*... and probably polytopes.*

I recommend <a href="http://polymake.org/doku.php/start">polymake</a> for general polytope computations, <a href="http://www.math.ucdavis.edu/~mkoeppe/latte/">LattE</a> for lattice-point enumeration, <a href="http://www.mathematik.uni-osnabrueck.de/normaliz/">Normaliz</a> for computations related to lattice polytopes, and <a href="http://www.4ti2.de/">4ti2</a> for Gröbner basis computations.