[sage-support] Groups and representation of an element
Hi,
My question is the following, I have a permutation group defined by
generators, g_1,..,g_n
So if these elements are in a list (lets call it L)
then I can do
S=PermutationGroup(L)
and I can check if a permutation g is in the group, just writting
g in S
Fine, but in the case that g is in S, how to find a representation of g
using the generators? i.e.,
g=g_{i_1}*...*g_{i_n}
I know the Schreier-Sims algorithm, which gives the membership of g, but
the combinations is given in terms of transversals (which you don't know
their
representation) and stabilizers.
Trying to save the representation of each of the generators of the
stabilizers
and the transversals is very slow and memory consuming compare with just
g in S.
Also, search algorithms like A* are not an option.
Is there any better way to check?
Thank you in advance for your time
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Re: [sage-support] Groups and representation of an element
On Sun, Oct 14, 2012 at 10:39 AM, domingo.domingogo...@gmail.com
wrote:
> Hi,
> My question is the following, I have a permutation group defined by
> generators, g_1,..,g_n
>
> So if these elements are in a list (lets call it L)
> then I can do
> S=PermutationGroup(L)
>
> and I can check if a permutation g is in the group, just writting
>
> g in S
>
> Fine, but in the case that g is in S, how to find a representation of g
> using the generators? i.e.,
>
> g=g_{i_1}*...*g_{i_n}
>
> I know the Schreier-Sims algorithm, which gives the membership of g, but
> the combinations is given in terms of transversals (which you don't know
> their
> representation) and stabilizers.
>
> Trying to save the representation of each of the generators of the
> stabilizers
> and the transversals is very slow and memory consuming compare with just
> g in S.
>
> Also, search algorithms like A* are not an option.
>
> Is there any better way to check?
The word problem method is described with examples at
http://www.sagemath.org/doc/reference/sage/groups/perm_gps/permgroup_element.html
>
> Thank you in advance for your time
>
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>
>
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Re: [sage-support] Groups and representation of an element
Thank you very much! Sorry, it was really clear. I didn't know the technical name. Best regards, Domingo -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
