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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