doc/operations.md

@@ -1,38 +1,40 @@
 ## Spaces and fields
 
-An obvious first choice of mathematical objects to implement in context-oriented style are algebra elements like spaces,
-rings and fields. Those are located in a `scientifik.kmath.operations.Algebra.kt` file. Alongside algebric context
-themselves, the file includes definitions for algebra elements such as `FieldElement`. A `FieldElement` object
-stores a reference to the `Field` which contains a additive and multiplicative operations for it, meaning
-it has one fixed context attached to it and does not require explicit external context. So those `MathElements` could be
-operated without context:
+An obvious first choice of mathematical objects to implement in a context-oriented style are algebraic elements like spaces,
+rings and fields. Those are located in the `scientifik.kmath.operations.Algebra.kt` file. Alongside common contexts, the file includes definitions for algebra elements like `FieldElement`. A `FieldElement` object
+stores a reference to the `Field` which contains additive and multiplicative operations, meaning
+it has one fixed context attached and does not require explicit external context. So those `MathElements` can be operated without context:
+
 ```kotlin
 val c1 = Complex(1.0, 2.0)
 val c2 = ComplexField.i
 val c3 = c1 + c2
 ```
-`ComplexField` also features special operations to mix complex numbers with real numbers like:
+
+`ComplexField` also features special operations to mix complex and real numbers, for example:
+
 ```kotlin
 val c1 = Complex(1.0,2.0)
-val c2 = ComplexField.run{ c1 - 1.0} //returns [re:0.0, im: 2.0]
+val c2 = ComplexField.run{ c1 - 1.0} // Returns: [re:0.0, im: 2.0]
 val c3 = ComplexField.run{ c1 - i*2.0}
 ```
 
 **Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
-that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for news.
+that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for updates.
 
 ## Nested fields
 
-Algebra contexts allow to create more complex structures. For example, it is possible to create a `Matrix` from complex
-elements like this:
+Contexts allow one to build more complex structures. For example, it is possible to create a `Matrix` from complex elements like so:
+
 ```kotlin
 val element = NDElements.create(field = ComplexField, shape = intArrayOf(2,2)){index: IntArray ->
     Complex(index[0] - index[1], index[0] + index[1])
 }
 ```
-The `element` in this example is a member of `Field` of 2-d structures, each element of which is a member of its own
-`ComplexField`. The important thing is that one does not need to create a special nd-structure to hold complex
-numbers and implements operations on it, one need just to provide a field for its elements.
 
-**Note**: Fields themselves do not solve problem of JVM boxing, but it is possible to solve with special contexts like
+The `element` in this example is a member of the `Field` of 2-d structures, each element of which is a member of its own
+`ComplexField`. The important thing is one does not need to create a special n-d class to hold complex
+numbers and implement operations on it, one just needs to provide a field for its elements.
+
+**Note**: Fields themselves do not solve the problem of JVM boxing, but it is possible to solve with special contexts like
 `BufferSpec`. This feature is in development phase.