[GAP Forum] Fast Orbit Computation for Custom Objects?

[Attila Egri-Nagy]

Dear Sven,

Most probably the orb package is what you need:
http://www.gap-system.org/Packages/orb.html

best,
attila

On Fri, May 17, 2013 at 6:53 PM, Sven Reichard
<Sven.Reichard at tu-dresden.de> wrote:
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> Dear Forum,
>
> I have the following data:
> - - A permutation group G;
> - - a set of objects obj;
> - - an action function.
>
> I would like to get the following:
> - - The union D of the orbits of obj under G (not necessarily sorted);
> - - the action H of G on D;
> - - orbit representatives.
>
> What I do is the following:
>
> orbits := Orbits(G, obj, action);
> representatives := List(orbits, Representative);
> D := Union(orbits); # sorted to accelerate the next step
> H := Action(G, D, action);
>
> This works well when action is a standard action such as OnSetsSets.
> However, for custom actions this can be very slow, suggesting that
> different algorithms are used. (In some of my examples, D has a
> million elements.)
>
> Is there a way in GAP4 to accelerate this process, for example by
> providing hash functions? In GAP3 there existed a solution in the
> contributed file coco.grp by Theißen based on work by Faradzev et al.
> The question is whether there is a better way than porting that file
> to GAP4.
>
> Regards,
> Sven Reichard.
>
> - --
>
> Institut für Algebra
> TU Dresden
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