[GAP Forum] Fast Orbit Computation for Custom Objects?

[Sven Reichard]

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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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