Mathics is a general-purpose computer algebra system (CAS). It is meant to be a free, light-weight alternative to Mathematica.
The homepage of Mathics is at http://www.mathics.org, where you can find installation instructions. There is also a server to use Mathics online at http://www.mathics.net.
Here is short a guide on how to install Mathics on your computer.
Please feel encouraged to contribute to Mathics! Create your own fork, make the desired changes, commit, and make a pull request.
Mathics is released under the GNU General Public License (GPL).