#19438: generators given by as_permutation_group in the wrong order
-------------------------------------+-------------------------------------
Reporter: pguillot | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.10
Component: group theory | Resolution:
Keywords: permutation | Merged in:
groups | Reviewers: Frédéric Chapoton,
Authors: Pierre Guillot | Dima Pasechnik
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pguillot/ticket_19438 | ffeb721ce7a670888acd2f396d806d1a5f04ea28
Dependencies: | Stopgaps:
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Comment (by pguillot):
> {{{
> sage:
PermutationGroup([[2,3,1],[3,1,2],[2,1,3],[3,2,1],[1,3,2],[2,3,1]])
> Permutation Group with generators [(2,3), (1,2), (1,2,3), (1,3,2),
(1,3)]
> }}}
Precisely, here canonicalize=True is assumed. Adding canonicalize= False
forces it to return the same generators, literally, yes.
I had assumed that canonicalize= False actually ''reduced'' the time
needed for the computation, since it simply does a little less. This is
confirmed by
(a) looking at the code for the class PermutationGroup_generic, which has
{{{
if canonicalize:
gens = sorted(set(gens))
}}}
and as far as I can tell, this is the one and only place where the flag is
used.
(b) When using GAP directly, if you try
{{{
G:= Group([(1,2,3), (1,3,2), (1,2), (1,3), (2,3), (1,2,3)]);
GeneratorsOfGroup(G);
}}}
then you get
{{{
[ (1,2,3), (1,3,2), (1,2), (1,3), (2,3), (1,2,3) ]
}}}
that is, they are kept in the same order ''by default.''
> It doesn't matter so much how the permutation group is represented, as
long as the isomorphism to the permutation group is given.
It would be best to just return the isomorphism itself (that is what GAP
does), yes. I'm not sure that Sage has anything on group homomorphisms,
though.
--
Ticket URL: <http://trac.sagemath.org/ticket/19438#comment:12>
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