It is probably worth your while to buy Mathematica, Maple, or Matlab, depending on your needs. I wish it weren't so, but this is one area in which the commercial tools are still vastly better than their free counterparts.
If you are a student, you can buy these at fairly afforable prices. Maple 14 Student Edition is only $99. Mathematica for Students is \$140, and Matlab/Simulink is \$99 for students. It is also possible that your school or department already has a site license, allowing you to obtain and use this software for no additional cost.
For symbolic calculations, you want either Mathematica or Maple, with Maple being more user-friendly, and Mathematica being more prevalent (in my experience) in actual research environments. Matlab's focus is on numerical calculations.
This post imported from StackExchange Physics at 2014-04-03 11:46 (UCT), posted by SE-user nibot