Group action

[Nathann Cohen]

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 ?

Thaank youuuuuuuuuuuuuuuuuuuuuuuuuu !!!!

Nathann

[David Joyner]

The short answer is yes, if you use GAP. The problem is that I don't
know the syntax for group actions in GAP well enough to give you a
beter answer quickly. If you post a specific question to GAP support, I think
it would be answered immediately.


>
> Thaank youuuuuuuuuuuuuuuuuuuuuuuuuu !!!!
>
> Nathann
>
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[Dima Pasechnik]

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: 

 

Thaank youuuuuuuuuuuuuuuuuuuuuuuuuu !!!!

Nathann

[Dima Pasechnik]

PS. it should not be hard to expand the ag.orbit method to incorporate the action type...

 

Thaank youuuuuuuuuuuuuuuuuuuuuuuuuu !!!!

Nathann

[Emil]

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

--

[Nathann Cohen]

> 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.

Yep. I wasted 30 minutes easily on that one too. Actually the elements
are always 1...n regardless of the graph's labelling (which often
starts at 0). That's a shame.

Nathann

[Mike Hansen]

This is because permutation groups used to not support arbitrary
domains. Since they do now, it should be easy to return an
automorphism group that actually acts on the vertices.

--Mike

[Nathann Cohen]

> 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 ] ]

THaaaaaaaank you Dima !! I finally got it to work thanks to you....
Too me some time to find out that Gap would return a totally weird
error message if the list you give as an argument is not sorted, and I
guess most of the time it takes to run the computation is devoted to
translating Gap object to Sage ones afterwards, but.... It works !!
;-))))

(But Gap definitely has the worst syntax ever)

Nathann

[Dima Pasechnik]

On Tuesday, 15 May 2012 09:54:15 UTC+2, Nathann Cohen wrote:

> 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 ] ]

THaaaaaaaank you Dima !! I finally got it to work thanks to you....
Too me some time to find out that Gap would return a totally weird
error message if the list you give as an argument is not sorted, and I
guess most of the time it takes to run the computation is devoted to

IMHO most of the time is spent on IPC, via pexpect...

[Nathann Cohen]

> IMHO most of the time is spent on IPC, via pexpect...

Oh, *THAT* is pexpect ? Then I guess I begin to understand why there
was so much fuss about it being slow some time ago ^^;

Nathann