SymPy
A computer algebra system written in pure Python
...Written entirely in Python, SymPy is easy to use, comprehensible and easily extensible. It’s also very lightweight as it solely depends on mpmath, a pure Python library for arbitrary floating point arithmetic.
SymPy has participated in every Google Summer of Code since 2007 and because of this has continuously improved. A lot more people have also contributed to it, and used it in their projects. Beyond being an interactive tool, it can be embedded in other apps and extended with custom functions.