[GAP Forum] Finding a representative which moves fewest points

Warwick Harvey wh at icparc.ic.ac.uk
Thu Apr 1 00:37:29 BST 2004

Dear GAP Forum,

I am a relative novice when it comes to GAP and group theory, so please
excuse me if I've missed something obvious.

What I would like is a function like RepresentativeAction which returns a
representative that moves as few points as possible.  Taking the example
from the manual:

gap> g:=Group((1,3,2),(2,4,3));;
gap> RepresentativeAction(g,1,3);

I would like instead the element (1,3,2), since this only moves 3 points
rather than 4.  I tried constructing cosets of the stabilizer of 1 and using
RepresentativeSmallest on the appropriate coset, but of course the notion of
smallest there is not what I want.

I have an algorithm in mind that I could use to construct a representative
of the form I desire, but don't want to re-invent the wheel if there's
already an easy way to do it.

Thanks for any tips.


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