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.
> See http://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! 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.
> 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.
> > - 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.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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