TITLE: Quantum Group Calculations in Mathematica
QUESTION [8 upvotes]: I'm trying to learn how to do algebraic manipulations in Mathematica but not finding the help very helpful. I'm going to ask about a specific quantum group example related to a previous  question of mine. For $SU_q(N)$, how would I use Mathematica to show that
$$
S(u^1_2)u^3_1 = q^{-1}u^3_1S(u^1_2).
$$
I am, of course, assuming that such a thing can be done in Mathematica. If I am wrong in this assumption, could someone please direct me a package that can do this calculation? Gap, Magma?

REPLY [7 votes]: I just found the link to the QuantumGroups Mathematica package by Scott Morrison mentioned by Noah: 
http://katlas.org/wiki/QuantumGroups%60