[GAP Forum] Re: S4 Symmerty

[yonggukim]

Dear Professor Alexander Hulpke:

Thank you very much for your help. I ran GAP following your instruction,
and the first reply was like this:

exceeded the permitted memory (`-o' command line option) at
l := Length( arg );
 called from
List( e, function ( i )
      return OnSets( i, g );
  end ) called from
act( p, gen ) called from
OrbitOp( G, D[1], gens, acts, act ) called from
op( G, D, gens, gens, act ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk>

Here the data file had sets of 4-elemenet sets with various sizes.
As a data file, I then chose sets of 4-elements sets with a fixed size.
Then I got just too many orbits. What is wrong?
Is there a command to compute the number of orbits?

Sincerely,
YGK

On Tue, 12 Jul 2005, Alexander Hulpke wrote:

> Dear GAP-forum,
>
> A user wrote:
>
> >
> > I am not a GAP expert. I have a data file containing a collections of
> > point sets, for instance,
> > {{1,2,3,4},{0,2,3,4}}
> > {{0,2,3,6},{0,1,3,6}}
> > ...
> > Here a permutation of 0,1,2,3 determines the action on the other
> > points
> > too. I would like to look those collections of sets which are not
> > related by the
> > permutation group S4. How can I do it using GAP?
> >
>
> I interpret your question that you have a group and want to get
> representatives of the orbits.
>
> First, permutation groups in GAP do not act on 0 -- it is probably
> easiest to use an editor to replace 0 by a number that is not used,
> say 9.
>
> The second thing you will have to do is to convert your objects into
> GAP-objects (in an editor):
>
> objects:=[
> [[1,2,3,4],[9,2,3,4]],
> [[9,2,3,6],[9,1,3,6]],
>
> and so on
> ];
> Read this file into GAP.
>
> Next we want to convert the objects into sets of sets. This means
> every inner and outer list must be sorted. Probably the easiest way
> to do this is:
>
> objects:=List(objects,i->Set(List(i,Set)));
>
> Now create the group (be careful that 0 again has to be translated.
> e.g. if you had S4 on the points 0,1,2,3, you would make with our 9
> translation:
>
> G:=Group((9,1,2,3),(9,1));
>
> Then you can compute orbits, picking one element each gives you
> representatives.
>
> orb:=Orbits(G,objects,OnSetsSets);
> List(orb,i->i[1]);
>
> Best,
>
>      Alexander Hulpke
>
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