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. 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 http://groups.google.com/group/sage-combinat-devel?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
