diff --git a/kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt b/kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt
index 65e915ef4..8c19395d3 100644
--- a/kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt
+++ b/kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt
@@ -2,8 +2,9 @@ package scientifik.kmath.commons.expressions
 
 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 import scientifik.kmath.expressions.Expression
-import scientifik.kmath.expressions.ExpressionField
+import scientifik.kmath.expressions.ExpressionContext
 import scientifik.kmath.operations.ExtendedField
+import scientifik.kmath.operations.Field
 import kotlin.properties.ReadOnlyProperty
 import kotlin.reflect.KProperty
 
@@ -112,7 +113,7 @@ fun DiffExpression.derivative(name: String) = derivative(name to 1)
 /**
  * A context for [DiffExpression] (not to be confused with [DerivativeStructure])
  */
-object DiffExpressionContext : ExpressionField<Double, DiffExpression> {
+object DiffExpressionContext : ExpressionContext<Double, DiffExpression>, Field<DiffExpression> {
     override fun variable(name: String, default: Double?) =
         DiffExpression { variable(name, default?.const()) }
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
index dae069879..73745f78f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
@@ -1,7 +1,6 @@
 package scientifik.kmath.expressions
 
-import scientifik.kmath.operations.Field
-import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.Algebra
 
 /**
  * An elementary function that could be invoked on a map of arguments
@@ -15,7 +14,7 @@ operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke
 /**
  * A context for expression construction
  */
-interface ExpressionContext<T, E> {
+interface ExpressionContext<T, E> : Algebra<E> {
     /**
      * Introduce a variable into expression context
      */
@@ -25,87 +24,13 @@ interface ExpressionContext<T, E> {
      * A constant expression which does not depend on arguments
      */
     fun const(value: T): E
-
-    fun produce(node: SyntaxTreeNode): E
 }
 
-interface ExpressionSpace<T, E> : Space<E>, ExpressionContext<T, E> {
-
-    fun produceSingular(value: String): E = variable(value)
-
-    fun produceUnary(operation: String, value: E): E {
-        return when (operation) {
-            UnaryNode.PLUS_OPERATION -> value
-            UnaryNode.MINUS_OPERATION -> -value
-            else -> error("Unary operation $operation is not supported by $this")
-        }
+fun <T, E> ExpressionContext<T, E>.produce(node: SyntaxTreeNode): E {
+    return when (node) {
+        is NumberNode -> error("Single number nodes are not supported")
+        is SingularNode -> variable(node.value)
+        is UnaryNode -> unaryOperation(node.operation, produce(node.value))
+        is BinaryNode -> binaryOperation(node.operation, produce(node.left), produce(node.right))
     }
-
-    fun produceBinary(operation: String, left: E, right: E): E {
-        return when (operation) {
-            BinaryNode.PLUS_OPERATION -> left + right
-            BinaryNode.MINUS_OPERATION -> left - right
-            else -> error("Binary operation $operation is not supported by $this")
-        }
-    }
-
-    override fun produce(node: SyntaxTreeNode): E {
-        return when (node) {
-            is NumberNode -> error("Single number nodes are not supported")
-            is SingularNode -> produceSingular(node.value)
-            is UnaryNode -> produceUnary(node.operation, produce(node.value))
-            is BinaryNode -> {
-                when (node.operation) {
-                    BinaryNode.TIMES_OPERATION -> {
-                        if (node.left is NumberNode) {
-                            return produce(node.right) * node.left.value
-                        } else if (node.right is NumberNode) {
-                            return produce(node.left) * node.right.value
-                        }
-                    }
-                    BinaryNode.DIV_OPERATION -> {
-                        if (node.right is NumberNode) {
-                            return produce(node.left) / node.right.value
-                        }
-                    }
-                }
-                produceBinary(node.operation, produce(node.left), produce(node.right))
-            }
-        }
-    }
-}
-
-interface ExpressionField<T, E> : Field<E>, ExpressionSpace<T, E> {
-    fun number(value: Number): E = one * value
-
-    override fun produce(node: SyntaxTreeNode): E {
-        if (node is BinaryNode) {
-            when (node.operation) {
-                BinaryNode.PLUS_OPERATION -> {
-                    if (node.left is NumberNode) {
-                        return produce(node.right) + one * node.left.value
-                    } else if (node.right is NumberNode) {
-                        return produce(node.left) + one * node.right.value
-                    }
-                }
-                BinaryNode.MINUS_OPERATION -> {
-                    if (node.left is NumberNode) {
-                        return one * node.left.value - produce(node.right)
-                    } else if (node.right is NumberNode) {
-                        return produce(node.left) - one * node.right.value
-                    }
-                }
-            }
-        }
-        return super.produce(node)
-    }
-
-    override fun produceBinary(operation: String, left: E, right: E): E {
-        return when (operation) {
-            BinaryNode.TIMES_OPERATION -> left * right
-            BinaryNode.DIV_OPERATION -> left / right
-            else -> super.produceBinary(operation, left, right)
-        }
-    }
-
 }
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressions.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressions.kt
index 7b5a93465..4f38e3a71 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressions.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressions.kt
@@ -3,7 +3,6 @@ package scientifik.kmath.expressions
 import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.Ring
 import scientifik.kmath.operations.Space
-import scientifik.kmath.operations.invoke
 
 internal class VariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
     override fun invoke(arguments: Map<String, T>): T =
@@ -28,41 +27,54 @@ internal class ProductExpression<T>(val context: Ring<T>, val first: Expression<
         context.multiply(first.invoke(arguments), second.invoke(arguments))
 }
 
-internal class ConstProductExpression<T>(val context: Space<T>, val expr: Expression<T>, val const: Number) :
+internal class ConstProductExpession<T>(val context: Space<T>, val expr: Expression<T>, val const: Number) :
     Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
 }
 
-internal class DivExpression<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) :
+internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) :
     Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = context.divide(expr.invoke(arguments), second.invoke(arguments))
 }
 
-open class FunctionalExpressionSpace<T>(val space: Space<T>) : Space<Expression<T>>, ExpressionSpace<T, Expression<T>> {
+open class FunctionalExpressionSpace<T>(
+    val space: Space<T>
+) : Space<Expression<T>>, ExpressionContext<T,Expression<T>> {
+
     override val zero: Expression<T> = ConstantExpression(space.zero)
 
     override fun const(value: T): Expression<T> = ConstantExpression(value)
+
     override fun variable(name: String, default: T?): Expression<T> = VariableExpression(name, default)
+
     override fun add(a: Expression<T>, b: Expression<T>): Expression<T> = SumExpression(space, a, b)
-    override fun multiply(a: Expression<T>, k: Number): Expression<T> = ConstProductExpression(space, a, k)
-    operator fun Expression<T>.plus(arg: T): Expression<T> = this + const(arg)
-    operator fun Expression<T>.minus(arg: T): Expression<T> = this - const(arg)
-    operator fun T.plus(arg: Expression<T>): Expression<T> = arg + this
-    operator fun T.minus(arg: Expression<T>): Expression<T> = arg - this
+
+    override fun multiply(a: Expression<T>, k: Number): Expression<T> = ConstProductExpession(space, a, k)
+
+
+    operator fun Expression<T>.plus(arg: T) = this + const(arg)
+    operator fun Expression<T>.minus(arg: T) = this - const(arg)
+
+    operator fun T.plus(arg: Expression<T>) = arg + this
+    operator fun T.minus(arg: Expression<T>) = arg - this
 }
 
-open class FunctionalExpressionField<T>(val field: Field<T>) :
-    ExpressionField<T, Expression<T>>,
-    FunctionalExpressionSpace<T>(field) {
+open class FunctionalExpressionField<T>(
+    val field: Field<T>
+) :  Field<Expression<T>>, ExpressionContext<T,Expression<T>>, FunctionalExpressionSpace<T>(field) {
 
     override val one: Expression<T>
         get() = const(this.field.one)
 
-    override fun number(value: Number): Expression<T> = const(field { one * value })
+    fun const(value: Double): Expression<T> = const(field.run { one*value})
+
     override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> = ProductExpression(field, a, b)
-    override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> = DivExpression(field, a, b)
-    operator fun Expression<T>.times(arg: T): Expression<T> = this * const(arg)
-    operator fun Expression<T>.div(arg: T): Expression<T> = this / const(arg)
-    operator fun T.times(arg: Expression<T>): Expression<T> = arg * this
-    operator fun T.div(arg: Expression<T>): Expression<T> = arg / this
-}
+
+    override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> = DivExpession(field, a, b)
+
+    operator fun Expression<T>.times(arg: T) = this * const(arg)
+    operator fun Expression<T>.div(arg: T) = this / const(arg)
+
+    operator fun T.times(arg: Expression<T>) = arg * this
+    operator fun T.div(arg: Expression<T>) = arg / this
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/SyntaxTreeNode.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/SyntaxTreeNode.kt
index fff3c5bc0..b4038f680 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/SyntaxTreeNode.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/SyntaxTreeNode.kt
@@ -8,9 +8,6 @@ data class NumberNode(val value: Number) : SyntaxTreeNode()
 
 data class UnaryNode(val operation: String, val value: SyntaxTreeNode) : SyntaxTreeNode() {
     companion object {
-        const val PLUS_OPERATION = "+"
-        const val MINUS_OPERATION = "-"
-        const val NOT_OPERATION = "!"
         const val ABS_OPERATION = "abs"
         const val SIN_OPERATION = "sin"
         const val COS_OPERATION = "cos"
@@ -22,10 +19,6 @@ data class UnaryNode(val operation: String, val value: SyntaxTreeNode) : SyntaxT
 
 data class BinaryNode(val operation: String, val left: SyntaxTreeNode, val right: SyntaxTreeNode) : SyntaxTreeNode() {
     companion object {
-        const val PLUS_OPERATION = "+"
-        const val MINUS_OPERATION = "-"
-        const val TIMES_OPERATION = "*"
-        const val DIV_OPERATION = "/"
         //TODO add operations
     }
 }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
index 485185526..b3282e5f3 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
@@ -6,9 +6,12 @@ annotation class KMathContext
 /**
  * Marker interface for any algebra
  */
-interface Algebra<T>
+interface Algebra<T> {
+    fun unaryOperation(operation: String, arg: T): T
+    fun binaryOperation(operation: String, left: T, right: T): T
+}
 
-inline operator fun <T : Algebra<*>, R> T.invoke(block: T.() -> R): R = run(block)
+inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = run(block)
 
 /**
  * Space-like operations without neutral element
@@ -24,7 +27,7 @@ interface SpaceOperations<T> : Algebra<T> {
      */
     fun multiply(a: T, k: Number): T
 
-    //Operation to be performed in this context
+    //Operation to be performed in this context. Could be moved to extensions in case of KEEP-176
     operator fun T.unaryMinus(): T = multiply(this, -1.0)
 
     operator fun T.plus(b: T): T = add(this, b)
@@ -32,6 +35,24 @@ interface SpaceOperations<T> : Algebra<T> {
     operator fun T.times(k: Number) = multiply(this, k.toDouble())
     operator fun T.div(k: Number) = multiply(this, 1.0 / k.toDouble())
     operator fun Number.times(b: T) = b * this
+
+    override fun unaryOperation(operation: String, arg: T): T = when (operation) {
+        PLUS_OPERATION -> arg
+        MINUS_OPERATION -> -arg
+        else -> error("Unary operation $operation not defined in $this")
+    }
+
+    override fun binaryOperation(operation: String, left: T, right: T): T = when (operation) {
+        PLUS_OPERATION -> add(left, right)
+        MINUS_OPERATION -> left - right
+        else -> error("Binary operation $operation not defined in $this")
+    }
+
+    companion object {
+        const val PLUS_OPERATION = "+"
+        const val MINUS_OPERATION = "-"
+        const val NOT_OPERATION = "!"
+    }
 }
 
 
@@ -60,6 +81,15 @@ interface RingOperations<T> : SpaceOperations<T> {
     fun multiply(a: T, b: T): T
 
     operator fun T.times(b: T): T = multiply(this, b)
+
+    override fun binaryOperation(operation: String, left: T, right: T): T = when (operation) {
+        TIMES_OPERATION -> multiply(left, right)
+        else -> super.binaryOperation(operation, left, right)
+    }
+
+    companion object{
+        const val TIMES_OPERATION = "*"
+    }
 }
 
 /**
@@ -85,6 +115,15 @@ interface FieldOperations<T> : RingOperations<T> {
     fun divide(a: T, b: T): T
 
     operator fun T.div(b: T): T = divide(this, b)
+
+    override fun binaryOperation(operation: String, left: T, right: T): T = when (operation) {
+        DIV_OPERATION -> divide(left, right)
+        else -> super.binaryOperation(operation, left, right)
+    }
+
+    companion object{
+        const val DIV_OPERATION = "/"
+    }
 }
 
 /**
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/VectorSpaceTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/VectorSpaceTest.kt
new file mode 100644
index 000000000..e69de29bb