Take the 2-minute tour ×  Let $A$ be a noncommutative finitely
generated algebra with a finitely generated set of relations.
Moreover, assume that $A$ is finite dimensional as a vector
space.  What I want to know is, can Mathematica (or any other
package) be used to find the dimension of $A$ given only the
generators of $A$ and the generators of the set of relations?
Or, even better, can Mathematica (or any other package) be used
to find a basis of $A$ given only the generators of $A$ and the
generators of the set of relations?  Basic examples would be
particularily helpful.  share|improve this question I use GAP
(gap-system.org) and the non-commutative Gröbner basis package
gbnp (mathdox.org/products/gbnp). You will find examples in the
manual. –  Leandro Vendramin Feb 2 '12 at 16:16 I used to use
Steve Linton's Vector Enumeration but this is now deprecated. – 
Bruce Westbury Feb 2 '12 at 16:18 Not really related, but still:
mathoverflow.net/questions/85400/… –  Alexander Chervov Feb 2
'12 at 17:48 If you kn