On Thursday, December 6, 2012 at 12:47:53 PM UTC, Dima Pasechnik wrote: > > On 2012-12-06, Nicolas M. Thiery <nicolas.thi...@u-psud.fr> wrote: > > On Thu, Dec 06, 2012 at 07:29:57AM +0000, Dima Pasechnik wrote: > >> I wonder if one can actually work in the endomorphism ring/algebra of a > >> CombinatorialFreeModule, and if yes, how. > > > > Not yet. I guess the closest approximation would be to take V \otimes V. > > But of course it is not endowed with composition, and it should really > > be V^* \otimes V (which makes a difference in non finite dimension). > > > >> Examples most appreciated. (Ideally, I would like to know how to > >> work with algebras specified by multiplication coefficients in this > >> framework) > > > > I am not sure what you mean. Can you be a bit more specific? > say, I have a permutation group acting on the basis elements of a > CombinatorialFreeModule, and I want to get hold of the endomorphisms > commuting with this action. Then it would be natural to represent > the ring of such endomorphisms by the multiplication coefficients. > (i.e. construct a regular representation of this ring). > > Another canonical example of "natural" regular representations is the quotient of a polynomial ring over a 0-dimensional ideal. Frankly, it is astonishing that given all the amount of stuff one can do with "combinatorial algebras", this is overlooked; this is perhaps the most basic example of use of linear algebra in computational algebraic geometry, after all.
https://groups.google.com/d/msg/sage-support/6Gprakjj1xQ/42E0LYfTBQAJ > Best, > Dima > > > > > > Cheers, > > Nicolas > > -- > > Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> > > http://Nicolas.Thiery.name/ > > > > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/d/optout.
