I have been playing with the Python SymPy package and created a repository with my test scripts and notes:
Might be helpful to someone. I just got started.
I had used Maxima before. SymPy and Maxima are both what Wikipedia calls “Computer Algebra Systems.” They have a nice list here:
I got a lot of use out of Maxima but I think it makes sense to switch the SymPy because it is written in Python and works well with other mainstream Python packages that I use like Matplotlib. They both fall under the SciPy umbrella of related tools so for me if I need some computer algebra I probably should stick with SymPy.
Maxima and SymPy are both free.