Maxima is a fairly complete computer algebra system written in Lisp with an emphasis on symbolic computation.
License: Open Source
Mathematica is a powerful commercial software known for its advanced symbolic computation, extensive graphing capabilities, and integration with other systems, making it suitable for professionals in various fields. In contrast, Maxima is an open-source alternative focused on symbolic mathematics with a good community support but lacks some of the advanced features and user-friendliness of Mathematica.