Yacas is an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical expressions. It uses its own programming language designed for symbolic as well as arbitrary-precision numerical computations. The system has a library of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library.
Interested? Have a look at screenshots to see how it actually looks like.
Yacas comes with extensive documentation covering the scripting language, implemented functionality and the algorithms used.
You have read the documentation, but still got questions? If they are not yet answered, don’t hesitate to ask them.