On 2012-12-20, Anton Sherwood <anton.sherw...@gmail.com> wrote: > I have a project in mind that involves the symmetry groups of the > regular four-dimensional polytopes. > I'm told that enumeration of a group from its generators is a > by-product of the Todd-Coxeter algorithm. > Unfortunately, I can't make sense of Wikipedia's description of TC, > nor of the one implementation of it that I've seen (in C++; > jenn3d.org). > > I hope that this is not the wrong place to ask, and that one of you > can point me to an implementation of Todd-Coxeter in Sage or Python > (Sage preferred, as I'd like to have the square roots handled > algebraically rather than numerically) -- or, as long as I'm wishing, > a list of the 14400 isometry matrices of the [5,3,3] group.
You can use GAP (and Sage's interface to GAP) for the task to run TC. Note that TC will return you a permutation representation, and not the one you are interested in. But this is beside the point, for you can produce the list much easier: 1) create the Coxeter reflections corresponding to the 4 generators of the [5,3,3] group. 2) list the elements of the group the generate using Sage. (Sage has MatrixGroup functionality; if this does not work, you can use GAP and if you need get the results into Sage). HTH, Dmitrii -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
