Hi there,
On Dec 3, 5:08 pm, Florent Hivert <florent.hiv...@univ-rouen.fr>
wrote:
> However, I thing it should be a method of the group:
> G.conjugacy_class(g).
that was my original idea, to keep it close to GAP original
definition.
> Or even of the element itself since it knows G as it's parent:
> g.conjugacy_class()
>
> def conjugacy_class(self):
> GG = self.parent()._gap_()
> gg = self._gap_()
> cc = GG.ConjugacyClass(gg).AsList().sage()
> return Set([G(x) for x in cc])
This also makes sense. I don't really know which choice would be
better. Maybe having both, doing something like
def conjugacy_class(self):
G = self.parent()
return G.conjugacy_class(g)
does that sound reasonable or would it be better to stick just to one
of them?
> And finally for those groups who are not known to gap, the fallback
> (sage-only) method should be in the category FiniteGroups to be inherited by
> any group.
I hadn't thought of that. Since all the groups I used are defined as
permutation groups I never ran into trouble, but now that you mention
it I see that GAP function doesn't work for matrix groups:
sage: F = GF(5)
sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: g = G(matrix(F,2,[1,2, -1, 1]))
sage: conjugacy_class_gap(g,G)
Traceback (most recent call last):
...
NotImplementedError
So I guess the right thing to do is something like
sage: def conjugacy_class(g,G):
... try: # Try to use GAP function if defined
... GG = G._gap_()
... gg = g._gap_()
... cc = GG.ConjugacyClass(gg).AsList().sage()
... return Set([G(x) for x in cc])
... except NotImplementedError: # If GAP doesn´t work, use
naive method
... return Set([x*g*x^(-1) for x in G])
maybe with some added checks to deal with abelian groups (trivial
conjugacy classes) and not using the naive method on infinite groups.
In which file should the code be included?
$SAGE_ROOT/devel/sage/sage/generic.py or somewhere else?
Cheers
Javier
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