Maxima is a computer algebra system written in common lisp. For me, it is an alternative to Mathematica. To install maxima with Mac OS X, I use Homebrew:
brew update && brew upgrade && brew install maxima
Then, open the ~/.emacs file and add two lines to load imaxima mode:
(add-to-list 'load-path "/usr/local/Cellar/maxima/5.25.1/share/maxima/5.25.1/emacs") (require 'maxima)
In Emacs, launch Maxima in imaxima mode by M-x imaxima. Then you can do what ever you want!