calebtaber / cas

An advanced math library, written in C++.

CAS

An advanced math library, written in C++. (CAS = Computer Algebra System)

Goal

The goal of this project is to create a well-written and understandable library that is capable of performing complex algebraic and trigonometric calculations. Basically, I hope to implement functionality for all math up to, but not including, calculus.

Changelog

01/16/2021
Single-variable linear equations can now be automatically solved.

01/03/2021
All basic arithmetic (+, -, *, /, ^), including parentheses, is supported.
All above operations are supported with terms that have exponents (i.e. 3x^(2) / 5x^(1) and the like is possible)
I just finished testing with a bunch of cases, and it seems that my shunting yard implementation is solid, so I will be moving on to equation and inequality functionality soon, as well as some trigonometry.

General Organization

With this project, I'm taking an object-oriented approach to math. The most basic element is a Term. Then comes the Expression, which is a vector of Term objects. Then would come the Equation and System (of equations) units, which are successive compositions of their predecessors. This structure, I believe, is the most efficient for implementing more and more complex mathematical concepts.

As for organizing the actual mathematical operations, I currently (as of 12/25/2020) am planning to put each level of math in its own file. For example, right now basic arithmetic functions are contained in the file math/Arithmetic.cpp. In doing this, I am trying to apply the Agile methodology of separating data structures from functions that manipulate them. So a Term would have a coefficient and a map of variables and their exponents, but it would not have the ability, for example, to perform addition on itself and another Term. An outside function from Arithmetic.cpp would need to be called on both Term objects, returning a new Term that contains the sum.

This separation of data from their manipulating functions, I have found, allows for a smoother implementation of new mathematical units and is just generally more logical.