Maxima CAS is a free, open-source computer algebra system. It runs on all modern operating systems and features a rich array of features that rival the commerical, closed-source computer algebra systems. Maxima is built on top of the LISP computer language. LISP, and Maxima, are extremely easy to extend.
To check tar.gz file integrity, do md5sum -c <file-root>.tar.gz.md5sum
on a commandline.