On Tuesday, March 22, 2011 1:34:44 AM UTC-7, Nicolas M. Thiéry wrote:
> > Is it already possible or would it be easy to implement a quotient > > of the free algebra by specifying relations between the generators? > > Unless Singular can provide something (but I guess that would be more > for skew-commutative algebras; Simon: can you confirm?), the proper > way to do this would be to use gap's KBMAG package. It should be > fairly straightforward, but not instantaneous either. > I don't know anything about KBMAG; I should look into that. Meanwhile, Singular does let you define certain quotients of free algebras. See <http://www.singular.uni-kl.de/Manual/3-1-0/sing_404.htm>. In Sage, I can define a GF(2)-algebra S to be the free algebra on x and y subject to the relation [x,y] = y^2: sage: singular.LIB('ncall.lib') sage: R=singular.ring(2,'(x,y)') sage: C = singular.matrix(2, 2, '(1,1,1,1)') sage: D = singular.matrix(2, 2, '(0, y*y, 0, 0)') sage: S = C.nc_algebra(D) sage: S.set_ring() sage: x = singular('x') sage: y = singular('y') sage: x*y x*y sage: y*x x*y+y^2 There are limitations on the sorts of algebras which can be defined this way -- I think they need to have a PBW basis, basically -- see <http://www.singular.uni-kl.de/Manual/3-1-0/sing_420.htm#SEC461> -- but Singular does give you some quotients of free algebras. -- John -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
