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David Joyner wrote in his e-mail message of 1996/02/05

I hope I am not beating this poor AbStab.g horse/thread to death but I

still am having problems with the Shrink command which I cannot

resolve. I hope I am not wasting bandwidth but I would like to respond in

the hopes of clarifying the actual result which, to me, suggests that

Shrink might be the cause of the problem. (Though quite possibly I'm

wrong.)

'Shrink' is *definitely* not the cause of the problem. It does exactely

what it should be doing. This can be seen as follows. If you define

r1,r2,r3,r4,f1,f2,...,f8 as in your e-mail message of 1996/01/31, and set

g1:=r4;; g2:=r3;; g3:=r2;; g4:=f4;; g5:=f3;; g6:=f2;; g7:=r1;;

and then evaluate the word found by 'Shrink':

g1^-2*g5^-1*g1*g4^-1*g1*g4^-1*g1^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-3 *g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^2*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1 *g5^-1*g1^2*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^-4*g5^-1*g7 *g5^-1*g1*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^-2*g5^-1*g1^-1*g5^-1*g7*g5^-1 *g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7^4*g5^-1*g1*g5^-1*g7^-3*g5^-1 *g1^-1*g5^-1*g7*g5^-1*g1^2*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^3*g5^-1*g1 *g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1;

You get the 2-cycle '(1,2)' (I just did it by cutting and pasting

everything into a GAP, and yes it worked). I also get '(1,2)'

when I evaluate the long word found by 'FactorPermGroupElement'.

If evaluating this word in Maple does not give '(1,2)' (or whatever

represents the 2-cycle in your Maple model), then there must be a

difference between the GAP and the Maple model.

Martin.

-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany

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