On 12/27/12 12:39 PM, Jernej Azarija wrote:
Hello!
I apologize for posting this question here but somehow I am not allowed
to drop questions to sage-support. Moreover I do not feel confident
enough to post this thing as a bug on the trac wiki.
Working with a large graph G on ~250 vertices I have noticed that
elements of the automorphism group of G permute ~50 vertices and that
most vertices are fixed by any automorphism. Hence most orbits of the
automorphism group contain just singletons. However sage simply discards
all vertices that are fixed by the automorphism . In my case this
resulted in an "incomplete" orbit containing just 50 elements. An
extreme case happens when one deals with an asymmetric graph
===
sage: G = graphs.RandomRegular(7,50)
sage: G.vertices()
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,
38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]
sage: G.automorphism_group().domain()
{1}
sage: G.automorphism_group().orbits()
[[1]]
===
This of course is not the desired result since one assumes orbits
partition the group.
Is this a bug or am I simply missing some parameter to resolve this issue?
Until we have proper support for this, you can do:
sage: g=Graph({'a': 'b', 'b': 'c'})
sage: p,q=g.automorphism_group(translation=True)
sage: pp=PermutationGroup(gap_group=p._gap_(), domain=sorted(q, key=q.get))
sage: pp
Permutation Group with generators [('c','a')]
(this also helps you see how to implement it...)
Unfortunately, there is a bug in the stabilizer method when the
permutation group has a custom domain, which is now fixed at
http://trac.sagemath.org/sage_trac/ticket/13893, which now needs review.
a workaround for the stabilizer bug is:
sage: pp.subgroup(gap_group=gap.Stabilizer(pp, pp._domain_to_gap['b']))
Subgroup of (Permutation Group with generators [('c','a')]) generated by
[('c','a')]
Thanks,
Jason
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