TITLE: Computer algebra system for Weyl algebra computations
QUESTION [7 upvotes]: Does anyone have a suggestion for the best computer program to perform calculations in the 2nd Weyl algebra?

REPLY [4 votes]: I use GAP (http://www.gap-system.org/) with the GBNP package (http://www.win.tue.nl/~amc/pub/grobner/chap0.html).
You define Weyl algebra as a quotient of free associative algebra by the ideal
$<x_1 x_2 - x_2 x_1 - 1>$.
Easy to generalize to arbitrary dimension and can handle Clifford algebras
(of arbitrary signatures) in the same setting.