Hi Sébastien!
On Thu, Jun 25, 2009 at 03:06:15PM -0700, slabbe wrote:
> This weekend I was introducing Sage to a friend. To illustrate Jmol, I
> showed him some 3d Cayley graphs of some finite groups :
>
> {{{
> sage: S = SymmetricGroup(4)
> sage: S.cayley_graph()
> Digraph on 24 vertices
> }}}
>
> Then, he asked me to show the Cayley graph of some groups he often
> works with :
>
> {{{
> sage: g = GL(2,GF(3)); g
> General Linear Group of degree 2 over Finite Field of size 3
> sage: g.order()
> 48
> sage: g.cayley_graph()
> Traceback (most recent call last):
> ...
> AttributeError: 'GeneralLinearGroup_finite_field' object has no
> attribute 'cayley_graph'
> }}}
>
>
> {{{
> sage: G = WeylGroup(['D',4])
> sage: G
> Weyl Group of type ['D', 4] (as a matrix group acting on the ambient
> space)
> sage: G.order()
> 192
> sage: G.cayley_graph()
> Traceback (most recent call last):
> ...
> AttributeError: 'WeylGroup_gens' object has no attribute
> 'cayley_graph'
> }}}
>
> The reason is that cayley_graph is implemented in the class
> sage.groups.group.FiniteGroup but both WeylGroup_gens and
> MatrixGroup_gap_finite_field inherits only from
> sage.groups.group.Group.
>
> I already begun a patch available in the sage-combinat tree. Mainly,
> the changes are :
>
> -class MatrixGroup_gap_finite_field(MatrixGroup_gap):
> +class MatrixGroup_gap_finite_field(MatrixGroup_gap, FiniteGroup):
>
> -class WeylGroup_gens(ClearCacheOnPickle, UniqueRepresentation,
> MatrixGroup_gens):
> +class WeylGroup_gens(ClearCacheOnPickle, UniqueRepresentation,
> MatrixGroup_gens, FiniteGroup):
>
> My question is the following : Am I right to assume that both
> WeylGroup_gens and MatrixGroup_gap_finite_field are always finite?
MatrixGroup_gap_finite_field, yes, I think so.
But for WeylGroup not necessarily: this also is used to build affine
Weyl groups which are infinite. On the other hand the upcoming root
system patch puts Weyl groups in the appropriate category:
FiniteWeylGroups() or AffineWeylGroups() or ... That's one of the
point of the category stuff: to be able to customize the inheritance
at run time depending on the properties of the parent one is
constructing.
That's not the complete end of the story though, since Cayley graphs
are currently implemented at two spots:
- Once in the abstract class FiniteGroup
- Once in the category FiniteSemigroups
This remains to be cleaned up, by merging the two implementations into
the FiniteSemigroups category. If I recall correctly, there are couple
things one wants to do differently for finite groups, so probably the
(yet to be created) category FiniteGroups will need to further
override/customize the Cayley graph method.
Do you feel like doing it? That would be great!
Cheers, Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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