A General Math Library that aims to provide support for any applications needing robust mathematical equation representation, evaluation and manipulation support
The Structure provided for encoding expressions is designed to let the user of the library extend it with any value structures or operators as they see fit and extend upon the default value structures and operators.
Expressions are set up in a tree fashion:
(4+5)/3.2*(x-3)
/
┌──┴───┐
+ *
┌┴┐ ┌┴──┐
4 5 3.2 -
┌┴┐
x 3
All Types in the tree (all types that are involved in calculations) are members of the class Expression. The Function of Expressions is simply to evaluate everything below them (recursively). This is done via the evaluate function.
The types that encode values like numbers or vectors are called Structures.
Structures are members of the class Expression and are a specific subset that evaluate to themselves (making them leaf nodes of the tree).
Some defalut Structure Types/Constructors include:
Number:Absolute,Measure
The types that evaluate Expressions into new Expressions are Operators.
An Operator is defined with respect to a class which acts as a constraint on Expressions in that they must have the typeclass' functions defined to be used in that operator. This ensures type safety when calling the operator and allows for the Operator to predict the return type of the operation. That is, if any Expression wants to be added (via Addition), they must first declare how they are Addable by defining the function add.
Some default constraint classes with their respective Operators include:
Addable:AdditionMultipliable:MultiplicationPowerable:PowerVectorSpace:Negation(&Addition& ScalarMultiplication)
Constraint classes can also be subclasses of others. For instance, VectorSpace is a subclass of Addable since vectors are addable and it is also a subclass of Multipliable, but only for a definition of scalar multiplication.