Mathematica http://www.wolfram.com and Maple http://www.maplesoft.com are both powerful tools to do symbolic computation. They both provide facilities for interactive algebra, calculus, discrete mathematics, graphics, numerical computation and many other areas of mathematics. Choice between these two is personal. Note that matlab's symbolic toolbox is based on maple.
Mathematica and Maple V6 are currently installed on stat network. There are two versions of both of them, text based and X-based. The command to bring up X-based mathematica is mathematica while is math for the text based version. maple and xmaple start maple in test mode and X mode respectively. When Maple begins running, it will automatically execute the commands in the file .mapleinit in your home directory, if it exists.