Yacas

Yacas is a multipurpose computer algebra system. The name is an acronym for Yet Another Computer Algebra System. Yacas is free software and published as such under the GPL.

Yacas provides a system for the symbolic calculation of expressions and comes with its own programming language, in which new algorithms can be developed, but can also be used as pre-existing. As input and output can be selected ASCII or OpenMath, but there are also commands for exporting to LaTeX. For the graphical representation of functions ( both in 2D and in 3D) is used Gnuplot.

Both Yacas and Gnuplot are available for many different operating systems. They are (among others) available on the website along with detailed documentation, where you can try online, the system also.

Although the software can not keep up with the commercial computer algebra systems, but would give a good insight into the functioning of these systems, so Harald Bögeholz in the " Special topic: Scientific software " of the computer magazine c't.