Maxima is an award winning, open-source software, which provides a powerful formulation of mathematical functions, and is mainly used for symbolic computing, including integral and differential calculus, and other partial function approximation techniques. It also provides support for other numerical capabilities, including floating-point arithmetic, fixed-point arithmetic, and even arithmetic with real numbers. It was developed by professors Richard Lazarus and Robert S. Baranovitch as a solution to the numerical analysis problems of the United States intelligence community. This software is based on a new concept called "clustered computing." This new concept basically says that we can effectively use many smaller units of calculation to solve much larger problems, and hence make computation more efficient and robust.
Aside from the Maxima library and its symbolic capability, this program comes bundled with over two hundred common lisp code libraries. These libraries enable programmers to utilize most of the language features offered by Maxima. This includes Common Lisp (CL) and Symbolic Computation. In Symbolic Computation, Maxima provides support for programming languages like Ocaml, C#, and Java. Common Lisp is the programming language that works on the Maxima platform, so it can be considered one of Maxima's core components.
For those who are curious about using this software, the best way to download it and try it out is through Maxima's website. Although the software is free, it is not actually open source. The only thing open source is related to are the libraries and applications associated with it, which include symbolic math and common lisp code library. This means that anyone can download and use the Maxima free software, but they can't develop programs or applications that make use of Maxima's symbolic capabilities. With that being said, however, the Maxima computer algebra system is an excellent tool for students of all levels to learn programming and mathematical concepts.