On Apr 8, 3:12 pm, "Nicolas M. Thiery" <nicolas.thi...@u-psud.fr> wrote:
> Hi Dima! > On Thu, Apr 07, 2011 at 10:55:32PM -0700, Dima Pasechnik wrote: > > > - is there a Sage implementation of permutation groups, or only the > > > gap implementation (it takes very long to go through the elements of a > > > permutation group, even in small examples)? > > Could you provide an example? > > GAP is very quick in enumerating the elements of a permutation group > > (it has a highly optimized code written in C to do the sorts of things > > related to permutation groups) – it might take a long time to send > > these > > elements to Sage, currently. > > This is actually due to an inefficiency in recent Linux kernels (e.g. > > ones distributed with Debian and > > Ubuntu). > > There is an ongoing project to speed this up in a serious way, so > > circumvent the use of IPC by creating a libGAP. > > Seehttp://trac.sagemath.org/sage_trac/ticket/6391 > > You are welcome to try helping with it if you have time. > I have been following that from a bit far away. Thanks so much for > your hard work on this; it will be a great improvement! that's mainly Willam and Volker who did the good work, I just chased down one particularly tricky thing... > Please specify > on the ticket when one can start trying it out relatively safely, and > my student Nicolas and myself will put it to work and stress. well, you can start trying it out - it's not going to format your hard disk :-) > > On the other hand, it could be the case that enumerating all the > > group elements is not implemented very efficiently, as this is not > > what one would ever do! Why would you need such a feature, except > > for teaching purposes? > We actually need that very often for research :-) Typically to > calculate some combinatorial statistics on a Coxeter group W, or to do > calculations in the group algebra. I for myself am studying a monoid > whose elements are functions from W to W. So W is fairly small w.r.t > the monoid, and I start by enumerating elements of W. I'd imagine one might use an iterator (GAP has such a feature, see Iterator) over a group then, rather than enumerating elements... Well, needless to say, enumerating elements of S_n is a trivial and fast task, and same applies to many "combinatorial" subgroups of S_n, e.g. to Young symmetrisers. > > > - there are several things not working for finite reflection groups > > > due to problems with matrices over the UCF (e.g., > > > reflecting_hyperplanes due to the fact that I cannot compute the > > > kernel of a matrix). > > UCF? > Universal Cyclotomic Field. That's Sage's implementation by Christian > of GAP's E(n,k) and arithmetic using the Zumbroich Basis. Well, do your computations in GAP then... (i.e. just do gap("blah; blah;") and then get the result back) Dima > Cheers, > Nicolas > -- > Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>http://Nicolas.Thiery.name/ -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
