On Fri, May 31, 2013 at 03:20:48PM -0400, Mark Shimozono wrote: > Ooh, I can see implementation issues. > They center around evaluating an inverse morphism.
Yup, there certainly is no generic way of computing inverse morphisms. Only in certain categories is this guaranteed to be computable / efficient (or let me know: I could win a lot of money breaking cryptographic schemes with that :-) ). > This is related to the issue of coercing into Hom-sets: how does a category > uniquely and algorithmically specify a morphism from its values on > a subset of its domain? That can only be done on a category-by-category bases, if not parent-by-parent. Namely each parent must provide a way to express its elements in terms of the generators (otherwise said a section to a free object sitting above it). And then the category can explain generically how to compute morphisms specified by generators when the domain is a free object. There are premises of this in MuPAD-Combinat and Sage, but not yet blown to something systematic. > Happily, I just now realized that for the semidirect product G \ltimes N of > groups (equipped with > homomorphism f: G ---> Aut(N)) one can get away with using only the monoid > structure of Aut(N) ! :-) Cheers, Nicolas -- Nicolas M. ThiƩry "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 http://groups.google.com/group/sage-combinat-devel?hl=en. For more options, visit https://groups.google.com/groups/opt_out.