> On Wednesday 22 October 2008, Mike Hansen wrote: > > Nicolas Thiery mentioned that F5 works for a class non-commutative > > rings so that might be a reason for including it. > > I don't see why F5 would be better suited for non-commutative rings than the > Buchberger (except for speed of course). The free algebras need quite some > attention and I agree that some way of computing Gröbner bases in them is > desired.
The class I mentioned to Mike was skew-commutative algebras. I once upon a time implemented a toy^3 F5 in MuPAD, in order to compute a Gröbner basis for an ideal generated by a certain regular sequence of homogeneous elements in the Weyl algebra (and in other related ORE-algebras). Having no zero reductions was appealing (and it was a good occasion to understand the principle of F5). For whatever its worth (probably nothing, except maybe the invariants), see line 1274- in: http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk/MuPAD-Combinat/lib/EXPERIMENTAL/Steenrod.mu, Oops, I don't even mention its F5 there ... The core idea behind F5 is pretty simple, which makes all its beauty! (I am not speaking about the advanced ideas for an efficient implementation which are way out of my competence). Having a toy implementation in Sage which displays how it can work in full generality (e.g. modules over a skew commutative polynomial ring) could be a nice pedagogical tool. All the best, Nicolas -- Nicolas M. Thiéry "Isil" <[EMAIL PROTECTED]> http://Nicolas.Thiery.name/ --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
