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Dear Forum,

I suggest the following default strategy for calculating

RepresentativeOperation(G,x,y,action);

The idea is to build up two partial Schreier trees Tx, Ty (w.r.t.

G.generators), rooted at x and y, respectively. One alternately

adds nodes to Tx and Ty until they have a node z, say, in common (if

one of the trees is completed and there is no such node then return

false). Given such a z, one uses Tx,Ty in the usual way to

get elements gx,gy such that z=action(x,gx)=action(y,gy),

and so the required element taking x to y is gx/gy.

If x and y are in the same G-orbit, then this approach should be

much faster than computing an orbit for x until y is found, and

much much faster than trying to compute a StabChain if the action is

OnPoints.

Regards, Leonard Soicher.

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