Does anyone if there exists a math program that can work with free associative algebras ? By work with associative algebras, I mean
- It can define any ideal $I$, being it left-,right- or twosided.
- It can define quotientrings $R/I$ and I can do summation and multiplication in it. (if it can work only with ideals generated by homogeneous elements, it's ok).
- It can calculate elements of the center of an associatieve algebra(= a quotient of a free algebra) of a certain degree (I don't need to find the complete center, just the elements of a certain degree).
Additionally, it would be nice if it were free (opensource or something like that) and it works on Windows.
Thanks in advance.
Forgot to mention: if it can be done in Sage, is there any good documentation on how to do those things ?