Hi Dan! On Tue, Dec 22, 2009 at 02:54:08PM -0800, Daniel Bump wrote: > I was unable to get a working combinat queue. With sage-4.3.alpha1 > I get errors in trac_7420-fix-infinite-coercion-discovery-loop.patch.
Oops. Hopeful the guards are fixed now. > I did however make a trac ticket: > > http://trac.sagemath.org/sage_trac/attachment/ticket/7751/ > > There are quite a few changes from yesterday. I took your advice and > made a class for Kazhdan Lusztig polynomials, with methods for the > R and P polynomials. I also added a trace feature, so that you > can follow the function calls. Try > > sage: R.<q>=QQ[] > sage: W = WeylGroup("F4", prefix = "s") > sage: [s1,s2,s3,s4]=W.simple_reflections() > sage: KL = KazhdanLusztigPolynomial(W,q,trace=true) > sage: KL.P(s4,s1*s2*s3*s4*s3*s2) What about using verbose? I don't know if this is usable right now, though. That's typically one place where we might need fine grained verbosity, as discussed last October on sage-devel. > If you omit the cache=true, it takes 50 seconds to compute this > polynomial. (However coxeter3 gives it instantly.) But speed is > much better than yesterday. I found a good speedup by caching > reduced words for Weyl group elements. I think it's 3 or 4 > times faster now. Could you give it a shot at caching first_descent instead? It should take less memory, and I expect the overhead of computing the reduced word from first_descent to be largely compensated by the extra gains coming from all the other spots where first_descent is used (with Bruhat order calculations in the first place). > At the moment I don't have it working for anything but > finite Weyl groups. > > I added a method to produce the reflections of the Weyl group. > This is implemented for finite Weyl groups only. The reflections > (i.e. conjugates of the simple reflections) are in bijection > witht he positive roots, and sometimes you want to know the > corresponding elements, so this returns a dictionary: > > sage: W = WeylGroup("A3", prefix = "s") > sage: W.reflections() > > {s1*s2*s3*s2*s1: (1, 0, 0, -1), > s1*s2*s1: (1, 0, -1, 0), > s1: (1, -1, 0, 0), > s2*s3*s2: (0, 1, 0, -1), > s2: (0, 1, -1, 0), > s3: (0, 0, 1, -1)} Very good. This was a long desired feature. You may want to use the method self.from_morphism as is done in simple_reflections: ... self.from_morphism(self.lattice().simple_reflection(i)) ... > I added a method to produce the Bruhat graph. This is a > graph structure on the Bruhat interval {t | u <= t <= v} > in which x and y are adjacent if x y^(-1) is a reflection. > (Introduced I think by Carrell and Peterson but inspired by > Deodhar.) So you can: > > sage: W = WeylGroup("A3",prefix="s") > sage: [s1,s2,s3] = W.simple_reflections() > sage: W.bruhat_graph(s1*s3,s2*s1*s2*s3*s2).plot() > sage: W.bruhat_graph(s1*s3,s2*s1*s2*s3*s2*s1).plot() Ok. > > > (1) The algorithms should be moved to coxeter_groups.py. > > > They are applicable to arbitrary coxeter groups. > > > I put them in weyl_groups.py because I'm more familiar > > > with that file and wanted to get a fast prototype. > > > > Ok. I can't promise to work on this shortly, so I'd suggest you give > > it a shot yourself. It's mostly a question of putting the methods for > > the parent in ParentMethods, and the methods for the elements in > > ElementMethods in the CoxeterGroups class (leaving for the moment the > > option handling to the constructor of WeylGroup). > > I will try to do this but it may not be until after Christmas. Sure! Merry Christmas! 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 post to this group, send email to sage-combinat-de...@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.
