> < ^ Date: Wed, 13 Jun 2001 15:23:54 +0100 (BST)
> < ^ From: Leonard Soicher <l.h.soicher@qmul.ac.uk >
> < ^ Subject: Re: Question on appropriateness of GAP for solving a particular problem

Dear Forum,

Pamb <pamb@mathematik.uni-wuerzburg.de> wrote:

I have a set S with 30 elements, together with a symmetric binary relation R, which
holds between some of the elements of S. I would like to find out all the
permutations of S which preserve the relation R, in the following precise sense
f: S to S, f bijection satisfying "a R b if and only if f(a) R f(b)".

Is there any program in GAP that would allow me to do that?

The GAP share package GRAPE can do this using nauty (so GRAPE must be
fully installed on a UNIX system).

First, use the GRAPE function `Graph' to define a GRAPE graph with
vertex-set S and with [a,b] an edge iff aRb. See the documentation.
For example, after defining S and R appropriately, you will enter
something like:
gamma:=Graph(Group(()),S,function(x,g) return x; end,R,true);

Then the permutations you require form a group, which is the
automorphism group of your graph gamma. This group is calculated by

-Leonard Soicher.

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