = b.w * b.w + b.x * b.x + b.y * b.y + b.z * b.z
+    override fun divide(left: Quaternion, right: Quaternion): Quaternion {
+        val s = right.w * right.w + right.x * right.x + right.y * right.y + right.z * right.z
 
         return Quaternion(
-            (b.w * a.w + b.x * a.x + b.y * a.y + b.z * a.z) / s,
-            (b.w * a.x - b.x * a.w - b.y * a.z + b.z * a.y) / s,
-            (b.w * a.y + b.x * a.z - b.y * a.w - b.z * a.x) / s,
-            (b.w * a.z - b.x * a.y + b.y * a.x - b.z * a.w) / s,
+            (right.w * left.w + right.x * left.x + right.y * left.y + right.z * left.z) / s,
+            (right.w * left.x - right.x * left.w - right.y * left.z + right.z * left.y) / s,
+            (right.w * left.y + right.x * left.z - right.y * left.w - right.z * left.x) / s,
+            (right.w * left.z - right.x * left.y + right.y * left.x - right.z * left.w) / s,
         )
     }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt
index 1baca0f55..661680565 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt
@@ -57,8 +57,8 @@ public open class FunctionalExpressionGroup<T, out A : Group<T>>(
     /**
      * Builds an Expression of addition of two another expressions.
      */
-    override fun add(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperation(GroupOps.PLUS_OPERATION, a, b)
+    override fun add(left: Expression<T>, right: Expression<T>): Expression<T> =
+        binaryOperation(GroupOps.PLUS_OPERATION, left, right)
 
 //    /**
 //     * Builds an Expression of multiplication of expression by number.
@@ -88,8 +88,8 @@ public open class FunctionalExpressionRing<T, out A : Ring<T>>(
     /**
      * Builds an Expression of multiplication of two expressions.
      */
-    override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, b)
+    override fun multiply(left: Expression<T>, right: Expression<T>): Expression<T> =
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(left, right)
 
     public operator fun Expression<T>.times(arg: T): Expression<T> = this * const(arg)
     public operator fun T.times(arg: Expression<T>): Expression<T> = arg * this
@@ -107,8 +107,8 @@ public open class FunctionalExpressionField<T, out A : Field<T>>(
     /**
      * Builds an Expression of division an expression by another one.
      */
-    override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperationFunction(FieldOps.DIV_OPERATION)(a, b)
+    override fun divide(left: Expression<T>, right: Expression<T>): Expression<T> =
+        binaryOperationFunction(FieldOps.DIV_OPERATION)(left, right)
 
     public operator fun Expression<T>.div(arg: T): Expression<T> = this / const(arg)
     public operator fun T.div(arg: Expression<T>): Expression<T> = arg / this
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt
index 360715408..dd3c46207 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt
@@ -31,15 +31,15 @@ public object MstGroup : Group<MST>, NumericAlgebra<MST>, ScaleOperations<MST> {
 
     override fun number(value: Number): MST.Numeric = MstNumericAlgebra.number(value)
     override fun bindSymbolOrNull(value: String): Symbol = MstNumericAlgebra.bindSymbolOrNull(value)
-    override fun add(a: MST, b: MST): MST.Binary = binaryOperationFunction(GroupOps.PLUS_OPERATION)(a, b)
+    override fun add(left: MST, right: MST): MST.Binary = binaryOperationFunction(GroupOps.PLUS_OPERATION)(left, right)
     override operator fun MST.unaryPlus(): MST.Unary =
         unaryOperationFunction(GroupOps.PLUS_OPERATION)(this)
 
     override operator fun MST.unaryMinus(): MST.Unary =
         unaryOperationFunction(GroupOps.MINUS_OPERATION)(this)
 
-    override operator fun MST.minus(b: MST): MST.Binary =
-        binaryOperationFunction(GroupOps.MINUS_OPERATION)(this, b)
+    override operator fun MST.minus(other: MST): MST.Binary =
+        binaryOperationFunction(GroupOps.MINUS_OPERATION)(this, other)
 
     override fun scale(a: MST, value: Double): MST.Binary =
         binaryOperationFunction(RingOps.TIMES_OPERATION)(a, number(value))
@@ -62,17 +62,17 @@ public object MstRing : Ring<MST>, NumbersAddOps<MST>, ScaleOperations<MST> {
 
     override fun number(value: Number): MST.Numeric = MstGroup.number(value)
     override fun bindSymbolOrNull(value: String): Symbol = MstNumericAlgebra.bindSymbolOrNull(value)
-    override fun add(a: MST, b: MST): MST.Binary = MstGroup.add(a, b)
+    override fun add(left: MST, right: MST): MST.Binary = MstGroup.add(left, right)
 
     override fun scale(a: MST, value: Double): MST.Binary =
         MstGroup.binaryOperationFunction(RingOps.TIMES_OPERATION)(a, MstGroup.number(value))
 
-    override fun multiply(a: MST, b: MST): MST.Binary =
-        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, b)
+    override fun multiply(left: MST, right: MST): MST.Binary =
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(left, right)
 
     override operator fun MST.unaryPlus(): MST.Unary = MstGroup { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstGroup { -this@unaryMinus }
-    override operator fun MST.minus(b: MST): MST.Binary = MstGroup { this@minus - b }
+    override operator fun MST.minus(other: MST): MST.Binary = MstGroup { this@minus - other }
 
     override fun binaryOperationFunction(operation: String): (left: MST, right: MST) -> MST.Binary =
         MstGroup.binaryOperationFunction(operation)
@@ -92,18 +92,18 @@ public object MstField : Field<MST>, NumbersAddOps<MST>, ScaleOperations<MST> {
 
     override fun bindSymbolOrNull(value: String): Symbol = MstNumericAlgebra.bindSymbolOrNull(value)
     override fun number(value: Number): MST.Numeric = MstRing.number(value)
-    override fun add(a: MST, b: MST): MST.Binary = MstRing.add(a, b)
+    override fun add(left: MST, right: MST): MST.Binary = MstRing.add(left, right)
 
     override fun scale(a: MST, value: Double): MST.Binary =
         MstGroup.binaryOperationFunction(RingOps.TIMES_OPERATION)(a, MstGroup.number(value))
 
-    override fun multiply(a: MST, b: MST): MST.Binary = MstRing.multiply(a, b)
-    override fun divide(a: MST, b: MST): MST.Binary =
-        binaryOperationFunction(FieldOps.DIV_OPERATION)(a, b)
+    override fun multiply(left: MST, right: MST): MST.Binary = MstRing.multiply(left, right)
+    override fun divide(left: MST, right: MST): MST.Binary =
+        binaryOperationFunction(FieldOps.DIV_OPERATION)(left, right)
 
     override operator fun MST.unaryPlus(): MST.Unary = MstRing { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstRing { -this@unaryMinus }
-    override operator fun MST.minus(b: MST): MST.Binary = MstRing { this@minus - b }
+    override operator fun MST.minus(other: MST): MST.Binary = MstRing { this@minus - other }
 
     override fun binaryOperationFunction(operation: String): (left: MST, right: MST) -> MST.Binary =
         MstRing.binaryOperationFunction(operation)
@@ -134,17 +134,17 @@ public object MstExtendedField : ExtendedField<MST>, NumericAlgebra<MST> {
     override fun asinh(arg: MST): MST.Unary = unaryOperationFunction(ExponentialOperations.ASINH_OPERATION)(arg)
     override fun acosh(arg: MST): MST.Unary = unaryOperationFunction(ExponentialOperations.ACOSH_OPERATION)(arg)
     override fun atanh(arg: MST): MST.Unary = unaryOperationFunction(ExponentialOperations.ATANH_OPERATION)(arg)
-    override fun add(a: MST, b: MST): MST.Binary = MstField.add(a, b)
+    override fun add(left: MST, right: MST): MST.Binary = MstField.add(left, right)
     override fun sqrt(arg: MST): MST = unaryOperationFunction(PowerOperations.SQRT_OPERATION)(arg)
 
     override fun scale(a: MST, value: Double): MST =
         binaryOperation(GroupOps.PLUS_OPERATION, a, number(value))
 
-    override fun multiply(a: MST, b: MST): MST.Binary = MstField.multiply(a, b)
-    override fun divide(a: MST, b: MST): MST.Binary = MstField.divide(a, b)
+    override fun multiply(left: MST, right: MST): MST.Binary = MstField.multiply(left, right)
+    override fun divide(left: MST, right: MST): MST.Binary = MstField.divide(left, right)
     override operator fun MST.unaryPlus(): MST.Unary = MstField { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstField { -this@unaryMinus }
-    override operator fun MST.minus(b: MST): MST.Binary = MstField { this@minus - b }
+    override operator fun MST.minus(other: MST): MST.Binary = MstField { this@minus - other }
 
     override fun power(arg: MST, pow: Number): MST.Binary =
         binaryOperationFunction(PowerOperations.POW_OPERATION)(arg, number(pow))
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt
index 089503dc8..704c4edd8 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt
@@ -168,22 +168,22 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
 
     // Basic math (+, -, *, /)
 
-    override fun add(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
-        derive(const { a.value + b.value }) { z ->
-            a.d += z.d
-            b.d += z.d
+    override fun add(left: AutoDiffValue<T>, right: AutoDiffValue<T>): AutoDiffValue<T> =
+        derive(const { left.value + right.value }) { z ->
+            left.d += z.d
+            right.d += z.d
         }
 
-    override fun multiply(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
-        derive(const { a.value * b.value }) { z ->
-            a.d += z.d * b.value
-            b.d += z.d * a.value
+    override fun multiply(left: AutoDiffValue<T>, right: AutoDiffValue<T>): AutoDiffValue<T> =
+        derive(const { left.value * right.value }) { z ->
+            left.d += z.d * right.value
+            right.d += z.d * left.value
         }
 
-    override fun divide(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
-        derive(const { a.value / b.value }) { z ->
-            a.d += z.d / b.value
-            b.d -= z.d * a.value / (b.value * b.value)
+    override fun divide(left: AutoDiffValue<T>, right: AutoDiffValue<T>): AutoDiffValue<T> =
+        derive(const { left.value / right.value }) { z ->
+            left.d += z.d / right.value
+            right.d -= z.d * left.value / (right.value * right.value)
         }
 
     override fun scale(a: AutoDiffValue<T>, value: Double): AutoDiffValue<T> =
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
index dde04a97a..3f9b43f03 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
@@ -100,12 +100,12 @@ public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>,
     /**
      * Element-wise addition.
      *
-     * @param a the augend.
-     * @param b the addend.
+     * @param left the augend.
+     * @param right the addend.
      * @return the sum.
      */
-    override fun add(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        zip(a, b) { aValue, bValue -> add(aValue, bValue) }
+    override fun add(left: StructureND<T>, right: StructureND<T>): StructureND<T> =
+        zip(left, right) { aValue, bValue -> add(aValue, bValue) }
 
     // TODO move to extensions after KEEP-176
 
@@ -134,7 +134,7 @@ public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>,
      * @param arg the addend.
      * @return the sum.
      */
-    public operator fun T.plus(arg: StructureND<T>): StructureND<T> = arg.map { value -> add(this@plus, value) }
+    public operator fun T.plus(arg: StructureND<T>): StructureND<T> = arg + this
 
     /**
      * Subtracts an ND structure from an element of it.
@@ -162,12 +162,12 @@ public interface RingOpsND<T, out A : RingOps<T>> : RingOps<StructureND<T>>, Gro
     /**
      * Element-wise multiplication.
      *
-     * @param a the multiplicand.
-     * @param b the multiplier.
+     * @param left the multiplicand.
+     * @param right the multiplier.
      * @return the product.
      */
-    override fun multiply(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        zip(a, b) { aValue, bValue -> multiply(aValue, bValue) }
+    override fun multiply(left: StructureND<T>, right: StructureND<T>): StructureND<T> =
+        zip(left, right) { aValue, bValue -> multiply(aValue, bValue) }
 
     //TODO move to extensions after KEEP-176
 
@@ -208,12 +208,12 @@ public interface FieldOpsND<T, out A : Field<T>> : FieldOps<StructureND<T>>, Rin
     /**
      * Element-wise division.
      *
-     * @param a the dividend.
-     * @param b the divisor.
+     * @param left the dividend.
+     * @param right the divisor.
      * @return the quotient.
      */
-    override fun divide(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        zip(a, b) { aValue, bValue -> divide(aValue, bValue) }
+    override fun divide(left: StructureND<T>, right: StructureND<T>): StructureND<T> =
+        zip(left, right) { aValue, bValue -> divide(aValue, bValue) }
 
     //TODO move to extensions after https://github.com/Kotlin/KEEP/blob/master/proposals/context-receivers.md
     /**
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
index 06534c5e5..c94988eef 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
@@ -73,7 +73,7 @@ internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.zipInline(
     r: BufferND<T>,
     crossinline block: A.(l: T, r: T) -> T
 ): BufferND<T> {
-    require(l.indexes == r.indexes)
+    require(l.indexes == r.indexes) { "Zip requires the same shapes, but found ${l.shape} on the left and ${r.shape} on the right" }
     val indexes = l.indexes
     return BufferND(indexes, bufferAlgebra.zipInline(l.buffer, r.buffer, block))
 }
@@ -114,6 +114,10 @@ public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.produce(
     initializer: A.(IntArray) -> T
 ): BufferND<T> = produce(shape, initializer)
 
+public fun <T, EA : Algebra<T>, A> A.produce(
+    initializer: EA.(IntArray) -> T
+): BufferND<T> where A : BufferAlgebraND<T, EA>, A : WithShape = produce(shape, initializer)
+
 //// group factories
 //public fun <T, A : Group<T>> A.ndAlgebra(
 //    bufferAlgebra: BufferAlgebra<T, A>,
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt
index 9eba401ab..c17632101 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt
@@ -20,7 +20,7 @@ import space.kscience.kmath.structures.MutableBufferFactory
  */
 public open class BufferND<out T>(
     public val indexes: ShapeIndex,
-    public val buffer: Buffer<T>,
+    public open val buffer: Buffer<T>,
 ) : StructureND<T> {
 
     override operator fun get(index: IntArray): T = buffer[indexes.offset(index)]
@@ -55,14 +55,14 @@ public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
  *
  * @param T the type of items.
  * @param strides The strides to access elements of [MutableBuffer] by linear indices.
- * @param mutableBuffer The underlying buffer.
+ * @param buffer The underlying buffer.
  */
 public class MutableBufferND<T>(
     strides: ShapeIndex,
-    public val mutableBuffer: MutableBuffer<T>,
-) : MutableStructureND<T>, BufferND<T>(strides, mutableBuffer) {
+    override val buffer: MutableBuffer<T>,
+) : MutableStructureND<T>, BufferND<T>(strides, buffer) {
     override fun set(index: IntArray, value: T) {
-        mutableBuffer[indexes.offset(index)] = value
+        buffer[indexes.offset(index)] = value
     }
 }
 
@@ -74,7 +74,7 @@ public inline fun <T, reified R : Any> MutableStructureND<T>.mapToMutableBuffer(
     crossinline transform: (T) -> R,
 ): MutableBufferND<R> {
     return if (this is MutableBufferND<T>)
-        MutableBufferND(this.indexes, factory.invoke(indexes.linearSize) { transform(mutableBuffer[it]) })
+        MutableBufferND(this.indexes, factory.invoke(indexes.linearSize) { transform(buffer[it]) })
     else {
         val strides = DefaultStrides(shape)
         MutableBufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
index 294c44ec4..1502a6fd0 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
@@ -10,42 +10,132 @@ import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.DoubleBuffer
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
+import kotlin.math.pow
+
+public class DoubleBufferND(
+    indexes: ShapeIndex,
+    override val buffer: DoubleBuffer,
+) : BufferND<Double>(indexes, buffer)
+
 
 public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(DoubleField.bufferAlgebra),
     ScaleOperations<StructureND<Double>>, ExtendedFieldOps<StructureND<Double>> {
 
-    override fun StructureND<Double>.toBufferND(): BufferND<Double> = when (this) {
-        is BufferND -> this
+    override fun StructureND<Double>.toBufferND(): DoubleBufferND = when (this) {
+        is DoubleBufferND -> this
         else -> {
             val indexer = indexerBuilder(shape)
-            BufferND(indexer, DoubleBuffer(indexer.linearSize) { offset -> get(indexer.index(offset)) })
+            DoubleBufferND(indexer, DoubleBuffer(indexer.linearSize) { offset -> get(indexer.index(offset)) })
         }
     }
 
-    //TODO do specialization
+    private inline fun mapInline(
+        arg: DoubleBufferND,
+        transform: (Double) -> Double
+    ): DoubleBufferND {
+        val indexes = arg.indexes
+        val array = arg.buffer.array
+        return DoubleBufferND(indexes, DoubleBuffer(indexes.linearSize) { transform(array[it]) })
+    }
 
-    override fun scale(a: StructureND<Double>, value: Double): BufferND<Double> =
+    private inline fun zipInline(
+        l: DoubleBufferND,
+        r: DoubleBufferND,
+        block: (l: Double, r: Double) -> Double
+    ): DoubleBufferND {
+        require(l.indexes == r.indexes) { "Zip requires the same shapes, but found ${l.shape} on the left and ${r.shape} on the right" }
+        val indexes = l.indexes
+        val lArray = l.buffer.array
+        val rArray = r.buffer.array
+        return DoubleBufferND(indexes, DoubleBuffer(indexes.linearSize) { block(lArray[it], rArray[it]) })
+    }
+
+    override fun StructureND<Double>.map(transform: DoubleField.(Double) -> Double): BufferND<Double> =
+        mapInline(toBufferND()) { DoubleField.transform(it) }
+
+
+    override fun zip(
+        left: StructureND<Double>,
+        right: StructureND<Double>,
+        transform: DoubleField.(Double, Double) -> Double
+    ): BufferND<Double> = zipInline(left.toBufferND(), right.toBufferND()) { l, r -> DoubleField.transform(l, r) }
+
+    override fun produce(shape: Shape, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND {
+        val indexer = indexerBuilder(shape)
+        return DoubleBufferND(
+            indexer,
+            DoubleBuffer(indexer.linearSize) { offset ->
+                elementAlgebra.initializer(indexer.index(offset))
+            }
+        )
+    }
+
+    override fun add(left: StructureND<Double>, right: StructureND<Double>): DoubleBufferND =
+        zipInline(left.toBufferND(), right.toBufferND()) { l, r -> l + r }
+
+    override fun multiply(left: StructureND<Double>, right: StructureND<Double>): DoubleBufferND =
+        zipInline(left.toBufferND(), right.toBufferND()) { l, r -> l * r }
+
+    override fun StructureND<Double>.unaryMinus(): DoubleBufferND = mapInline(toBufferND()) { -it }
+
+    override fun StructureND<Double>.div(other: StructureND<Double>): DoubleBufferND =
+        zipInline(toBufferND(), other.toBufferND()) { l, r -> l / r }
+
+    override fun StructureND<Double>.plus(arg: Double): DoubleBufferND = mapInline(toBufferND()) { it + arg }
+
+    override fun StructureND<Double>.minus(arg: Double): StructureND<Double> = mapInline(toBufferND()) { it - arg }
+
+    override fun Double.plus(arg: StructureND<Double>): StructureND<Double> = arg + this
+
+    override fun Double.minus(arg: StructureND<Double>): StructureND<Double> = mapInline(arg.toBufferND()) { this - it }
+
+    override fun scale(a: StructureND<Double>, value: Double): DoubleBufferND =
         mapInline(a.toBufferND()) { it * value }
 
-    override fun power(arg: StructureND<Double>, pow: Number): BufferND<Double> =
-        mapInline(arg.toBufferND()) { power(it, pow) }
+    override fun power(arg: StructureND<Double>, pow: Number): DoubleBufferND =
+        mapInline(arg.toBufferND()) { it.pow(pow.toDouble()) }
 
-    override fun exp(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { exp(it) }
-    override fun ln(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { ln(it) }
+    override fun exp(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.exp(it) }
 
-    override fun sin(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { sin(it) }
-    override fun cos(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { cos(it) }
-    override fun tan(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { tan(it) }
-    override fun asin(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { asin(it) }
-    override fun acos(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { acos(it) }
-    override fun atan(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { atan(it) }
+    override fun ln(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.ln(it) }
 
-    override fun sinh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { sinh(it) }
-    override fun cosh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { cosh(it) }
-    override fun tanh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { tanh(it) }
-    override fun asinh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { asinh(it) }
-    override fun acosh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { acosh(it) }
-    override fun atanh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { atanh(it) }
+    override fun sin(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.sin(it) }
+
+    override fun cos(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.cos(it) }
+
+    override fun tan(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.tan(it) }
+
+    override fun asin(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.asin(it) }
+
+    override fun acos(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.acos(it) }
+
+    override fun atan(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.atan(it) }
+
+    override fun sinh(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.sinh(it) }
+
+    override fun cosh(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.cosh(it) }
+
+    override fun tanh(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.tanh(it) }
+
+    override fun asinh(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.asinh(it) }
+
+    override fun acosh(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.acosh(it) }
+
+    override fun atanh(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { kotlin.math.atanh(it) }
 
     public companion object : DoubleFieldOpsND()
 }
@@ -54,7 +144,7 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(D
 public class DoubleFieldND(override val shape: Shape) :
     DoubleFieldOpsND(), FieldND<Double, DoubleField>, NumbersAddOps<StructureND<Double>> {
 
-    override fun number(value: Number): BufferND<Double> {
+    override fun number(value: Number): DoubleBufferND {
         val d = value.toDouble() // minimize conversions
         return produce(shape) { d }
     }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index d731ee4ee..d0b0c0b73 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -121,11 +121,11 @@ public interface GroupOps<T> : Algebra<T> {
     /**
      * Addition of two elements.
      *
-     * @param a the augend.
-     * @param b the addend.
+     * @param left the augend.
+     * @param right the addend.
      * @return the sum.
      */
-    public fun add(a: T, b: T): T
+    public fun add(left: T, right: T): T
 
     // Operations to be performed in this context. Could be moved to extensions in case of KEEP-176.
 
@@ -149,19 +149,19 @@ public interface GroupOps<T> : Algebra<T> {
      * Addition of two elements.
      *
      * @receiver the augend.
-     * @param b the addend.
+     * @param other the addend.
      * @return the sum.
      */
-    public operator fun T.plus(b: T): T = add(this, b)
+    public operator fun T.plus(other: T): T = add(this, other)
 
     /**
      * Subtraction of two elements.
      *
      * @receiver the minuend.
-     * @param b the subtrahend.
+     * @param other the subtrahend.
      * @return the difference.
      */
-    public operator fun T.minus(b: T): T = add(this, -b)
+    public operator fun T.minus(other: T): T = add(this, -other)
     // Dynamic dispatch of operations
     override fun unaryOperationFunction(operation: String): (arg: T) -> T = when (operation) {
         PLUS_OPERATION -> { arg -> +arg }
@@ -210,18 +210,18 @@ public interface RingOps<T> : GroupOps<T> {
     /**
      * Multiplies two elements.
      *
-     * @param a the multiplier.
-     * @param b the multiplicand.
+     * @param left the multiplier.
+     * @param right the multiplicand.
      */
-    public fun multiply(a: T, b: T): T
+    public fun multiply(left: T, right: T): T
 
     /**
      * Multiplies this element by scalar.
      *
      * @receiver the multiplier.
-     * @param b the multiplicand.
+     * @param other the multiplicand.
      */
-    public operator fun T.times(b: T): T = multiply(this, b)
+    public operator fun T.times(other: T): T = multiply(this, other)
 
     override fun binaryOperationFunction(operation: String): (left: T, right: T) -> T = when (operation) {
         TIMES_OPERATION -> ::multiply
@@ -260,20 +260,20 @@ public interface FieldOps<T> : RingOps<T> {
     /**
      * Division of two elements.
      *
-     * @param a the dividend.
-     * @param b the divisor.
+     * @param left the dividend.
+     * @param right the divisor.
      * @return the quotient.
      */
-    public fun divide(a: T, b: T): T
+    public fun divide(left: T, right: T): T
 
     /**
      * Division of two elements.
      *
      * @receiver the dividend.
-     * @param b the divisor.
+     * @param other the divisor.
      * @return the quotient.
      */
-    public operator fun T.div(b: T): T = divide(this, b)
+    public operator fun T.div(other: T): T = divide(this, other)
 
     override fun binaryOperationFunction(operation: String): (left: T, right: T) -> T = when (operation) {
         DIV_OPERATION -> ::divide
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 97e35e4b0..5a713049e 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -34,10 +34,10 @@ public object BigIntField : Field<BigInt>, NumbersAddOps<BigInt>, ScaleOperation
 
     @Suppress("EXTENSION_SHADOWED_BY_MEMBER")
     override fun BigInt.unaryMinus(): BigInt = -this
-    override fun add(a: BigInt, b: BigInt): BigInt = a.plus(b)
+    override fun add(left: BigInt, right: BigInt): BigInt = left.plus(right)
     override fun scale(a: BigInt, value: Double): BigInt = a.times(number(value))
-    override fun multiply(a: BigInt, b: BigInt): BigInt = a.times(b)
-    override fun divide(a: BigInt, b: BigInt): BigInt = a.div(b)
+    override fun multiply(left: BigInt, right: BigInt): BigInt = left.times(right)
+    override fun divide(left: BigInt, right: BigInt): BigInt = left.div(right)
 
     public operator fun String.unaryPlus(): BigInt = this.parseBigInteger() ?: error("Can't parse $this as big integer")
     public operator fun String.unaryMinus(): BigInt =
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt
index 5a14e7734..bc05f3904 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt
@@ -134,8 +134,8 @@ public open class BufferRingOps<T, A: Ring<T>>(
     override val bufferFactory: BufferFactory<T>,
 ) : BufferAlgebra<T, A>, RingOps<Buffer<T>>{
 
-    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l + r }
-    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l * r }
+    override fun add(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l + r }
+    override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l * r }
     override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
 
     override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> =
@@ -153,9 +153,9 @@ public open class BufferFieldOps<T, A : Field<T>>(
     bufferFactory: BufferFactory<T>,
 ) : BufferRingOps<T, A>(elementAlgebra, bufferFactory), BufferAlgebra<T, A>, FieldOps<Buffer<T>>, ScaleOperations<Buffer<T>> {
 
-    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l + r }
-    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l * r }
-    override fun divide(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l / r }
+    override fun add(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l + r }
+    override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l * r }
+    override fun divide(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l / r }
 
     override fun scale(a: Buffer<T>, value: Double): Buffer<T> = a.map { scale(it, value) }
     override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt
index 2580cd6f8..29b25aae8 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt
@@ -15,36 +15,37 @@ import kotlin.math.*
  * [ExtendedFieldOps] over [DoubleBuffer].
  */
 public abstract class DoubleBufferOps : ExtendedFieldOps<Buffer<Double>>, Norm<Buffer<Double>, Double> {
+
     override fun Buffer<Double>.unaryMinus(): DoubleBuffer = if (this is DoubleBuffer) {
         DoubleBuffer(size) { -array[it] }
     } else {
         DoubleBuffer(size) { -get(it) }
     }
 
-    override fun add(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
-        require(b.size == a.size) {
-            "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} "
+    override fun add(left: Buffer<Double>, right: Buffer<Double>): DoubleBuffer {
+        require(right.size == left.size) {
+            "The size of the first buffer ${left.size} should be the same as for second one: ${right.size} "
         }
 
-        return if (a is DoubleBuffer && b is DoubleBuffer) {
-            val aArray = a.array
-            val bArray = b.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] + bArray[it] })
-        } else DoubleBuffer(DoubleArray(a.size) { a[it] + b[it] })
+        return if (left is DoubleBuffer && right is DoubleBuffer) {
+            val aArray = left.array
+            val bArray = right.array
+            DoubleBuffer(DoubleArray(left.size) { aArray[it] + bArray[it] })
+        } else DoubleBuffer(DoubleArray(left.size) { left[it] + right[it] })
     }
 
-    override fun Buffer<Double>.plus(b: Buffer<Double>): DoubleBuffer = add(this, b)
+    override fun Buffer<Double>.plus(other: Buffer<Double>): DoubleBuffer = add(this, other)
 
-    override fun Buffer<Double>.minus(b: Buffer<Double>): DoubleBuffer {
-        require(b.size == this.size) {
-            "The size of the first buffer ${this.size} should be the same as for second one: ${b.size} "
+    override fun Buffer<Double>.minus(other: Buffer<Double>): DoubleBuffer {
+        require(other.size == this.size) {
+            "The size of the first buffer ${this.size} should be the same as for second one: ${other.size} "
         }
 
-        return if (this is DoubleBuffer && b is DoubleBuffer) {
+        return if (this is DoubleBuffer && other is DoubleBuffer) {
             val aArray = this.array
-            val bArray = b.array
+            val bArray = other.array
             DoubleBuffer(DoubleArray(this.size) { aArray[it] - bArray[it] })
-        } else DoubleBuffer(DoubleArray(this.size) { this[it] - b[it] })
+        } else DoubleBuffer(DoubleArray(this.size) { this[it] - other[it] })
     }
 
     //
@@ -66,29 +67,29 @@ public abstract class DoubleBufferOps : ExtendedFieldOps<Buffer<Double>>, Norm<B
 //        } else RealBuffer(DoubleArray(a.size) { a[it] / kValue })
 //    }
 
-    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
-        require(b.size == a.size) {
-            "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} "
+    override fun multiply(left: Buffer<Double>, right: Buffer<Double>): DoubleBuffer {
+        require(right.size == left.size) {
+            "The size of the first buffer ${left.size} should be the same as for second one: ${right.size} "
         }
 
-        return if (a is DoubleBuffer && b is DoubleBuffer) {
-            val aArray = a.array
-            val bArray = b.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] * bArray[it] })
+        return if (left is DoubleBuffer && right is DoubleBuffer) {
+            val aArray = left.array
+            val bArray = right.array
+            DoubleBuffer(DoubleArray(left.size) { aArray[it] * bArray[it] })
         } else
-            DoubleBuffer(DoubleArray(a.size) { a[it] * b[it] })
+            DoubleBuffer(DoubleArray(left.size) { left[it] * right[it] })
     }
 
-    override fun divide(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
-        require(b.size == a.size) {
-            "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} "
+    override fun divide(left: Buffer<Double>, right: Buffer<Double>): DoubleBuffer {
+        require(right.size == left.size) {
+            "The size of the first buffer ${left.size} should be the same as for second one: ${right.size} "
         }
 
-        return if (a is DoubleBuffer && b is DoubleBuffer) {
-            val aArray = a.array
-            val bArray = b.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] / bArray[it] })
-        } else DoubleBuffer(DoubleArray(a.size) { a[it] / b[it] })
+        return if (left is DoubleBuffer && right is DoubleBuffer) {
+            val aArray = left.array
+            val bArray = right.array
+            DoubleBuffer(DoubleArray(left.size) { aArray[it] / bArray[it] })
+        } else DoubleBuffer(DoubleArray(left.size) { left[it] / right[it] })
     }
 
     override fun sin(arg: Buffer<Double>): DoubleBuffer = if (arg is DoubleBuffer) {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt
index c1775296c..1168dc6ba 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt
@@ -73,10 +73,10 @@ public object DoubleField : ExtendedField<Double>, Norm<Double, Double>, ScaleOp
             else -> super<ExtendedField>.binaryOperationFunction(operation)
         }
 
-    override inline fun add(a: Double, b: Double): Double = a + b
+    override inline fun add(left: Double, right: Double): Double = left + right
 
-    override inline fun multiply(a: Double, b: Double): Double = a * b
-    override inline fun divide(a: Double, b: Double): Double = a / b
+    override inline fun multiply(left: Double, right: Double): Double = left * right
+    override inline fun divide(left: Double, right: Double): Double = left / right
 
     override inline fun scale(a: Double, value: Double): Double = a * value
 
@@ -102,10 +102,10 @@ public object DoubleField : ExtendedField<Double>, Norm<Double, Double>, ScaleOp
     override inline fun norm(arg: Double): Double = abs(arg)
 
     override inline fun Double.unaryMinus(): Double = -this
-    override inline fun Double.plus(b: Double): Double = this + b
-    override inline fun Double.minus(b: Double): Double = this - b
-    override inline fun Double.times(b: Double): Double = this * b
-    override inline fun Double.div(b: Double): Double = this / b
+    override inline fun Double.plus(other: Double): Double = this + other
+    override inline fun Double.minus(other: Double): Double = this - other
+    override inline fun Double.times(other: Double): Double = this * other
+    override inline fun Double.div(other: Double): Double = this / other
 }
 
 public val Double.Companion.algebra: DoubleField get() = DoubleField
@@ -126,12 +126,12 @@ public object FloatField : ExtendedField<Float>, Norm<Float, Float> {
             else -> super.binaryOperationFunction(operation)
         }
 
-    override inline fun add(a: Float, b: Float): Float = a + b
+    override inline fun add(left: Float, right: Float): Float = left + right
     override fun scale(a: Float, value: Double): Float = a * value.toFloat()
 
-    override inline fun multiply(a: Float, b: Float): Float = a * b
+    override inline fun multiply(left: Float, right: Float): Float = left * right
 
-    override inline fun divide(a: Float, b: Float): Float = a / b
+    override inline fun divide(left: Float, right: Float): Float = left / right
 
     override inline fun sin(arg: Float): Float = kotlin.math.sin(arg)
     override inline fun cos(arg: Float): Float = kotlin.math.cos(arg)
@@ -155,10 +155,10 @@ public object FloatField : ExtendedField<Float>, Norm<Float, Float> {
     override inline fun norm(arg: Float): Float = abs(arg)
 
     override inline fun Float.unaryMinus(): Float = -this
-    override inline fun Float.plus(b: Float): Float = this + b
-    override inline fun Float.minus(b: Float): Float = this - b
-    override inline fun Float.times(b: Float): Float = this * b
-    override inline fun Float.div(b: Float): Float = this / b
+    override inline fun Float.plus(other: Float): Float = this + other
+    override inline fun Float.minus(other: Float): Float = this - other
+    override inline fun Float.times(other: Float): Float = this * other
+    override inline fun Float.div(other: Float): Float = this / other
 }
 
 public val Float.Companion.algebra: FloatField get() = FloatField
@@ -175,14 +175,14 @@ public object IntRing : Ring<Int>, Norm<Int, Int>, NumericAlgebra<Int> {
         get() = 1
 
     override fun number(value: Number): Int = value.toInt()
-    override inline fun add(a: Int, b: Int): Int = a + b
-    override inline fun multiply(a: Int, b: Int): Int = a * b
+    override inline fun add(left: Int, right: Int): Int = left + right
+    override inline fun multiply(left: Int, right: Int): Int = left * right
     override inline fun norm(arg: Int): Int = abs(arg)
 
     override inline fun Int.unaryMinus(): Int = -this
-    override inline fun Int.plus(b: Int): Int = this + b
-    override inline fun Int.minus(b: Int): Int = this - b
-    override inline fun Int.times(b: Int): Int = this * b
+    override inline fun Int.plus(other: Int): Int = this + other
+    override inline fun Int.minus(other: Int): Int = this - other
+    override inline fun Int.times(other: Int): Int = this * other
 }
 
 public val Int.Companion.algebra: IntRing get() = IntRing
@@ -199,14 +199,14 @@ public object ShortRing : Ring<Short>, Norm<Short, Short>, NumericAlgebra<Short>
         get() = 1
 
     override fun number(value: Number): Short = value.toShort()
-    override inline fun add(a: Short, b: Short): Short = (a + b).toShort()
-    override inline fun multiply(a: Short, b: Short): Short = (a * b).toShort()
+    override inline fun add(left: Short, right: Short): Short = (left + right).toShort()
+    override inline fun multiply(left: Short, right: Short): Short = (left * right).toShort()
     override fun norm(arg: Short): Short = if (arg > 0) arg else (-arg).toShort()
 
     override inline fun Short.unaryMinus(): Short = (-this).toShort()
-    override inline fun Short.plus(b: Short): Short = (this + b).toShort()
-    override inline fun Short.minus(b: Short): Short = (this - b).toShort()
-    override inline fun Short.times(b: Short): Short = (this * b).toShort()
+    override inline fun Short.plus(other: Short): Short = (this + other).toShort()
+    override inline fun Short.minus(other: Short): Short = (this - other).toShort()
+    override inline fun Short.times(other: Short): Short = (this * other).toShort()
 }
 
 public val Short.Companion.algebra: ShortRing get() = ShortRing
@@ -223,14 +223,14 @@ public object ByteRing : Ring<Byte>, Norm<Byte, Byte>, NumericAlgebra<Byte> {
         get() = 1
 
     override fun number(value: Number): Byte = value.toByte()
-    override inline fun add(a: Byte, b: Byte): Byte = (a + b).toByte()
-    override inline fun multiply(a: Byte, b: Byte): Byte = (a * b).toByte()
+    override inline fun add(left: Byte, right: Byte): Byte = (left + right).toByte()
+    override inline fun multiply(left: Byte, right: Byte): Byte = (left * right).toByte()
     override fun norm(arg: Byte): Byte = if (arg > 0) arg else (-arg).toByte()
 
     override inline fun Byte.unaryMinus(): Byte = (-this).toByte()
-    override inline fun Byte.plus(b: Byte): Byte = (this + b).toByte()
-    override inline fun Byte.minus(b: Byte): Byte = (this - b).toByte()
-    override inline fun Byte.times(b: Byte): Byte = (this * b).toByte()
+    override inline fun Byte.plus(other: Byte): Byte = (this + other).toByte()
+    override inline fun Byte.minus(other: Byte): Byte = (this - other).toByte()
+    override inline fun Byte.times(other: Byte): Byte = (this * other).toByte()
 }
 
 public val Byte.Companion.algebra: ByteRing get() = ByteRing
@@ -247,14 +247,14 @@ public object LongRing : Ring<Long>, Norm<Long, Long>, NumericAlgebra<Long> {
         get() = 1L
 
     override fun number(value: Number): Long = value.toLong()
-    override inline fun add(a: Long, b: Long): Long = a + b
-    override inline fun multiply(a: Long, b: Long): Long = a * b
+    override inline fun add(left: Long, right: Long): Long = left + right
+    override inline fun multiply(left: Long, right: Long): Long = left * right
     override fun norm(arg: Long): Long = abs(arg)
 
     override inline fun Long.unaryMinus(): Long = (-this)
-    override inline fun Long.plus(b: Long): Long = (this + b)
-    override inline fun Long.minus(b: Long): Long = (this - b)
-    override inline fun Long.times(b: Long): Long = (this * b)
+    override inline fun Long.plus(other: Long): Long = (this + other)
+    override inline fun Long.minus(other: Long): Long = (this - other)
+    override inline fun Long.times(other: Long): Long = (this * other)
 }
 
 public val Long.Companion.algebra: LongRing get() = LongRing
diff --git a/kmath-core/src/jvmMain/kotlin/space/kscience/kmath/operations/BigNumbers.kt b/kmath-core/src/jvmMain/kotlin/space/kscience/kmath/operations/BigNumbers.kt
index 69dd858c4..3a9c242fc 100644
--- a/kmath-core/src/jvmMain/kotlin/space/kscience/kmath/operations/BigNumbers.kt
+++ b/kmath-core/src/jvmMain/kotlin/space/kscience/kmath/operations/BigNumbers.kt
@@ -18,9 +18,9 @@ public object JBigIntegerField : Ring<BigInteger>, NumericAlgebra<BigInteger> {
     override val one: BigInteger get() = BigInteger.ONE
 
     override fun number(value: Number): BigInteger = BigInteger.valueOf(value.toLong())
-    override fun add(a: BigInteger, b: BigInteger): BigInteger = a.add(b)
-    override operator fun BigInteger.minus(b: BigInteger): BigInteger = subtract(b)
-    override fun multiply(a: BigInteger, b: BigInteger): BigInteger = a.multiply(b)
+    override fun add(left: BigInteger, right: BigInteger): BigInteger = left.add(right)
+    override operator fun BigInteger.minus(other: BigInteger): BigInteger = subtract(other)
+    override fun multiply(left: BigInteger, right: BigInteger): BigInteger = left.multiply(right)
 
     override operator fun BigInteger.unaryMinus(): BigInteger = negate()
 }
@@ -39,15 +39,15 @@ public abstract class JBigDecimalFieldBase internal constructor(
     override val one: BigDecimal
         get() = BigDecimal.ONE
 
-    override fun add(a: BigDecimal, b: BigDecimal): BigDecimal = a.add(b)
-    override operator fun BigDecimal.minus(b: BigDecimal): BigDecimal = subtract(b)
+    override fun add(left: BigDecimal, right: BigDecimal): BigDecimal = left.add(right)
+    override operator fun BigDecimal.minus(other: BigDecimal): BigDecimal = subtract(other)
     override fun number(value: Number): BigDecimal = BigDecimal.valueOf(value.toDouble())
 
     override fun scale(a: BigDecimal, value: Double): BigDecimal =
         a.multiply(value.toBigDecimal(mathContext), mathContext)
 
-    override fun multiply(a: BigDecimal, b: BigDecimal): BigDecimal = a.multiply(b, mathContext)
-    override fun divide(a: BigDecimal, b: BigDecimal): BigDecimal = a.divide(b, mathContext)
+    override fun multiply(left: BigDecimal, right: BigDecimal): BigDecimal = left.multiply(right, mathContext)
+    override fun divide(left: BigDecimal, right: BigDecimal): BigDecimal = left.divide(right, mathContext)
     override fun power(arg: BigDecimal, pow: Number): BigDecimal = arg.pow(pow.toInt(), mathContext)
     override fun sqrt(arg: BigDecimal): BigDecimal = arg.sqrt(mathContext)
     override operator fun BigDecimal.unaryMinus(): BigDecimal = negate(mathContext)
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
index 54b285a70..e862c0b9d 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
@@ -104,12 +104,12 @@ public class PolynomialSpace<T, C>(
         Polynomial(coefficients.map { -it })
     }
 
-    override fun add(a: Polynomial<T>, b: Polynomial<T>): Polynomial<T> {
-        val dim = max(a.coefficients.size, b.coefficients.size)
+    override fun add(left: Polynomial<T>, right: Polynomial<T>): Polynomial<T> {
+        val dim = max(left.coefficients.size, right.coefficients.size)
 
         return ring {
             Polynomial(List(dim) { index ->
-                a.coefficients.getOrElse(index) { zero } + b.coefficients.getOrElse(index) { zero }
+                left.coefficients.getOrElse(index) { zero } + right.coefficients.getOrElse(index) { zero }
             })
         }
     }
diff --git a/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean2DSpace.kt b/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean2DSpace.kt
index e8b1ce95b..5e3cbff83 100644
--- a/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean2DSpace.kt
+++ b/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean2DSpace.kt
@@ -47,7 +47,7 @@ public object Euclidean2DSpace : GeometrySpace<Vector2D>, ScaleOperations<Vector
     override fun Vector2D.unaryMinus(): Vector2D = Vector2D(-x, -y)
 
     override fun Vector2D.distanceTo(other: Vector2D): Double = (this - other).norm()
-    override fun add(a: Vector2D, b: Vector2D): Vector2D = Vector2D(a.x + b.x, a.y + b.y)
+    override fun add(left: Vector2D, right: Vector2D): Vector2D = Vector2D(left.x + right.x, left.y + right.y)
     override fun scale(a: Vector2D, value: Double): Vector2D = Vector2D(a.x * value, a.y * value)
     override fun Vector2D.dot(other: Vector2D): Double = x * other.x + y * other.y
 }
diff --git a/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean3DSpace.kt b/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean3DSpace.kt
index d567bee9a..96f307ed6 100644
--- a/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean3DSpace.kt
+++ b/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean3DSpace.kt
@@ -47,8 +47,8 @@ public object Euclidean3DSpace : GeometrySpace<Vector3D>, ScaleOperations<Vector
 
     override fun Vector3D.distanceTo(other: Vector3D): Double = (this - other).norm()
 
-    override fun add(a: Vector3D, b: Vector3D): Vector3D =
-        Vector3D(a.x + b.x, a.y + b.y, a.z + b.z)
+    override fun add(left: Vector3D, right: Vector3D): Vector3D =
+        Vector3D(left.x + right.x, left.y + right.y, left.z + right.z)
 
     override fun scale(a: Vector3D, value: Double): Vector3D =
         Vector3D(a.x * value, a.y * value, a.z * value)
diff --git a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt
index 7c719ccd7..a495577c3 100644
--- a/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt
+++ b/kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt
@@ -67,10 +67,10 @@ public interface IndexedHistogramSpace<T : Comparable<T>, V : Any>
 
     public fun produce(builder: HistogramBuilder<T>.() -> Unit): IndexedHistogram<T, V>
 
-    override fun add(a: IndexedHistogram<T, V>, b: IndexedHistogram<T, V>): IndexedHistogram<T, V> {
-        require(a.context == this) { "Can't operate on a histogram produced by external space" }
-        require(b.context == this) { "Can't operate on a histogram produced by external space" }
-        return IndexedHistogram(this, histogramValueSpace { a.values + b.values })
+    override fun add(left: IndexedHistogram<T, V>, right: IndexedHistogram<T, V>): IndexedHistogram<T, V> {
+        require(left.context == this) { "Can't operate on a histogram produced by external space" }
+        require(right.context == this) { "Can't operate on a histogram produced by external space" }
+        return IndexedHistogram(this, histogramValueSpace { left.values + right.values })
     }
 
     override fun scale(a: IndexedHistogram<T, V>, value: Double): IndexedHistogram<T, V> {
diff --git a/kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/TreeHistogramSpace.kt b/kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/TreeHistogramSpace.kt
index 96f945f6a..cc54d7e1a 100644
--- a/kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/TreeHistogramSpace.kt
+++ b/kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/TreeHistogramSpace.kt
@@ -88,20 +88,20 @@ public class TreeHistogramSpace(
         TreeHistogramBuilder(binFactory).apply(block).build()
 
     override fun add(
-        a: UnivariateHistogram,
-        b: UnivariateHistogram,
+        left: UnivariateHistogram,
+        right: UnivariateHistogram,
     ): UnivariateHistogram {
 //        require(a.context == this) { "Histogram $a does not belong to this context" }
 //        require(b.context == this) { "Histogram $b does not belong to this context" }
         val bins = TreeMap<Double, UnivariateBin>().apply {
-            (a.bins.map { it.domain } union b.bins.map { it.domain }).forEach { def ->
+            (left.bins.map { it.domain } union right.bins.map { it.domain }).forEach { def ->
                 put(
                     def.center,
                     UnivariateBin(
                         def,
-                        value = (a[def.center]?.value ?: 0.0) + (b[def.center]?.value ?: 0.0),
-                        standardDeviation = (a[def.center]?.standardDeviation
-                            ?: 0.0) + (b[def.center]?.standardDeviation ?: 0.0)
+                        value = (left[def.center]?.value ?: 0.0) + (right[def.center]?.value ?: 0.0),
+                        standardDeviation = (left[def.center]?.standardDeviation
+                            ?: 0.0) + (right[def.center]?.standardDeviation ?: 0.0)
                     )
                 )
             }
diff --git a/kmath-jafama/src/main/kotlin/space/kscience/kmath/jafama/KMathJafama.kt b/kmath-jafama/src/main/kotlin/space/kscience/kmath/jafama/KMathJafama.kt
index 1a6e3325b..645a14e30 100644
--- a/kmath-jafama/src/main/kotlin/space/kscience/kmath/jafama/KMathJafama.kt
+++ b/kmath-jafama/src/main/kotlin/space/kscience/kmath/jafama/KMathJafama.kt
@@ -28,10 +28,10 @@ public object JafamaDoubleField : ExtendedField<Double>, Norm<Double, Double>, S
             else -> super<ExtendedField>.binaryOperationFunction(operation)
         }
 
-    override inline fun add(a: Double, b: Double): Double = a + b
+    override inline fun add(left: Double, right: Double): Double = left + right
 
-    override inline fun multiply(a: Double, b: Double): Double = a * b
-    override inline fun divide(a: Double, b: Double): Double = a / b
+    override inline fun multiply(left: Double, right: Double): Double = left * right
+    override inline fun divide(left: Double, right: Double): Double = left / right
 
     override inline fun scale(a: Double, value: Double): Double = a * value
 
@@ -57,10 +57,10 @@ public object JafamaDoubleField : ExtendedField<Double>, Norm<Double, Double>, S
     override inline fun norm(arg: Double): Double = FastMath.abs(arg)
 
     override inline fun Double.unaryMinus(): Double = -this
-    override inline fun Double.plus(b: Double): Double = this + b
-    override inline fun Double.minus(b: Double): Double = this - b
-    override inline fun Double.times(b: Double): Double = this * b
-    override inline fun Double.div(b: Double): Double = this / b
+    override inline fun Double.plus(other: Double): Double = this + other
+    override inline fun Double.minus(other: Double): Double = this - other
+    override inline fun Double.times(other: Double): Double = this * other
+    override inline fun Double.div(other: Double): Double = this / other
 }
 
 /**
@@ -79,10 +79,10 @@ public object StrictJafamaDoubleField : ExtendedField<Double>, Norm<Double, Doub
             else -> super<ExtendedField>.binaryOperationFunction(operation)
         }
 
-    override inline fun add(a: Double, b: Double): Double = a + b
+    override inline fun add(left: Double, right: Double): Double = left + right
 
-    override inline fun multiply(a: Double, b: Double): Double = a * b
-    override inline fun divide(a: Double, b: Double): Double = a / b
+    override inline fun multiply(left: Double, right: Double): Double = left * right
+    override inline fun divide(left: Double, right: Double): Double = left / right
 
     override inline fun scale(a: Double, value: Double): Double = a * value
 
@@ -108,8 +108,8 @@ public object StrictJafamaDoubleField : ExtendedField<Double>, Norm<Double, Doub
     override inline fun norm(arg: Double): Double = StrictFastMath.abs(arg)
 
     override inline fun Double.unaryMinus(): Double = -this
-    override inline fun Double.plus(b: Double): Double = this + b
-    override inline fun Double.minus(b: Double): Double = this - b
-    override inline fun Double.times(b: Double): Double = this * b
-    override inline fun Double.div(b: Double): Double = this / b
+    override inline fun Double.plus(other: Double): Double = this + other
+    override inline fun Double.minus(other: Double): Double = this - other
+    override inline fun Double.times(other: Double): Double = this * other
+    override inline fun Double.div(other: Double): Double = this / other
 }
diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
index d65ad0dc9..792890a2d 100644
--- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
+++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
@@ -72,11 +72,11 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
  */
 public sealed interface Nd4jArrayGroupOps<T, out S : Ring<T>> : GroupOpsND<T, S>, Nd4jArrayAlgebra<T, S> {
 
-    override fun add(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
-        a.ndArray.add(b.ndArray).wrap()
+    override fun add(left: StructureND<T>, right: StructureND<T>): Nd4jArrayStructure<T> =
+        left.ndArray.add(right.ndArray).wrap()
 
-    override operator fun StructureND<T>.minus(b: StructureND<T>): Nd4jArrayStructure<T> =
-        ndArray.sub(b.ndArray).wrap()
+    override operator fun StructureND<T>.minus(other: StructureND<T>): Nd4jArrayStructure<T> =
+        ndArray.sub(other.ndArray).wrap()
 
     override operator fun StructureND<T>.unaryMinus(): Nd4jArrayStructure<T> =
         ndArray.neg().wrap()
@@ -94,8 +94,8 @@ public sealed interface Nd4jArrayGroupOps<T, out S : Ring<T>> : GroupOpsND<T, S>
 @OptIn(UnstableKMathAPI::class)
 public sealed interface Nd4jArrayRingOps<T, out R : Ring<T>> : RingOpsND<T, R>, Nd4jArrayGroupOps<T, R> {
 
-    override fun multiply(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
-        a.ndArray.mul(b.ndArray).wrap()
+    override fun multiply(left: StructureND<T>, right: StructureND<T>): Nd4jArrayStructure<T> =
+        left.ndArray.mul(right.ndArray).wrap()
 //
 //    override operator fun Nd4jArrayStructure<T>.minus(b: Number): Nd4jArrayStructure<T> {
 //        check(this)
@@ -132,8 +132,8 @@ public sealed interface Nd4jArrayRingOps<T, out R : Ring<T>> : RingOpsND<T, R>,
  */
 public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldOpsND<T, F>, Nd4jArrayRingOps<T, F> {
 
-    override fun divide(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
-        a.ndArray.div(b.ndArray).wrap()
+    override fun divide(left: StructureND<T>, right: StructureND<T>): Nd4jArrayStructure<T> =
+        left.ndArray.div(right.ndArray).wrap()
 
     public operator fun Number.div(b: StructureND<T>): Nd4jArrayStructure<T> = b.ndArray.rdiv(this).wrap()
 
diff --git a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt
index c1bbace86..e0be72d4b 100644
--- a/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt
+++ b/kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/SamplerAlgebra.kt
@@ -41,8 +41,8 @@ public class SamplerSpace<T : Any, out S>(public val algebra: S) : Group<Sampler
 
     override val zero: Sampler<T> = ConstantSampler(algebra.zero)
 
-    override fun add(a: Sampler<T>, b: Sampler<T>): Sampler<T> = BasicSampler { generator ->
-        a.sample(generator).zip(b.sample(generator)) { aValue, bValue -> algebra { aValue + bValue } }
+    override fun add(left: Sampler<T>, right: Sampler<T>): Sampler<T> = BasicSampler { generator ->
+        left.sample(generator).zip(right.sample(generator)) { aValue, bValue -> algebra { aValue + bValue } }
     }
 
     override fun scale(a: Sampler<T>, value: Double): Sampler<T> = BasicSampler { generator ->
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt
index 6076748d9..810ebe777 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt
@@ -5,7 +5,7 @@
 
 package space.kscience.kmath.tensors.api
 
-import space.kscience.kmath.operations.Algebra
+import space.kscience.kmath.operations.RingOps
 
 /**
  * Algebra over a ring on [Tensor].
@@ -13,7 +13,7 @@ import space.kscience.kmath.operations.Algebra
  *
  * @param T the type of items in the tensors.
  */
-public interface TensorAlgebra<T> : Algebra<Tensor<T>> {
+public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
     /**
      * Returns a single tensor value of unit dimension if tensor shape equals to [1].
      *
@@ -53,7 +53,7 @@ public interface TensorAlgebra<T> : Algebra<Tensor<T>> {
      * @param other tensor to be added.
      * @return the sum of this tensor and [other].
      */
-    public operator fun Tensor<T>.plus(other: Tensor<T>): Tensor<T>
+    override fun Tensor<T>.plus(other: Tensor<T>): Tensor<T>
 
     /**
      * Adds the scalar [value] to each element of this tensor.
@@ -93,7 +93,7 @@ public interface TensorAlgebra<T> : Algebra<Tensor<T>> {
      * @param other tensor to be subtracted.
      * @return the difference between this tensor and [other].
      */
-    public operator fun Tensor<T>.minus(other: Tensor<T>): Tensor<T>
+    override fun Tensor<T>.minus(other: Tensor<T>): Tensor<T>
 
     /**
      * Subtracts the scalar [value] from each element of this tensor.
@@ -134,7 +134,7 @@ public interface TensorAlgebra<T> : Algebra<Tensor<T>> {
      * @param other tensor to be multiplied.
      * @return the product of this tensor and [other].
      */
-    public operator fun Tensor<T>.times(other: Tensor<T>): Tensor<T>
+    override fun Tensor<T>.times(other: Tensor<T>): Tensor<T>
 
     /**
      * Multiplies the scalar [value] by each element of this tensor.
@@ -155,7 +155,7 @@ public interface TensorAlgebra<T> : Algebra<Tensor<T>> {
      *
      * @return tensor negation of the original tensor.
      */
-    public operator fun Tensor<T>.unaryMinus(): Tensor<T>
+    override fun Tensor<T>.unaryMinus(): Tensor<T>
 
     /**
      * Returns the tensor at index i
@@ -323,4 +323,8 @@ public interface TensorAlgebra<T> : Algebra<Tensor<T>> {
      * @return the index of maximum value of each row of the input tensor in the given dimension [dim].
      */
     public fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): Tensor<T>
+
+    override fun add(left: Tensor<T>, right: Tensor<T>): Tensor<T> = left + right
+
+    override fun multiply(left: Tensor<T>, right: Tensor<T>): Tensor<T> = left * right
 }
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt
index e0451c2eb..1f5778d5e 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt
@@ -27,7 +27,7 @@ internal fun <T> Tensor<T>.copyToBufferedTensor(): BufferedTensor<T> =
 internal fun <T> Tensor<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
     is BufferedTensor<T> -> this
     is MutableBufferND<T> -> if (this.indexes == TensorLinearStructure(this.shape)) {
-        BufferedTensor(this.shape, this.mutableBuffer, 0)
+        BufferedTensor(this.shape, this.buffer, 0)
     } else {
         this.copyToBufferedTensor()
     }
diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
index fca23bc16..a914542bc 100644
--- a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
+++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
@@ -88,17 +88,17 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
         }
     }.asStructure()
 
-    override fun add(a: StructureND<Double>, b: StructureND<Double>): ViktorStructureND =
-        (a.f64Buffer + b.f64Buffer).asStructure()
+    override fun add(left: StructureND<Double>, right: StructureND<Double>): ViktorStructureND =
+        (left.f64Buffer + right.f64Buffer).asStructure()
 
     override fun scale(a: StructureND<Double>, value: Double): ViktorStructureND =
         (a.f64Buffer * value).asStructure()
 
-    override inline fun StructureND<Double>.plus(b: StructureND<Double>): ViktorStructureND =
-        (f64Buffer + b.f64Buffer).asStructure()
+    override inline fun StructureND<Double>.plus(other: StructureND<Double>): ViktorStructureND =
+        (f64Buffer + other.f64Buffer).asStructure()
 
-    override inline fun StructureND<Double>.minus(b: StructureND<Double>): ViktorStructureND =
-        (f64Buffer - b.f64Buffer).asStructure()
+    override inline fun StructureND<Double>.minus(other: StructureND<Double>): ViktorStructureND =
+        (f64Buffer - other.f64Buffer).asStructure()
 
     override inline fun StructureND<Double>.times(k: Number): ViktorStructureND =
         (f64Buffer * k.toDouble()).asStructure()

From 4513b06e87d4bb2a16266eb5cba5e96167c0e0cd Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 17 Oct 2021 13:09:21 +0300
Subject: [PATCH 04/10] Shapeless ND and Buffer algebras

---
 .idea/copyright/kmath.xml                     |   6 -
 .idea/copyright/profiles_settings.xml         |  21 ---
 .idea/scopes/Apply_copyright.xml              |   4 -
 .../space/kscience/kmath/nd/AlgebraND.kt      |   4 +-
 .../kmath/operations/NumericAlgebra.kt        |   2 +-
 .../kscience/kmath/viktor/ViktorFieldOpsND.kt | 124 ++++++++++++++++++
 .../kmath/viktor/ViktorStructureND.kt         | 100 +-------------
 7 files changed, 130 insertions(+), 131 deletions(-)
 delete mode 100644 .idea/copyright/kmath.xml
 delete mode 100644 .idea/copyright/profiles_settings.xml
 delete mode 100644 .idea/scopes/Apply_copyright.xml
 create mode 100644 kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt

diff --git a/.idea/copyright/kmath.xml b/.idea/copyright/kmath.xml
deleted file mode 100644
index 1070e5d33..000000000
--- a/.idea/copyright/kmath.xml
+++ /dev/null
@@ -1,6 +0,0 @@
-<component name="CopyrightManager">
-    <copyright>
-        <option name="notice" value="Copyright 2018-2021 KMath contributors.&#10;Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file." />
-        <option name="myName" value="kmath" />
-    </copyright>
-</component>
diff --git a/.idea/copyright/profiles_settings.xml b/.idea/copyright/profiles_settings.xml
deleted file mode 100644
index b538bdf41..000000000
--- a/.idea/copyright/profiles_settings.xml
+++ /dev/null
@@ -1,21 +0,0 @@
-<component name="CopyrightManager">
-  <settings default="kmath">
-    <module2copyright>
-      <element module="Apply copyright" copyright="kmath" />
-    </module2copyright>
-    <LanguageOptions name="Groovy">
-      <option name="fileTypeOverride" value="1" />
-    </LanguageOptions>
-    <LanguageOptions name="HTML">
-      <option name="fileTypeOverride" value="1" />
-      <option name="prefixLines" value="false" />
-    </LanguageOptions>
-    <LanguageOptions name="Properties">
-      <option name="fileTypeOverride" value="1" />
-    </LanguageOptions>
-    <LanguageOptions name="XML">
-      <option name="fileTypeOverride" value="1" />
-      <option name="prefixLines" value="false" />
-    </LanguageOptions>
-  </settings>
-</component>
\ No newline at end of file
diff --git a/.idea/scopes/Apply_copyright.xml b/.idea/scopes/Apply_copyright.xml
deleted file mode 100644
index 0eb589133..000000000
--- a/.idea/scopes/Apply_copyright.xml
+++ /dev/null
@@ -1,4 +0,0 @@
-<component name="DependencyValidationManager">
-    <scope name="Apply copyright"
-           pattern="!file[*]:*//testData//*&amp;&amp;!file[*]:testData//*&amp;&amp;!file[*]:*.gradle.kts&amp;&amp;!file[*]:*.gradle&amp;&amp;!file[group:kotlin-ultimate]:*/&amp;&amp;!file[kotlin.libraries]:stdlib/api//*"/>
-</component>
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
index 3f9b43f03..b4e8b7487 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
@@ -203,7 +203,9 @@ public interface RingND<T, out A : Ring<T>> : Ring<StructureND<T>>, RingOpsND<T,
  * @param T the type of the element contained in ND structure.
  * @param A the type field over structure elements.
  */
-public interface FieldOpsND<T, out A : Field<T>> : FieldOps<StructureND<T>>, RingOpsND<T, A>,
+public interface FieldOpsND<T, out A : Field<T>> :
+    FieldOps<StructureND<T>>,
+    RingOpsND<T, A>,
     ScaleOperations<StructureND<T>> {
     /**
      * Element-wise division.
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
index ca88ad42d..5f6848211 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
@@ -150,7 +150,7 @@ public interface ScaleOperations<T> : Algebra<T> {
  * TODO to be removed and replaced by extensions after multiple receivers are there
  */
 @UnstableKMathAPI
-public interface NumbersAddOps<T> : Ring<T>, NumericAlgebra<T> {
+public interface NumbersAddOps<T> : RingOps<T>, NumericAlgebra<T> {
     /**
      * Addition of element and scalar.
      *
diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt
new file mode 100644
index 000000000..c72553a64
--- /dev/null
+++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt
@@ -0,0 +1,124 @@
+/*
+ * 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 file.
+ */
+
+package space.kscience.kmath.viktor
+
+import org.jetbrains.bio.viktor.F64Array
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.nd.*
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.ExtendedFieldOps
+import space.kscience.kmath.operations.NumbersAddOps
+
+@OptIn(UnstableKMathAPI::class)
+@Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+public open class ViktorFieldOpsND :
+    FieldOpsND<Double, DoubleField>,
+    ExtendedFieldOps<StructureND<Double>> {
+
+    public val StructureND<Double>.f64Buffer: F64Array
+        get() = when (this) {
+            is ViktorStructureND -> this.f64Buffer
+            else -> produce(shape) { this@f64Buffer[it] }.f64Buffer
+        }
+
+    override val elementAlgebra: DoubleField get() = DoubleField
+
+    override fun produce(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
+        F64Array(*shape).apply {
+            DefaultStrides(shape).indices().forEach { index ->
+                set(value = DoubleField.initializer(index), indices = index)
+            }
+        }.asStructure()
+
+    override fun StructureND<Double>.unaryMinus(): StructureND<Double> = -1 * this
+
+    override fun StructureND<Double>.map(transform: DoubleField.(Double) -> Double): ViktorStructureND =
+        F64Array(*shape).apply {
+            DefaultStrides(shape).indices().forEach { index ->
+                set(value = DoubleField.transform(this@map[index]), indices = index)
+            }
+        }.asStructure()
+
+    override fun StructureND<Double>.mapIndexed(
+        transform: DoubleField.(index: IntArray, Double) -> Double,
+    ): ViktorStructureND = F64Array(*shape).apply {
+        DefaultStrides(shape).indices().forEach { index ->
+            set(value = DoubleField.transform(index, this@mapIndexed[index]), indices = index)
+        }
+    }.asStructure()
+
+    override fun zip(
+        left: StructureND<Double>,
+        right: StructureND<Double>,
+        transform: DoubleField.(Double, Double) -> Double,
+    ): ViktorStructureND {
+        require(left.shape.contentEquals(right.shape))
+        return F64Array(*left.shape).apply {
+            DefaultStrides(left.shape).indices().forEach { index ->
+                set(value = DoubleField.transform(left[index], right[index]), indices = index)
+            }
+        }.asStructure()
+    }
+
+    override fun add(left: StructureND<Double>, right: StructureND<Double>): ViktorStructureND =
+        (left.f64Buffer + right.f64Buffer).asStructure()
+
+    override fun scale(a: StructureND<Double>, value: Double): ViktorStructureND =
+        (a.f64Buffer * value).asStructure()
+
+    override fun StructureND<Double>.plus(other: StructureND<Double>): ViktorStructureND =
+        (f64Buffer + other.f64Buffer).asStructure()
+
+    override fun StructureND<Double>.minus(other: StructureND<Double>): ViktorStructureND =
+        (f64Buffer - other.f64Buffer).asStructure()
+
+    override fun StructureND<Double>.times(k: Number): ViktorStructureND =
+        (f64Buffer * k.toDouble()).asStructure()
+
+    override fun StructureND<Double>.plus(arg: Double): ViktorStructureND =
+        (f64Buffer.plus(arg)).asStructure()
+
+    override fun sin(arg: StructureND<Double>): ViktorStructureND = arg.map { sin(it) }
+    override fun cos(arg: StructureND<Double>): ViktorStructureND = arg.map { cos(it) }
+    override fun tan(arg: StructureND<Double>): ViktorStructureND = arg.map { tan(it) }
+    override fun asin(arg: StructureND<Double>): ViktorStructureND = arg.map { asin(it) }
+    override fun acos(arg: StructureND<Double>): ViktorStructureND = arg.map { acos(it) }
+    override fun atan(arg: StructureND<Double>): ViktorStructureND = arg.map { atan(it) }
+
+    override fun power(arg: StructureND<Double>, pow: Number): ViktorStructureND = arg.map { it.pow(pow) }
+
+    override fun exp(arg: StructureND<Double>): ViktorStructureND = arg.f64Buffer.exp().asStructure()
+
+    override fun ln(arg: StructureND<Double>): ViktorStructureND = arg.f64Buffer.log().asStructure()
+
+    override fun sinh(arg: StructureND<Double>): ViktorStructureND = arg.map { sinh(it) }
+
+    override fun cosh(arg: StructureND<Double>): ViktorStructureND = arg.map { cosh(it) }
+
+    override fun asinh(arg: StructureND<Double>): ViktorStructureND = arg.map { asinh(it) }
+
+    override fun acosh(arg: StructureND<Double>): ViktorStructureND = arg.map { acosh(it) }
+
+    override fun atanh(arg: StructureND<Double>): ViktorStructureND = arg.map { atanh(it) }
+
+    public companion object : ViktorFieldOpsND()
+}
+
+public val DoubleField.viktorAlgebra: ViktorFieldOpsND get() = ViktorFieldOpsND
+
+public open class ViktorFieldND(
+    override val shape: Shape
+) : ViktorFieldOpsND(), FieldND<Double, DoubleField>, NumbersAddOps<StructureND<Double>> {
+    override val zero: ViktorStructureND by lazy { F64Array.full(init = 0.0, shape = shape).asStructure() }
+    override val one: ViktorStructureND by lazy { F64Array.full(init = 1.0, shape = shape).asStructure() }
+
+    override fun number(value: Number): ViktorStructureND =
+        F64Array.full(init = value.toDouble(), shape = shape).asStructure()
+}
+
+public fun DoubleField.viktorAlgebra(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)
+
+public fun ViktorFieldND(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)
\ No newline at end of file
diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
index a914542bc..0d29983f9 100644
--- a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
+++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt
@@ -7,12 +7,8 @@ package space.kscience.kmath.viktor
 
 import org.jetbrains.bio.viktor.F64Array
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.*
-import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOps
-import space.kscience.kmath.operations.ScaleOperations
+import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.MutableStructureND
 
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 public class ViktorStructureND(public val f64Buffer: F64Array) : MutableStructureND<Double> {
@@ -31,96 +27,4 @@ public class ViktorStructureND(public val f64Buffer: F64Array) : MutableStructur
 
 public fun F64Array.asStructure(): ViktorStructureND = ViktorStructureND(this)
 
-@OptIn(UnstableKMathAPI::class)
-@Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, DoubleField>,
-    NumbersAddOps<StructureND<Double>>, ExtendedField<StructureND<Double>>,
-    ScaleOperations<StructureND<Double>> {
 
-    public val StructureND<Double>.f64Buffer: F64Array
-        get() = when {
-            !shape.contentEquals(this@ViktorFieldND.shape) -> throw ShapeMismatchException(
-                this@ViktorFieldND.shape,
-                shape
-            )
-            this is ViktorStructureND && this.f64Buffer.shape.contentEquals(this@ViktorFieldND.shape) -> this.f64Buffer
-            else -> produce(shape) { this@f64Buffer[it] }.f64Buffer
-        }
-
-    override val zero: ViktorStructureND by lazy { F64Array.full(init = 0.0, shape = shape).asStructure() }
-    override val one: ViktorStructureND by lazy { F64Array.full(init = 1.0, shape = shape).asStructure() }
-
-    private val strides: Strides = DefaultStrides(shape)
-
-    override val elementAlgebra: DoubleField get() = DoubleField
-
-    override fun produce(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
-        F64Array(*shape).apply {
-            this@ViktorFieldND.strides.indices().forEach { index ->
-                set(value = DoubleField.initializer(index), indices = index)
-            }
-        }.asStructure()
-
-    override fun StructureND<Double>.unaryMinus(): StructureND<Double> = -1 * this
-
-    override fun StructureND<Double>.map(transform: DoubleField.(Double) -> Double): ViktorStructureND =
-        F64Array(*this@ViktorFieldND.shape).apply {
-            this@ViktorFieldND.strides.indices().forEach { index ->
-                set(value = DoubleField.transform(this@map[index]), indices = index)
-            }
-        }.asStructure()
-
-    override fun StructureND<Double>.mapIndexed(
-        transform: DoubleField.(index: IntArray, Double) -> Double,
-    ): ViktorStructureND = F64Array(*this@ViktorFieldND.shape).apply {
-        this@ViktorFieldND.strides.indices().forEach { index ->
-            set(value = DoubleField.transform(index, this@mapIndexed[index]), indices = index)
-        }
-    }.asStructure()
-
-    override fun zip(
-        left: StructureND<Double>,
-        right: StructureND<Double>,
-        transform: DoubleField.(Double, Double) -> Double,
-    ): ViktorStructureND = F64Array(*shape).apply {
-        this@ViktorFieldND.strides.indices().forEach { index ->
-            set(value = DoubleField.transform(left[index], right[index]), indices = index)
-        }
-    }.asStructure()
-
-    override fun add(left: StructureND<Double>, right: StructureND<Double>): ViktorStructureND =
-        (left.f64Buffer + right.f64Buffer).asStructure()
-
-    override fun scale(a: StructureND<Double>, value: Double): ViktorStructureND =
-        (a.f64Buffer * value).asStructure()
-
-    override inline fun StructureND<Double>.plus(other: StructureND<Double>): ViktorStructureND =
-        (f64Buffer + other.f64Buffer).asStructure()
-
-    override inline fun StructureND<Double>.minus(other: StructureND<Double>): ViktorStructureND =
-        (f64Buffer - other.f64Buffer).asStructure()
-
-    override inline fun StructureND<Double>.times(k: Number): ViktorStructureND =
-        (f64Buffer * k.toDouble()).asStructure()
-
-    override inline fun StructureND<Double>.plus(arg: Double): ViktorStructureND =
-        (f64Buffer.plus(arg)).asStructure()
-
-    override fun number(value: Number): ViktorStructureND =
-        F64Array.full(init = value.toDouble(), shape = shape).asStructure()
-
-    override fun sin(arg: StructureND<Double>): ViktorStructureND = arg.map { sin(it) }
-    override fun cos(arg: StructureND<Double>): ViktorStructureND = arg.map { cos(it) }
-    override fun tan(arg: StructureND<Double>): ViktorStructureND = arg.map { tan(it) }
-    override fun asin(arg: StructureND<Double>): ViktorStructureND = arg.map { asin(it) }
-    override fun acos(arg: StructureND<Double>): ViktorStructureND = arg.map { acos(it) }
-    override fun atan(arg: StructureND<Double>): ViktorStructureND = arg.map { atan(it) }
-
-    override fun power(arg: StructureND<Double>, pow: Number): ViktorStructureND = arg.map { it.pow(pow) }
-
-    override fun exp(arg: StructureND<Double>): ViktorStructureND = arg.f64Buffer.exp().asStructure()
-
-    override fun ln(arg: StructureND<Double>): ViktorStructureND = arg.f64Buffer.log().asStructure()
-}
-
-public fun ViktorFieldND(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)

From 6de43ee4bae0f224c44b798e82e00a60921d9b74 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 17 Oct 2021 13:52:40 +0300
Subject: [PATCH 05/10] update multik module

---
 .../src/main/kotlin/space/kscience/kmath/tensors/multik.kt     | 3 +++
 settings.gradle.kts                                            | 1 +
 2 files changed, 4 insertions(+)

diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
index 820a793ac..fc6d7dd56 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
@@ -7,6 +7,7 @@ package space.kscience.kmath.tensors
 
 import org.jetbrains.kotlinx.multik.api.Multik
 import org.jetbrains.kotlinx.multik.api.linalg.dot
+import org.jetbrains.kotlinx.multik.api.math.exp
 import org.jetbrains.kotlinx.multik.api.ndarray
 import org.jetbrains.kotlinx.multik.ndarray.operations.minus
 import org.jetbrains.kotlinx.multik.ndarray.operations.plus
@@ -18,4 +19,6 @@ fun main() {
     2 + (-a) - 2
 
     a dot a
+
+    a.exp()
 }
\ No newline at end of file
diff --git a/settings.gradle.kts b/settings.gradle.kts
index dc70cbb9e..e73381bf2 100644
--- a/settings.gradle.kts
+++ b/settings.gradle.kts
@@ -32,6 +32,7 @@ include(
     ":kmath-histograms",
     ":kmath-commons",
     ":kmath-viktor",
+    ":kmath-multik",
     ":kmath-optimization",
     ":kmath-stat",
     ":kmath-nd4j",

From 9b9fe07044ff25b8ebc8bb25b57d951bae02dd36 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 17 Oct 2021 16:42:46 +0300
Subject: [PATCH 06/10] Specialized operations for ND algebra

---
 .../kmath/operations/mixedNDOperations.kt     | 24 ++++++++++++++++
 .../DerivativeStructureExpression.kt          |  8 +++---
 .../kscience/kmath/complex/Quaternion.kt      | 14 +++++-----
 .../space/kscience/kmath/nd/DoubleFieldND.kt  | 28 +++++++++++++++++++
 .../kmath/operations/NumericAlgebra.kt        | 20 ++++++-------
 5 files changed, 73 insertions(+), 21 deletions(-)
 create mode 100644 examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt

diff --git a/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt b/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt
new file mode 100644
index 000000000..628344ceb
--- /dev/null
+++ b/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt
@@ -0,0 +1,24 @@
+package space.kscience.kmath.operations
+
+import space.kscience.kmath.commons.linear.CMLinearSpace
+import space.kscience.kmath.linear.matrix
+import space.kscience.kmath.nd.DoubleBufferND
+import space.kscience.kmath.nd.Shape
+import space.kscience.kmath.nd.Structure2D
+import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.viktor.ViktorStructureND
+import space.kscience.kmath.viktor.viktorAlgebra
+
+fun main() {
+    val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.produce(Shape(2, 2)) { (i, j) ->
+        if (i == j) 2.0 else 0.0
+    }
+
+    val cmMatrix: Structure2D<Double> = CMLinearSpace.matrix(2, 2)(0.0, 1.0, 0.0, 3.0)
+
+    val res: DoubleBufferND = DoubleField.ndAlgebra {
+        exp(viktorStructure) + 2.0 * cmMatrix
+    }
+
+    println(res)
+}
\ No newline at end of file
diff --git a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
index d42e40d1e..4d2bd6237 100644
--- a/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
+++ b/kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
@@ -99,10 +99,10 @@ public class DerivativeStructureField(
     override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
     override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
 
-    override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())
-    override operator fun DerivativeStructure.minus(b: Number): DerivativeStructure = subtract(b.toDouble())
-    override operator fun Number.plus(b: DerivativeStructure): DerivativeStructure = b + this
-    override operator fun Number.minus(b: DerivativeStructure): DerivativeStructure = b - this
+    override operator fun DerivativeStructure.plus(other: Number): DerivativeStructure = add(other.toDouble())
+    override operator fun DerivativeStructure.minus(other: Number): DerivativeStructure = subtract(other.toDouble())
+    override operator fun Number.plus(other: DerivativeStructure): DerivativeStructure = other + this
+    override operator fun Number.minus(other: DerivativeStructure): DerivativeStructure = other - this
 }
 
 /**
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
index 9fdd60e1f..47cc61313 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt
@@ -158,16 +158,16 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
         return Quaternion(ln(n), th * arg.x, th * arg.y, th * arg.z)
     }
 
-    override operator fun Number.plus(b: Quaternion): Quaternion = Quaternion(toDouble() + b.w, b.x, b.y, b.z)
+    override operator fun Number.plus(other: Quaternion): Quaternion = Quaternion(toDouble() + other.w, other.x, other.y, other.z)
 
-    override operator fun Number.minus(b: Quaternion): Quaternion =
-        Quaternion(toDouble() - b.w, -b.x, -b.y, -b.z)
+    override operator fun Number.minus(other: Quaternion): Quaternion =
+        Quaternion(toDouble() - other.w, -other.x, -other.y, -other.z)
 
-    override operator fun Quaternion.plus(b: Number): Quaternion = Quaternion(w + b.toDouble(), x, y, z)
-    override operator fun Quaternion.minus(b: Number): Quaternion = Quaternion(w - b.toDouble(), x, y, z)
+    override operator fun Quaternion.plus(other: Number): Quaternion = Quaternion(w + other.toDouble(), x, y, z)
+    override operator fun Quaternion.minus(other: Number): Quaternion = Quaternion(w - other.toDouble(), x, y, z)
 
-    override operator fun Number.times(b: Quaternion): Quaternion =
-        Quaternion(toDouble() * b.w, toDouble() * b.x, toDouble() * b.y, toDouble() * b.z)
+    override operator fun Number.times(other: Quaternion): Quaternion =
+        Quaternion(toDouble() * other.w, toDouble() * other.x, toDouble() * other.y, toDouble() * other.z)
 
     override fun Quaternion.unaryMinus(): Quaternion = Quaternion(-w, -x, -y, -z)
     override fun norm(arg: Quaternion): Quaternion = sqrt(arg.conjugate * arg)
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
index 1502a6fd0..6235971a2 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
@@ -81,6 +81,34 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(D
     override fun StructureND<Double>.div(other: StructureND<Double>): DoubleBufferND =
         zipInline(toBufferND(), other.toBufferND()) { l, r -> l / r }
 
+    override fun divide(left: StructureND<Double>, right: StructureND<Double>): DoubleBufferND =
+        zipInline(left.toBufferND(), right.toBufferND()) { l: Double, r: Double -> l / r }
+
+    override fun StructureND<Double>.div(arg: Double): DoubleBufferND =
+        mapInline(toBufferND()) { it / arg }
+
+    override fun Double.div(arg: StructureND<Double>): DoubleBufferND =
+        mapInline(arg.toBufferND()) { this / it }
+
+    override fun StructureND<Double>.unaryPlus(): DoubleBufferND = toBufferND()
+
+    override fun StructureND<Double>.plus(other: StructureND<Double>): DoubleBufferND =
+        zipInline(toBufferND(), other.toBufferND()) { l: Double, r: Double -> l + r }
+
+    override fun StructureND<Double>.minus(other: StructureND<Double>): DoubleBufferND =
+        zipInline(toBufferND(), other.toBufferND()) { l: Double, r: Double -> l - r }
+
+    override fun StructureND<Double>.times(other: StructureND<Double>): DoubleBufferND =
+        zipInline(toBufferND(), other.toBufferND()) { l: Double, r: Double -> l * r }
+
+    override fun StructureND<Double>.times(k: Number): DoubleBufferND =
+        mapInline(toBufferND()) { it * k.toDouble() }
+
+    override fun StructureND<Double>.div(k: Number): DoubleBufferND =
+        mapInline(toBufferND()) { it / k.toDouble() }
+
+    override fun Number.times(other: StructureND<Double>): DoubleBufferND = other * this
+
     override fun StructureND<Double>.plus(arg: Double): DoubleBufferND = mapInline(toBufferND()) { it + arg }
 
     override fun StructureND<Double>.minus(arg: Double): StructureND<Double> = mapInline(toBufferND()) { it - arg }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
index 5f6848211..6be3449f9 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt
@@ -139,10 +139,10 @@ public interface ScaleOperations<T> : Algebra<T> {
      * Multiplication of this number by element.
      *
      * @receiver the multiplier.
-     * @param b the multiplicand.
+     * @param other the multiplicand.
      * @return the product.
      */
-    public operator fun Number.times(b: T): T = b * this
+    public operator fun Number.times(other: T): T = other * this
 }
 
 /**
@@ -155,33 +155,33 @@ public interface NumbersAddOps<T> : RingOps<T>, NumericAlgebra<T> {
      * Addition of element and scalar.
      *
      * @receiver the augend.
-     * @param b the addend.
+     * @param other the addend.
      */
-    public operator fun T.plus(b: Number): T = this + number(b)
+    public operator fun T.plus(other: Number): T = this + number(other)
 
     /**
      * Addition of scalar and element.
      *
      * @receiver the augend.
-     * @param b the addend.
+     * @param other the addend.
      */
-    public operator fun Number.plus(b: T): T = b + this
+    public operator fun Number.plus(other: T): T = other + this
 
     /**
      * Subtraction of element from number.
      *
      * @receiver the minuend.
-     * @param b the subtrahend.
+     * @param other the subtrahend.
      * @receiver the difference.
      */
-    public operator fun T.minus(b: Number): T = this - number(b)
+    public operator fun T.minus(other: Number): T = this - number(other)
 
     /**
      * Subtraction of number from element.
      *
      * @receiver the minuend.
-     * @param b the subtrahend.
+     * @param other the subtrahend.
      * @receiver the difference.
      */
-    public operator fun Number.minus(b: T): T = -b + this
+    public operator fun Number.minus(other: T): T = -other + this
 }
\ No newline at end of file

From 827f115a9257235e8e36ee43af06937e2488eb75 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 17 Oct 2021 21:12:14 +0300
Subject: [PATCH 07/10] Multik wrapper

---
 benchmarks/build.gradle.kts                   |   1 +
 .../kmath/benchmarks/NDFieldBenchmark.kt      |  24 +++-
 .../space/kscience/kmath/nd/ShapeIndex.kt     |  15 +-
 .../kscience/kmath/multik/MultikOpsND.kt      | 135 ++++++++++++++++++
 .../kmath/multik/MultikTensorAlgebra.kt       |  30 ++--
 .../kscience/kmath/multik/MultikNDTest.kt     |  13 ++
 .../kscience/kmath/nd4j/Nd4jArrayAlgebra.kt   |   5 +-
 .../tensors/core/tensorAlgebraExtensions.kt   |  10 +-
 8 files changed, 204 insertions(+), 29 deletions(-)
 create mode 100644 kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
 create mode 100644 kmath-multik/src/test/kotlin/space/kscience/kmath/multik/MultikNDTest.kt

diff --git a/benchmarks/build.gradle.kts b/benchmarks/build.gradle.kts
index 686c491b9..cca3d312d 100644
--- a/benchmarks/build.gradle.kts
+++ b/benchmarks/build.gradle.kts
@@ -48,6 +48,7 @@ kotlin {
                 implementation(project(":kmath-nd4j"))
                 implementation(project(":kmath-kotlingrad"))
                 implementation(project(":kmath-viktor"))
+                implementation(projects.kmathMultik)
                 implementation("org.nd4j:nd4j-native:1.0.0-M1")
                 //    uncomment if your system supports AVX2
                 //    val os = System.getProperty("os.name")
diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
index 7f7c03412..672aa4307 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
@@ -9,6 +9,7 @@ import kotlinx.benchmark.Benchmark
 import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
+import space.kscience.kmath.multik.multikND
 import space.kscience.kmath.nd.BufferedFieldOpsND
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.ndAlgebra
@@ -17,8 +18,9 @@ import space.kscience.kmath.nd4j.nd4j
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.tensors.core.DoubleTensor
-import space.kscience.kmath.tensors.core.ones
+import space.kscience.kmath.tensors.core.one
 import space.kscience.kmath.tensors.core.tensorAlgebra
+import space.kscience.kmath.viktor.viktorAlgebra
 
 @State(Scope.Benchmark)
 internal class NDFieldBenchmark {
@@ -43,16 +45,30 @@ internal class NDFieldBenchmark {
         blackhole.consume(res)
     }
 
+    @Benchmark
+    fun multikAdd(blackhole: Blackhole) = with(multikField) {
+        var res: StructureND<Double> = one(shape)
+        repeat(n) { res += 1.0 }
+        blackhole.consume(res)
+    }
+
+    @Benchmark
+    fun viktorAdd(blackhole: Blackhole) = with(viktorField) {
+        var res: StructureND<Double> = one(shape)
+        repeat(n) { res += 1.0 }
+        blackhole.consume(res)
+    }
+
     @Benchmark
     fun tensorAdd(blackhole: Blackhole) = with(Double.tensorAlgebra) {
-        var res: DoubleTensor = ones(dim, dim)
+        var res: DoubleTensor = one(shape)
         repeat(n) { res = res + 1.0 }
         blackhole.consume(res)
     }
 
     @Benchmark
     fun tensorInPlaceAdd(blackhole: Blackhole) = with(Double.tensorAlgebra) {
-        val res: DoubleTensor = ones(dim, dim)
+        val res: DoubleTensor = one(shape)
         repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
@@ -72,5 +88,7 @@ internal class NDFieldBenchmark {
         private val specializedField = DoubleField.ndAlgebra
         private val genericField = BufferedFieldOpsND(DoubleField, Buffer.Companion::boxing)
         private val nd4jField = DoubleField.nd4j
+        private val multikField = DoubleField.multikND
+        private val viktorField = DoubleField.viktorAlgebra
     }
 }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt
index bdbae70c2..a78bcfa70 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt
@@ -105,16 +105,15 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
 
     override fun hashCode(): Int = shape.contentHashCode()
 
-    @ThreadLocal
-    public companion object {
-        //private val defaultStridesCache = HashMap<IntArray, Strides>()
 
+    public companion object {
         /**
          * Cached builder for default strides
          */
-        public operator fun invoke(shape: IntArray): Strides = DefaultStrides(shape)
-            //defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
-
-        //TODO fix cache
+        public operator fun invoke(shape: IntArray): Strides =
+            defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
     }
-}
\ No newline at end of file
+}
+
+@ThreadLocal
+private val defaultStridesCache = HashMap<IntArray, Strides>()
\ No newline at end of file
diff --git a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
new file mode 100644
index 000000000..d6996d427
--- /dev/null
+++ b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
@@ -0,0 +1,135 @@
+package space.kscience.kmath.multik
+
+import org.jetbrains.kotlinx.multik.api.mk
+import org.jetbrains.kotlinx.multik.api.zeros
+import org.jetbrains.kotlinx.multik.ndarray.data.*
+import org.jetbrains.kotlinx.multik.ndarray.operations.*
+import space.kscience.kmath.nd.FieldOpsND
+import space.kscience.kmath.nd.RingOpsND
+import space.kscience.kmath.nd.Shape
+import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.operations.*
+
+/**
+ * A ring algebra for Multik operations
+ */
+public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
+    public val type: DataType,
+    override val elementAlgebra: A
+) : RingOpsND<T, A> {
+
+    protected fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+
+    override fun produce(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
+        val res = mk.zeros<T, DN>(shape, type).asDNArray()
+        for (index in res.multiIndices) {
+            res[index] = elementAlgebra.initializer(index)
+        }
+        return res.wrap()
+    }
+
+    protected fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
+        this
+    } else {
+        produce(shape) { get(it) }
+    }
+
+    override fun StructureND<T>.map(transform: A.(T) -> T): MultikTensor<T> {
+        //taken directly from Multik sources
+        val array = asMultik().array
+        val data = initMemoryView<T>(array.size, type)
+        var count = 0
+        for (el in array) data[count++] = elementAlgebra.transform(el)
+        return NDArray(data, shape = array.shape, dim = array.dim).wrap()
+    }
+
+    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): MultikTensor<T> {
+        //taken directly from Multik sources
+        val array = asMultik().array
+        val data = initMemoryView<T>(array.size, type)
+        val indexIter = array.multiIndices.iterator()
+        var index = 0
+        for (item in array) {
+            if (indexIter.hasNext()) {
+                data[index++] = elementAlgebra.transform(indexIter.next(), item)
+            } else {
+                throw ArithmeticException("Index overflow has happened.")
+            }
+        }
+        return NDArray(data, shape = array.shape, dim = array.dim).wrap()
+    }
+
+    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): MultikTensor<T> {
+        require(left.shape.contentEquals(right.shape)) { "ND array shape mismatch" } //TODO replace by ShapeMismatchException
+        val leftArray = left.asMultik().array
+        val rightArray = right.asMultik().array
+        val data = initMemoryView<T>(leftArray.size, type)
+        var counter = 0
+        val leftIterator = leftArray.iterator()
+        val rightIterator = rightArray.iterator()
+        //iterating them together
+        while (leftIterator.hasNext()) {
+            data[counter++] = elementAlgebra.transform(leftIterator.next(), rightIterator.next())
+        }
+        return NDArray(data, shape = leftArray.shape, dim = leftArray.dim).wrap()
+    }
+
+    override fun StructureND<T>.unaryMinus(): MultikTensor<T> = asMultik().array.unaryMinus().wrap()
+
+    override fun add(left: StructureND<T>, right: StructureND<T>): MultikTensor<T> =
+        (left.asMultik().array + right.asMultik().array).wrap()
+
+    override fun StructureND<T>.plus(arg: T): MultikTensor<T> =
+        asMultik().array.plus(arg).wrap()
+
+    override fun StructureND<T>.minus(arg: T): MultikTensor<T> = asMultik().array.minus(arg).wrap()
+
+    override fun T.plus(arg: StructureND<T>): MultikTensor<T> = arg + this
+
+    override fun T.minus(arg: StructureND<T>): MultikTensor<T> = arg.map { this@minus - it }
+
+    override fun multiply(left: StructureND<T>, right: StructureND<T>): MultikTensor<T> =
+        left.asMultik().array.times(right.asMultik().array).wrap()
+
+    override fun StructureND<T>.times(arg: T): MultikTensor<T> =
+        asMultik().array.times(arg).wrap()
+
+    override fun T.times(arg: StructureND<T>): MultikTensor<T> = arg * this
+
+    override fun StructureND<T>.unaryPlus(): MultikTensor<T> = asMultik()
+
+    override fun StructureND<T>.plus(other: StructureND<T>): MultikTensor<T> =
+        asMultik().array.plus(other.asMultik().array).wrap()
+
+    override fun StructureND<T>.minus(other: StructureND<T>): MultikTensor<T> =
+        asMultik().array.minus(other.asMultik().array).wrap()
+
+    override fun StructureND<T>.times(other: StructureND<T>): MultikTensor<T> =
+        asMultik().array.times(other.asMultik().array).wrap()
+}
+
+/**
+ * A field algebra for multik operations
+ */
+public class MultikFieldOpsND<T, A : Field<T>> internal constructor(
+    type: DataType,
+    elementAlgebra: A
+) : MultikRingOpsND<T, A>(type, elementAlgebra), FieldOpsND<T, A> {
+    override fun StructureND<T>.div(other: StructureND<T>): StructureND<T> =
+        asMultik().array.div(other.asMultik().array).wrap()
+}
+
+public val DoubleField.multikND: MultikFieldOpsND<Double, DoubleField>
+    get() = MultikFieldOpsND(DataType.DoubleDataType, DoubleField)
+
+public val FloatField.multikND: MultikFieldOpsND<Float, FloatField>
+    get() = MultikFieldOpsND(DataType.FloatDataType, FloatField)
+
+public val ShortRing.multikND: MultikRingOpsND<Short, ShortRing>
+    get() = MultikRingOpsND(DataType.ShortDataType, ShortRing)
+
+public val IntRing.multikND: MultikRingOpsND<Int, IntRing>
+    get() = MultikRingOpsND(DataType.IntDataType, IntRing)
+
+public val LongRing.multikND: MultikRingOpsND<Long, LongRing>
+    get() = MultikRingOpsND(DataType.LongDataType, LongRing)
\ No newline at end of file
diff --git a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
index b25d3ef56..e9e56e06e 100644
--- a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
+++ b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
@@ -5,6 +5,8 @@
 
 package space.kscience.kmath.multik
 
+import org.jetbrains.kotlinx.multik.api.mk
+import org.jetbrains.kotlinx.multik.api.zeros
 import org.jetbrains.kotlinx.multik.ndarray.data.*
 import org.jetbrains.kotlinx.multik.ndarray.operations.*
 import space.kscience.kmath.misc.PerformancePitfall
@@ -30,6 +32,7 @@ public value class MultikTensor<T>(public val array: MutableMultiArray<T, DN>) :
 
 
 public abstract class MultikTensorAlgebra<T>(
+    public val type: DataType,
     public val elementAlgebra: Ring<T>,
     public val comparator: Comparator<T>
 ) : TensorAlgebra<T> {
@@ -38,15 +41,19 @@ public abstract class MultikTensorAlgebra<T>(
      * Convert a tensor to [MultikTensor] if necessary. If tensor is converted, changes on the resulting tensor
      * are not reflected back onto the source
      */
-    public fun Tensor<T>.asMultik(): MultikTensor<T> {
+    private fun Tensor<T>.asMultik(): MultikTensor<T> {
         return if (this is MultikTensor) {
             this
         } else {
-            TODO()
+            val res = mk.zeros<T, DN>(shape, type).asDNArray()
+            for (index in res.multiIndices) {
+                res[index] = this[index]
+            }
+            res.wrap()
         }
     }
 
-    public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+    private fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
 
     override fun Tensor<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
         get(intArrayOf(0))
@@ -77,8 +84,7 @@ public abstract class MultikTensorAlgebra<T>(
         }
     }
 
-    //TODO avoid additional copy
-    override fun T.minus(other: Tensor<T>): MultikTensor<T> = -(other - this)
+    override fun T.minus(other: Tensor<T>): MultikTensor<T> = (-(other.asMultik().array - this)).wrap()
 
     override fun Tensor<T>.minus(value: T): MultikTensor<T> =
         asMultik().array.deepCopy().apply { minusAssign(value) }.wrap()
@@ -130,13 +136,9 @@ public abstract class MultikTensorAlgebra<T>(
     override fun Tensor<T>.unaryMinus(): MultikTensor<T> =
         asMultik().array.unaryMinus().wrap()
 
-    override fun Tensor<T>.get(i: Int): MultikTensor<T> {
-        TODO("Not yet implemented")
-    }
+    override fun Tensor<T>.get(i: Int): MultikTensor<T> = asMultik().array.mutableView(i).wrap()
 
-    override fun Tensor<T>.transpose(i: Int, j: Int): MultikTensor<T> {
-        TODO("Not yet implemented")
-    }
+    override fun Tensor<T>.transpose(i: Int, j: Int): MultikTensor<T> = asMultik().array.transpose(i, j).wrap()
 
     override fun Tensor<T>.view(shape: IntArray): MultikTensor<T> {
         require(shape.all { it > 0 })
@@ -158,16 +160,14 @@ public abstract class MultikTensorAlgebra<T>(
         }.wrap()
     }
 
-    override fun Tensor<T>.viewAs(other: Tensor<T>): MultikTensor<T> {
-        TODO("Not yet implemented")
-    }
+    override fun Tensor<T>.viewAs(other: Tensor<T>): MultikTensor<T> = view(other.shape)
 
     override fun Tensor<T>.dot(other: Tensor<T>): MultikTensor<T> {
         TODO("Not yet implemented")
     }
 
     override fun diagonalEmbedding(diagonalEntries: Tensor<T>, offset: Int, dim1: Int, dim2: Int): MultikTensor<T> {
-        TODO("Not yet implemented")
+        TODO("Diagonal embedding not implemented")
     }
 
     override fun Tensor<T>.sum(): T = asMultik().array.reduceMultiIndexed { _: IntArray, acc: T, t: T ->
diff --git a/kmath-multik/src/test/kotlin/space/kscience/kmath/multik/MultikNDTest.kt b/kmath-multik/src/test/kotlin/space/kscience/kmath/multik/MultikNDTest.kt
new file mode 100644
index 000000000..9dd9854c7
--- /dev/null
+++ b/kmath-multik/src/test/kotlin/space/kscience/kmath/multik/MultikNDTest.kt
@@ -0,0 +1,13 @@
+package space.kscience.kmath.multik
+
+import org.junit.jupiter.api.Test
+import space.kscience.kmath.nd.one
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.invoke
+
+internal class MultikNDTest {
+    @Test
+    fun basicAlgebra(): Unit = DoubleField.multikND{
+        one(2,2) + 1.0
+    }
+}
\ No newline at end of file
diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
index 792890a2d..259b1a934 100644
--- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
+++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
@@ -38,6 +38,7 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
         return struct
     }
 
+    @OptIn(PerformancePitfall::class)
     override fun StructureND<T>.map(transform: C.(T) -> T): Nd4jArrayStructure<T> {
         val newStruct = ndArray.dup().wrap()
         newStruct.elements().forEach { (idx, value) -> newStruct[idx] = elementAlgebra.transform(value) }
@@ -117,7 +118,7 @@ public sealed interface Nd4jArrayRingOps<T, out R : Ring<T>> : RingOpsND<T, R>,
          * Creates a most suitable implementation of [RingND] using reified class.
          */
         @Suppress("UNCHECKED_CAST")
-        public inline fun <reified T : Number> auto(vararg shape: Int): Nd4jArrayRingOps<T, Ring<T>> = when {
+        public inline fun <reified T : Number> auto(): Nd4jArrayRingOps<T, Ring<T>> = when {
             T::class == Int::class -> IntRing.nd4j as Nd4jArrayRingOps<T, Ring<T>>
             else -> throw UnsupportedOperationException("This factory method only supports Long type.")
         }
@@ -142,7 +143,7 @@ public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldOpsND<T, F>,
          * Creates a most suitable implementation of [FieldND] using reified class.
          */
         @Suppress("UNCHECKED_CAST")
-        public inline fun <reified T : Any> auto(vararg shape: Int): Nd4jArrayField<T, Field<T>> = when {
+        public inline fun <reified T : Any> auto(): Nd4jArrayField<T, Field<T>> = when {
             T::class == Float::class -> FloatField.nd4j as Nd4jArrayField<T, Field<T>>
             T::class == Double::class -> DoubleField.nd4j as Nd4jArrayField<T, Field<T>>
             else -> throw UnsupportedOperationException("This factory method only supports Float and Double types.")
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt
index b73f95054..916388ba9 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/tensorAlgebraExtensions.kt
@@ -5,4 +5,12 @@
 
 package space.kscience.kmath.tensors.core
 
-public fun DoubleTensorAlgebra.ones(vararg shape: Int): DoubleTensor = ones(intArrayOf(*shape))
\ No newline at end of file
+import space.kscience.kmath.nd.Shape
+import kotlin.jvm.JvmName
+
+@JvmName("varArgOne")
+public fun DoubleTensorAlgebra.one(vararg shape: Int): DoubleTensor = ones(intArrayOf(*shape))
+public fun DoubleTensorAlgebra.one(shape: Shape): DoubleTensor = ones(shape)
+@JvmName("varArgZero")
+public fun DoubleTensorAlgebra.zero(vararg shape: Int): DoubleTensor = zeros(intArrayOf(*shape))
+public fun DoubleTensorAlgebra.zero(shape: Shape): DoubleTensor = zeros(shape)
\ No newline at end of file

From a81ab474f73c2a6ce1ef3819d3c39df34c139065 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Mon, 18 Oct 2021 11:35:09 +0300
Subject: [PATCH 08/10] Add multik tensor factories and benchmarks

---
 .../kmath/benchmarks/NDFieldBenchmark.kt      | 12 +++++++++
 .../kmath/benchmarks/ViktorLogBenchmark.kt    |  4 +--
 .../kmath/functions/matrixIntegration.kt      |  4 +--
 .../kscience/kmath/operations/complexDemo.kt  |  6 ++---
 .../kmath/operations/mixedNDOperations.kt     |  2 +-
 .../kscience/kmath/structures/ComplexND.kt    |  4 +--
 .../kmath/structures/StreamDoubleFieldND.kt   |  8 +++---
 .../kscience/kmath/complex/ComplexFieldND.kt  |  2 +-
 .../kmath/linear/BufferedLinearSpace.kt       |  2 +-
 .../kmath/linear/DoubleLinearSpace.kt         |  2 +-
 .../space/kscience/kmath/nd/AlgebraND.kt      | 10 ++++----
 .../kscience/kmath/nd/BufferAlgebraND.kt      | 10 ++++----
 .../space/kscience/kmath/nd/DoubleFieldND.kt  |  4 +--
 .../space/kscience/kmath/nd/ShortRingND.kt    |  2 +-
 .../kscience/kmath/nd/algebraNDExtentions.kt  | 12 ++++-----
 .../kscience/kmath/structures/NDFieldTest.kt  |  4 +--
 .../kmath/structures/NumberNDFieldTest.kt     |  4 +--
 .../kscience/kmath/multik/MultikOpsND.kt      |  8 +++---
 .../kmath/multik/MultikTensorAlgebra.kt       | 25 +++++++++++++++----
 .../kscience/kmath/nd4j/Nd4jArrayAlgebra.kt   |  2 +-
 .../kmath/nd4j/Nd4jArrayAlgebraTest.kt        |  8 +++---
 .../kmath/tensors/core/DoubleTensorAlgebra.kt |  2 +-
 .../kscience/kmath/viktor/ViktorFieldOpsND.kt |  4 +--
 23 files changed, 84 insertions(+), 57 deletions(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
index 672aa4307..8f9a3e2b8 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
@@ -9,7 +9,12 @@ import kotlinx.benchmark.Benchmark
 import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
+import org.jetbrains.kotlinx.multik.api.Multik
+import org.jetbrains.kotlinx.multik.api.ones
+import org.jetbrains.kotlinx.multik.ndarray.data.DN
+import org.jetbrains.kotlinx.multik.ndarray.data.DataType
 import space.kscience.kmath.multik.multikND
+import space.kscience.kmath.multik.multikTensorAlgebra
 import space.kscience.kmath.nd.BufferedFieldOpsND
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.ndAlgebra
@@ -73,6 +78,13 @@ internal class NDFieldBenchmark {
         blackhole.consume(res)
     }
 
+    @Benchmark
+    fun multikInPlaceAdd(blackhole: Blackhole) = with(DoubleField.multikTensorAlgebra) {
+        val res = Multik.ones<Double, DN>(shape, DataType.DoubleDataType).wrap()
+        repeat(n) { res += 1.0 }
+        blackhole.consume(res)
+    }
+
 //    @Benchmark
 //    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
 //        var res: StructureND<Double> = one(dim, dim)
diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
index ef2adaad8..a9d1e68fc 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
@@ -23,7 +23,7 @@ internal class ViktorLogBenchmark {
     @Benchmark
     fun realFieldLog(blackhole: Blackhole) {
         with(realField) {
-            val fortyTwo = produce(shape) { 42.0 }
+            val fortyTwo = structureND(shape) { 42.0 }
             var res = one(shape)
             repeat(n) { res = ln(fortyTwo) }
             blackhole.consume(res)
@@ -33,7 +33,7 @@ internal class ViktorLogBenchmark {
     @Benchmark
     fun viktorFieldLog(blackhole: Blackhole) {
         with(viktorField) {
-            val fortyTwo = produce(shape) { 42.0 }
+            val fortyTwo = structureND(shape) { 42.0 }
             var res = one
             repeat(n) { res = ln(fortyTwo) }
             blackhole.consume(res)
diff --git a/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt b/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
index 609afb47e..4b6ac475c 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
@@ -9,7 +9,7 @@ import space.kscience.kmath.integration.gaussIntegrator
 import space.kscience.kmath.integration.integrate
 import space.kscience.kmath.integration.value
 import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.produce
+import space.kscience.kmath.nd.structureND
 import space.kscience.kmath.nd.withNdAlgebra
 import space.kscience.kmath.operations.algebra
 import space.kscience.kmath.operations.invoke
@@ -18,7 +18,7 @@ fun main(): Unit = Double.algebra {
     withNdAlgebra(2, 2) {
 
         //Produce a diagonal StructureND
-        fun diagonal(v: Double) = produce {  (i, j) ->
+        fun diagonal(v: Double) = structureND { (i, j) ->
             if (i == j) v else 0.0
         }
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt b/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
index 67d83d77c..3b9c32f4b 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
@@ -11,7 +11,7 @@ import space.kscience.kmath.complex.bufferAlgebra
 import space.kscience.kmath.complex.ndAlgebra
 import space.kscience.kmath.nd.BufferND
 import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.produce
+import space.kscience.kmath.nd.structureND
 
 fun main() = Complex.algebra {
     val complex = 2 + 2 * i
@@ -24,14 +24,14 @@ fun main() = Complex.algebra {
     println(buffer)
 
     // 2d element
-    val element: BufferND<Complex> = ndAlgebra.produce(2, 2) { (i, j) ->
+    val element: BufferND<Complex> = ndAlgebra.structureND(2, 2) { (i, j) ->
         Complex(i - j, i + j)
     }
     println(element)
 
     // 1d element operation
     val result: StructureND<Complex> = ndAlgebra{
-        val a = produce(8) { (it) -> i * it - it.toDouble() }
+        val a = structureND(8) { (it) -> i * it - it.toDouble() }
         val b = 3
         val c = Complex(1.0, 1.0)
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt b/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt
index 628344ceb..f517046ee 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt
@@ -10,7 +10,7 @@ import space.kscience.kmath.viktor.ViktorStructureND
 import space.kscience.kmath.viktor.viktorAlgebra
 
 fun main() {
-    val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.produce(Shape(2, 2)) { (i, j) ->
+    val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.structureND(Shape(2, 2)) { (i, j) ->
         if (i == j) 2.0 else 0.0
     }
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
index 42636fafb..61df3d065 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
@@ -12,7 +12,7 @@ import space.kscience.kmath.linear.transpose
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.nd.ndAlgebra
-import space.kscience.kmath.nd.produce
+import space.kscience.kmath.nd.structureND
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
 import kotlin.system.measureTimeMillis
@@ -55,7 +55,7 @@ fun complexExample() {
             val x = one * 2.5
             operator fun Number.plus(other: Complex) = Complex(this.toDouble() + other.re, other.im)
             //a structure generator specific to this context
-            val matrix = produce { (k, l) -> k + l * i }
+            val matrix = structureND { (k, l) -> k + l * i }
             //Perform sum
             val sum = matrix + x + 1.0
 
diff --git a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
index dfd06973e..2b3e72136 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
@@ -22,12 +22,12 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
 
     private val strides = DefaultStrides(shape)
     override val elementAlgebra: DoubleField get() = DoubleField
-    override val zero: BufferND<Double> by lazy { produce(shape) { zero } }
-    override val one: BufferND<Double> by lazy { produce(shape) { one } }
+    override val zero: BufferND<Double> by lazy { structureND(shape) { zero } }
+    override val one: BufferND<Double> by lazy { structureND(shape) { one } }
 
     override fun number(value: Number): BufferND<Double> {
         val d = value.toDouble() // minimize conversions
-        return produce(shape) { d }
+        return structureND(shape) { d }
     }
 
     private val StructureND<Double>.buffer: DoubleBuffer
@@ -40,7 +40,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
             else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
         }
 
-    override fun produce(shape: Shape, initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
+    override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
         val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
             val index = strides.index(offset)
             DoubleField.initializer(index)
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
index 3951b5de0..9d5b1cddd 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
@@ -67,7 +67,7 @@ public class ComplexFieldND(override val shape: Shape) :
 
     override fun number(value: Number): BufferND<Complex> {
         val d = value.toDouble() // minimize conversions
-        return produce(shape) { d.toComplex() }
+        return structureND(shape) { d.toComplex() }
     }
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
index 39dbe3a81..f72b9bd81 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
@@ -24,7 +24,7 @@ public class BufferedLinearSpace<T, out A : Ring<T>>(
     private val ndAlgebra = BufferedRingOpsND(bufferAlgebra)
 
     override fun buildMatrix(rows: Int, columns: Int, initializer: A.(i: Int, j: Int) -> T): Matrix<T> =
-        ndAlgebra.produce(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
+        ndAlgebra.structureND(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
 
     override fun buildVector(size: Int, initializer: A.(Int) -> T): Point<T> =
         bufferAlgebra.buffer(size) { elementAlgebra.initializer(it) }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
index ec6040af0..91db33bce 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
@@ -23,7 +23,7 @@ public object DoubleLinearSpace : LinearSpace<Double, DoubleField> {
         rows: Int,
         columns: Int,
         initializer: DoubleField.(i: Int, j: Int) -> Double
-    ): Matrix<Double> = DoubleFieldOpsND.produce(intArrayOf(rows, columns)) { (i, j) ->
+    ): Matrix<Double> = DoubleFieldOpsND.structureND(intArrayOf(rows, columns)) { (i, j) ->
         DoubleField.initializer(i, j)
     }.as2D()
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
index b4e8b7487..30cb01146 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
@@ -39,9 +39,9 @@ public interface AlgebraND<T, out C : Algebra<T>> {
     public val elementAlgebra: C
 
     /**
-     * Produces a new NDStructure using given initializer function.
+     * Produces a new [StructureND] using given initializer function.
      */
-    public fun produce(shape: Shape, initializer: C.(IntArray) -> T): StructureND<T>
+    public fun structureND(shape: Shape, initializer: C.(IntArray) -> T): StructureND<T>
 
     /**
      * Maps elements from one structure to another one by applying [transform] to them.
@@ -149,7 +149,7 @@ public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>,
 }
 
 public interface GroupND<T, out A : Group<T>> : Group<StructureND<T>>, GroupOpsND<T, A>, WithShape {
-    override val zero: StructureND<T> get() = produce(shape) { elementAlgebra.zero }
+    override val zero: StructureND<T> get() = structureND(shape) { elementAlgebra.zero }
 }
 
 /**
@@ -193,7 +193,7 @@ public interface RingOpsND<T, out A : RingOps<T>> : RingOps<StructureND<T>>, Gro
 }
 
 public interface RingND<T, out A : Ring<T>> : Ring<StructureND<T>>, RingOpsND<T, A>, GroupND<T, A>, WithShape {
-    override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
+    override val one: StructureND<T> get() = structureND(shape) { elementAlgebra.one }
 }
 
 
@@ -240,5 +240,5 @@ public interface FieldOpsND<T, out A : Field<T>> :
 }
 
 public interface FieldND<T, out A : Field<T>> : Field<StructureND<T>>, FieldOpsND<T, A>, RingND<T, A>, WithShape {
-    override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
+    override val one: StructureND<T> get() = structureND(shape) { elementAlgebra.one }
 }
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
index c94988eef..1f231ce9f 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
@@ -16,7 +16,7 @@ public interface BufferAlgebraND<T, out A : Algebra<T>> : AlgebraND<T, A> {
     public val bufferAlgebra: BufferAlgebra<T, A>
     override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
 
-    override fun produce(shape: Shape, initializer: A.(IntArray) -> T): BufferND<T> {
+    override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): BufferND<T> {
         val indexer = indexerBuilder(shape)
         return BufferND(
             indexer,
@@ -109,14 +109,14 @@ public val <T, A : Ring<T>> BufferAlgebra<T, A>.nd: BufferedRingOpsND<T, A> get(
 public val <T, A : Field<T>> BufferAlgebra<T, A>.nd: BufferedFieldOpsND<T, A> get() = BufferedFieldOpsND(this)
 
 
-public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.produce(
+public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.structureND(
     vararg shape: Int,
     initializer: A.(IntArray) -> T
-): BufferND<T> = produce(shape, initializer)
+): BufferND<T> = structureND(shape, initializer)
 
-public fun <T, EA : Algebra<T>, A> A.produce(
+public fun <T, EA : Algebra<T>, A> A.structureND(
     initializer: EA.(IntArray) -> T
-): BufferND<T> where A : BufferAlgebraND<T, EA>, A : WithShape = produce(shape, initializer)
+): BufferND<T> where A : BufferAlgebraND<T, EA>, A : WithShape = structureND(shape, initializer)
 
 //// group factories
 //public fun <T, A : Group<T>> A.ndAlgebra(
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
index 6235971a2..961f5869a 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
@@ -60,7 +60,7 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(D
         transform: DoubleField.(Double, Double) -> Double
     ): BufferND<Double> = zipInline(left.toBufferND(), right.toBufferND()) { l, r -> DoubleField.transform(l, r) }
 
-    override fun produce(shape: Shape, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND {
+    override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND {
         val indexer = indexerBuilder(shape)
         return DoubleBufferND(
             indexer,
@@ -174,7 +174,7 @@ public class DoubleFieldND(override val shape: Shape) :
 
     override fun number(value: Number): DoubleBufferND {
         val d = value.toDouble() // minimize conversions
-        return produce(shape) { d }
+        return structureND(shape) { d }
     }
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
index 65c1f71b4..827f0e21e 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
@@ -23,7 +23,7 @@ public class ShortRingND(
 
     override fun number(value: Number): BufferND<Short> {
         val d = value.toShort() // minimize conversions
-        return produce(shape) { d }
+        return structureND(shape) { d }
     }
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
index 7bc18a4dd..0e694bcb3 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
@@ -11,24 +11,24 @@ import space.kscience.kmath.operations.Ring
 import kotlin.jvm.JvmName
 
 
-public fun <T, A : Algebra<T>> AlgebraND<T, A>.produce(
+public fun <T, A : Algebra<T>> AlgebraND<T, A>.structureND(
     shapeFirst: Int,
     vararg shapeRest: Int,
     initializer: A.(IntArray) -> T
-): StructureND<T> = produce(Shape(shapeFirst, *shapeRest), initializer)
+): StructureND<T> = structureND(Shape(shapeFirst, *shapeRest), initializer)
 
-public fun <T, A : Group<T>> AlgebraND<T, A>.zero(shape: Shape): StructureND<T> = produce(shape) { zero }
+public fun <T, A : Group<T>> AlgebraND<T, A>.zero(shape: Shape): StructureND<T> = structureND(shape) { zero }
 
 @JvmName("zeroVarArg")
 public fun <T, A : Group<T>> AlgebraND<T, A>.zero(
     shapeFirst: Int,
     vararg shapeRest: Int,
-): StructureND<T> = produce(shapeFirst, *shapeRest) { zero }
+): StructureND<T> = structureND(shapeFirst, *shapeRest) { zero }
 
-public fun <T, A : Ring<T>> AlgebraND<T, A>.one(shape: Shape): StructureND<T> = produce(shape) { one }
+public fun <T, A : Ring<T>> AlgebraND<T, A>.one(shape: Shape): StructureND<T> = structureND(shape) { one }
 
 @JvmName("oneVarArg")
 public fun <T, A : Ring<T>> AlgebraND<T, A>.one(
     shapeFirst: Int,
     vararg shapeRest: Int,
-): StructureND<T> = produce(shapeFirst, *shapeRest) { one }
\ No newline at end of file
+): StructureND<T> = structureND(shapeFirst, *shapeRest) { one }
\ No newline at end of file
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
index 2009eb64f..82172af62 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
@@ -7,7 +7,7 @@ package space.kscience.kmath.structures
 
 import space.kscience.kmath.nd.get
 import space.kscience.kmath.nd.ndAlgebra
-import space.kscience.kmath.nd.produce
+import space.kscience.kmath.nd.structureND
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.testutils.FieldVerifier
@@ -22,7 +22,7 @@ internal class NDFieldTest {
 
     @Test
     fun testStrides() {
-        val ndArray = DoubleField.ndAlgebra.produce(10, 10) { (it[0] + it[1]).toDouble() }
+        val ndArray = DoubleField.ndAlgebra.structureND(10, 10) { (it[0] + it[1]).toDouble() }
         assertEquals(ndArray[5, 5], 10.0)
     }
 }
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
index 907301a53..61eb6acc8 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
@@ -20,8 +20,8 @@ import kotlin.test.assertEquals
 @Suppress("UNUSED_VARIABLE")
 class NumberNDFieldTest {
     val algebra = DoubleField.ndAlgebra
-    val array1 = algebra.produce(3, 3) { (i, j) -> (i + j).toDouble() }
-    val array2 = algebra.produce(3, 3) { (i, j) -> (i - j).toDouble() }
+    val array1 = algebra.structureND(3, 3) { (i, j) -> (i + j).toDouble() }
+    val array2 = algebra.structureND(3, 3) { (i, j) -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
diff --git a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
index d6996d427..9ee5087e9 100644
--- a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
+++ b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
@@ -18,9 +18,9 @@ public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
     override val elementAlgebra: A
 ) : RingOpsND<T, A> {
 
-    protected fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+    public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
 
-    override fun produce(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
+    override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
         val res = mk.zeros<T, DN>(shape, type).asDNArray()
         for (index in res.multiIndices) {
             res[index] = elementAlgebra.initializer(index)
@@ -28,10 +28,10 @@ public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
         return res.wrap()
     }
 
-    protected fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
+    public fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
         this
     } else {
-        produce(shape) { get(it) }
+        structureND(shape) { get(it) }
     }
 
     override fun StructureND<T>.map(transform: A.(T) -> T): MultikTensor<T> {
diff --git a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
index e9e56e06e..c229a44bf 100644
--- a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
+++ b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
@@ -11,7 +11,7 @@ import org.jetbrains.kotlinx.multik.ndarray.data.*
 import org.jetbrains.kotlinx.multik.ndarray.operations.*
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.mapInPlace
-import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.*
 import space.kscience.kmath.tensors.api.Tensor
 import space.kscience.kmath.tensors.api.TensorAlgebra
 
@@ -31,7 +31,7 @@ public value class MultikTensor<T>(public val array: MutableMultiArray<T, DN>) :
 }
 
 
-public abstract class MultikTensorAlgebra<T>(
+public class MultikTensorAlgebra<T> internal constructor(
     public val type: DataType,
     public val elementAlgebra: Ring<T>,
     public val comparator: Comparator<T>
@@ -41,7 +41,7 @@ public abstract class MultikTensorAlgebra<T>(
      * Convert a tensor to [MultikTensor] if necessary. If tensor is converted, changes on the resulting tensor
      * are not reflected back onto the source
      */
-    private fun Tensor<T>.asMultik(): MultikTensor<T> {
+    public fun Tensor<T>.asMultik(): MultikTensor<T> {
         return if (this is MultikTensor) {
             this
         } else {
@@ -53,7 +53,7 @@ public abstract class MultikTensorAlgebra<T>(
         }
     }
 
-    private fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+    public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
 
     override fun Tensor<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
         get(intArrayOf(0))
@@ -196,4 +196,19 @@ public abstract class MultikTensorAlgebra<T>(
     override fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): MultikTensor<T> {
         TODO("Not yet implemented")
     }
-}
\ No newline at end of file
+}
+
+public val DoubleField.multikTensorAlgebra: MultikTensorAlgebra<Double>
+    get() = MultikTensorAlgebra(DataType.DoubleDataType, DoubleField) { o1, o2 -> o1.compareTo(o2) }
+
+public val FloatField.multikTensorAlgebra: MultikTensorAlgebra<Float>
+    get() = MultikTensorAlgebra(DataType.FloatDataType, FloatField) { o1, o2 -> o1.compareTo(o2) }
+
+public val ShortRing.multikTensorAlgebra: MultikTensorAlgebra<Short>
+    get() = MultikTensorAlgebra(DataType.ShortDataType, ShortRing) { o1, o2 -> o1.compareTo(o2) }
+
+public val IntRing.multikTensorAlgebra: MultikTensorAlgebra<Int>
+    get() = MultikTensorAlgebra(DataType.IntDataType, IntRing) { o1, o2 -> o1.compareTo(o2) }
+
+public val LongRing.multikTensorAlgebra: MultikTensorAlgebra<Long>
+    get() = MultikTensorAlgebra(DataType.LongDataType, LongRing) { o1, o2 -> o1.compareTo(o2) }
\ No newline at end of file
diff --git a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
index 259b1a934..1f312849a 100644
--- a/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
+++ b/kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
@@ -32,7 +32,7 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
      */
     public val StructureND<T>.ndArray: INDArray
 
-    override fun produce(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
+    override fun structureND(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
         val struct = Nd4j.create(*shape)!!.wrap()
         struct.indicesIterator().forEach { struct[it] = elementAlgebra.initializer(it) }
         return struct
diff --git a/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt b/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
index 465937fa9..103416120 100644
--- a/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
+++ b/kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
@@ -9,7 +9,7 @@ import org.nd4j.linalg.factory.Nd4j
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.one
-import space.kscience.kmath.nd.produce
+import space.kscience.kmath.nd.structureND
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.IntRing
 import space.kscience.kmath.operations.invoke
@@ -23,7 +23,7 @@ import kotlin.test.fail
 internal class Nd4jArrayAlgebraTest {
     @Test
     fun testProduce() {
-        val res = DoubleField.nd4j.produce(2, 2) { it.sum().toDouble() }
+        val res = DoubleField.nd4j.structureND(2, 2) { it.sum().toDouble() }
         val expected = (Nd4j.create(2, 2) ?: fail()).asDoubleStructure()
         expected[intArrayOf(0, 0)] = 0.0
         expected[intArrayOf(0, 1)] = 1.0
@@ -58,9 +58,9 @@ internal class Nd4jArrayAlgebraTest {
 
     @Test
     fun testSin() = DoubleField.nd4j{
-        val initial = produce(2, 2) { (i, j) -> if (i == j) PI / 2 else 0.0 }
+        val initial = structureND(2, 2) { (i, j) -> if (i == j) PI / 2 else 0.0 }
         val transformed = sin(initial)
-        val expected = produce(2, 2) { (i, j) -> if (i == j) 1.0 else 0.0 }
+        val expected = structureND(2, 2) { (i, j) -> if (i == j) 1.0 else 0.0 }
 
         println(transformed)
         assertTrue { StructureND.contentEquals(transformed, expected) }
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
index 594070cd2..16ed4b834 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
@@ -22,7 +22,7 @@ import kotlin.math.*
 public open class DoubleTensorAlgebra :
     TensorPartialDivisionAlgebra<Double>,
     AnalyticTensorAlgebra<Double>,
-    LinearOpsTensorAlgebra<Double> {
+    LinearOpsTensorAlgebra<Double>{
 
     public companion object : DoubleTensorAlgebra()
 
diff --git a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt
index c72553a64..aaa113e56 100644
--- a/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt
+++ b/kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt
@@ -21,12 +21,12 @@ public open class ViktorFieldOpsND :
     public val StructureND<Double>.f64Buffer: F64Array
         get() = when (this) {
             is ViktorStructureND -> this.f64Buffer
-            else -> produce(shape) { this@f64Buffer[it] }.f64Buffer
+            else -> structureND(shape) { this@f64Buffer[it] }.f64Buffer
         }
 
     override val elementAlgebra: DoubleField get() = DoubleField
 
-    override fun produce(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
+    override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
         F64Array(*shape).apply {
             DefaultStrides(shape).indices().forEach { index ->
                 set(value = DoubleField.initializer(index), indices = index)

From dccc92bf2fd9f979e70386a25d1ff1db231d368f Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Mon, 18 Oct 2021 12:52:24 +0300
Subject: [PATCH 09/10] Switch to multik-default

---
 .../kotlin/space/kscience/kmath/tensors/multik.kt  | 14 +++++++-------
 kmath-multik/build.gradle.kts                      |  2 +-
 .../space/kscience/kmath/multik/MultikOpsND.kt     |  4 +++-
 3 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
index fc6d7dd56..5383b5c3e 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.tensors
 
+import edu.mcgill.kaliningraph.power
 import org.jetbrains.kotlinx.multik.api.Multik
 import org.jetbrains.kotlinx.multik.api.linalg.dot
 import org.jetbrains.kotlinx.multik.api.math.exp
@@ -12,13 +13,12 @@ import org.jetbrains.kotlinx.multik.api.ndarray
 import org.jetbrains.kotlinx.multik.ndarray.operations.minus
 import org.jetbrains.kotlinx.multik.ndarray.operations.plus
 import org.jetbrains.kotlinx.multik.ndarray.operations.unaryMinus
+import space.kscience.kmath.multik.multikND
+import space.kscience.kmath.nd.one
+import space.kscience.kmath.operations.DoubleField
 
-fun main() {
-    val a = Multik.ndarray(intArrayOf(1, 2, 3))
+fun main(): Unit = with(DoubleField.multikND) {
+    val a = Multik.ndarray(intArrayOf(1, 2, 3)).asType<Double>().wrap()
     val b = Multik.ndarray(doubleArrayOf(1.0, 2.0, 3.0))
-    2 + (-a) - 2
-
-    a dot a
-
-    a.exp()
+    one(a.shape) - a + power()
 }
\ No newline at end of file
diff --git a/kmath-multik/build.gradle.kts b/kmath-multik/build.gradle.kts
index 16a7ab652..df2292f2e 100644
--- a/kmath-multik/build.gradle.kts
+++ b/kmath-multik/build.gradle.kts
@@ -6,7 +6,7 @@ description = "JetBrains Multik connector"
 
 dependencies {
     api(project(":kmath-tensors"))
-    api("org.jetbrains.kotlinx:multik-api:0.1.0")
+    api("org.jetbrains.kotlinx:multik-default:0.1.0")
 }
 
 readme {
diff --git a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
index 9ee5087e9..4068ba9b9 100644
--- a/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
+++ b/kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
@@ -1,5 +1,7 @@
 package space.kscience.kmath.multik
 
+import org.jetbrains.kotlinx.multik.api.math.cos
+import org.jetbrains.kotlinx.multik.api.math.sin
 import org.jetbrains.kotlinx.multik.api.mk
 import org.jetbrains.kotlinx.multik.api.zeros
 import org.jetbrains.kotlinx.multik.ndarray.data.*
@@ -18,7 +20,7 @@ public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
     override val elementAlgebra: A
 ) : RingOpsND<T, A> {
 
-    public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+    public fun MutableMultiArray<T, *>.wrap(): MultikTensor<T> = MultikTensor(this.asDNArray())
 
     override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
         val res = mk.zeros<T, DN>(shape, type).asDNArray()

From bfc6cbe5d8fdda11db1ffd8dd6da73271a184eaa Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@users.noreply.github.com>
Date: Mon, 18 Oct 2021 13:04:36 +0300
Subject: [PATCH 10/10] Update multik.kt

---
 .../src/main/kotlin/space/kscience/kmath/tensors/multik.kt    | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
index 5383b5c3e..b1cf435d4 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/multik.kt
@@ -20,5 +20,5 @@ import space.kscience.kmath.operations.DoubleField
 fun main(): Unit = with(DoubleField.multikND) {
     val a = Multik.ndarray(intArrayOf(1, 2, 3)).asType<Double>().wrap()
     val b = Multik.ndarray(doubleArrayOf(1.0, 2.0, 3.0))
-    one(a.shape) - a + power()
-}
\ No newline at end of file
+    one(a.shape) - a
+}