Actually, I think that by calling "conjugacy_classes_representatives"
conjugacy classes are already computed, so didn't want to do all the
work twice. A possible improvement of the algorithm could be something
like this:
def conjugacy_classes(G):
classes = []
G_set = Set(G)
while len(G_set)!=0:
g = G_set[0]
cg = conjugacy_class(G,g)
classes.append(cg)
G_set = G_set.symmetric_difference(cg)
return Set(classes)
but since I am not a group theorist, I don't know if there is a better
algorithm out there, so I assumed that GAP function would be more
efficient than anything I could possibly come up with, that's why I
was asking if there was a native SAGE wrapping of it.
Concerning the math, I need the conjugacy classes as sets in order to
compute some invariants given by noncommutative geometry, where
bicovariant differential calculi over (the Hopf algebra of) finite
groups are in 1-1 correspondence with (unions of) conjugacy classes
satisfying certain properties. My hope is that the NC invariants yield
some information about the group itself, and am trying to compute a
number of examples to get some intuition on what's going on.
Anyway, I got first version of my program running and was able to
compute things for a dozen not-so-small groups without much trouble,
so I guess what I have might do the trick for now.
Thank you all for your help!
Cheers
Javier
On Apr 15, 9:04 pm, David Joyner <[email protected]> wrote:
> I don't see how conjugacyclass can be done more efficiently.
> Of course,
>
> def conjugacyclasses(group):
> return Set([conjugacyclass(group, g) for g in group])
>
> should really be
>
> def conjugacyclasses(group):
> reps = group.conjugacy_classes_representatives()
> return Set([conjugacyclass(group, g) for g in reps])
>
> But really even this is impossible to do fast for large groups.
> For computational problems involving permutation groups, my
> understanding was that you should generally try very hard to
> only deal with *representatives* of conjugacy classes, but
> the original question seemed to indicate he didn't want to use
> that command for some reason.
>
> Maybe I'm misunderstanding something?
>
>
>
> > - Robert
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