One thing to watch out for is that the generators returned by
automorphism_group contain symbols that may not be the actual vertices. I
realised this once after several frustrating hours of bizarre results from my
program. I'm not sure if this is still the case in recent versions.
Emil
On 15 May 2012, at 00:04, Dima Pasechnik <dimp...@gmail.com> wrote:
>
>
> On Tuesday, 15 May 2012 01:02:46 UTC+2, Dima Pasechnik wrote:
>
>
> On Monday, 14 May 2012 16:57:40 UTC+2, Nathann Cohen wrote:
> Hellooooooo everybody !!!
>
> I would like to play with groups in Sage but I do not know how. I
> actually get my groups from a graph in the following way :
>
> sage: g = graphs.PetersenGraph()
> sage: ag = g.automorphism_group()
> sage: type(ag)
> <class
> 'sage.groups.perm_gps.permgroup.PermutationGroup_generic_with_category'>
>
> What I would like to do with this group is to consider it as a group
> action on my vertices and compute the orbits of some *sets* of
> vertices. Indeed, the method ag.orbits() would give me the list of all
> orbits of my vertices, but I would like to compute the orbit of a Set
> of vertices, that is all sets of the form "gg * my_set for gg in ag".
>
> Is there any way to achieve it with Sage ?
>
> Well, you can call GAP, e.g. as follows:
>
> sage: gap("Orbit("+str(ag._gap_())+",[1,2,7],OnSets);")
> [ [ 1, 2, 7 ], [ 1, 2, 3 ], [ 1, 6, 9 ], [ 2, 3, 4 ], [ 3, 4, 10 ],
> [ 1, 6, 8 ], [ 3, 4, 8 ], [ 4, 9, 10 ], [ 4, 7, 9 ], [ 5, 8, 10 ],
> [ 2, 5, 7 ], [ 5, 6, 8 ], [ 3, 5, 8 ], [ 4, 6, 9 ], [ 5, 7, 10 ],
> [ 5, 7, 9 ], [ 6, 7, 9 ], [ 3, 6, 8 ], [ 1, 6, 10 ], [ 2, 7, 9 ],
> [ 1, 2, 10 ], [ 2, 3, 8 ], [ 6, 8, 9 ], [ 1, 5, 10 ], [ 2, 3, 7 ],
> [ 1, 4, 10 ], [ 5, 7, 8 ], [ 3, 4, 9 ], [ 4, 5, 10 ], [ 1, 2, 6 ] ]
> sage:
>
> PS. it should not be hard to expand the ag.orbit method to incorporate the
> action type...
>
>
>
> Thaank youuuuuuuuuuuuuuuuuuuuuuuuuu !!!!
>
> Nathann
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