Dear GAP Forum,
A couple of weeks ago, David Wales asked about constructing associative
algebras given by generators and relations.
There are essentially two ways to do this:
1. Non-commutative Groebner basis
2. Vector enumeration
Craig Struble has already replied offering access to their NCGB software. Aside
from this, there is no library code, or code in any released or deposited
package for GAP 4 to do any of these things, however I can suggest a couple
more directions that might help:
1. There is a GAP 3 package that links to my stand-alone C vector enumerator
code. You may find the vector enumerator a bit tricky to compile on modern
systems, but I can try and help.
2. I have a prototype vector enumerator written in GAP 4, which I would be
happy to supply to anyone interested. It's only the core algorithm, and, in
many respects a very crude implementation, but I believe that it is correct,
and might work OK for small problems.