SymPy
SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.
youtube Enthought - SymPy - Part 1 | SciPy 2014 | Aaron Meurer, Jason K Moore, Matthew Rocklin