Hi all, > Jean Michel wrote: > >> The list of inversions, in my view, should preferably be a list >> of reflections (which does not need the existence of roots and makes >> sense for abstract Coxeter groups).
Indeed, in trac_12774-coxeter-ms.patch, there is already a Coxeter group element method which returns inversions in reflection form: sage: W = WeylGroup(['A',2],prefix="s") sage: w = W.from_reduced_word([1,2,1]) sage: w.length_decreasing_reflections_right() [s1, s1*s2*s1, s2] If everyone hates the name, let me know and I'll change it. > It seems to me that inversions could have a switch such > that it returns either the positive root or the corresponding > reflection. (The second could be valid in an arbitrary Coxeter > group.) > > In other words, something like this: > > sage: w.inversions() > [alpha[1], alpha[1] + alpha[2], alpha[2]] > > sage: w.inversions(reflections=True) > [s1,s1*s2*s1,s2] I'm a little leery of calling the above Coxeter group method "inversions" and simultaneously giving the Weyl group inversions method the option of returning reflections in addition to (co)roots, as there would then be two different ways of getting the reflections. But I aim to please. Chime in, whoever cares! --Mark -- 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.
