Mathics is implementation of Mathematica (actually it is now called Wolfram language) using sympy, ply, and django.<p>It also provides jupyter kernel.<p>The original author was hired by Wolfram, but the project still lives on!<p><a href="http://mathics.github.io" rel="nofollow">http://mathics.github.io</a><p>Maxima is older than Mathematica and written in LISP. One of its contributors has written MockMMA to implement Mathematica in LISP:<p><a href="https://people.eecs.berkeley.edu/~fateman/lisp/" rel="nofollow">https://people.eecs.berkeley.edu/~fateman/lisp/</a>