> < ^ Date: Tue, 20 Sep 1994 14:30:00 +0000 (GMT)
> < ^ From: Chris Wensley <c.d.wensley@bangor.ac.uk >
> ^ Subject: MapByFunction

Dear GAP Forum

It seems reasonable to hope that  MappingByFunction  can be used
inside a loop to produce a list of homomorphisms.  However, it
appears that the definition of  f(x)  may depend only on  x  and
constants, and not the loop variable or associated parameters.
Is there a way round this?
The following listing illustrates the problem.
----------------------------------------------------------------
gap> c6 := Group( (1,2,3,4,5,6) );;
gap> c6.name := "c6";;
gap> pow := 0 * [1..6];;
gap> for i in [1..6] do pow[i] := MappingByFunction( c6, c6, x->x^i ); od;
gap> pow;
[ MappingByFunction( c6, c6, function ( x )
return x ^ i;
|
|  (6 times --- all using  "i")
|
end ), MappingByFunction( c6, c6, function ( x )
return x ^ i;
end ) ]
gap> g:=(1,2,3,4,5,6);;
gap> for i in [1..6] do Print( g^pow[i],", "); od; Print("\n");
(1,2,3,4,5,6), (1,3,5)(2,4,6), (1,4)(2,5)(3,6), (1,5,3)(2,6,4),
(1,6,5,4,3,2), (),
gap> # Note: "i" now has value 6
gap> for j in [1..6] do Print( g^pow[j],", "); od; Print("\n");
(), (), (), (), (), (),
gap> LogTo();
---------------------------------------------------------------
Chris Wensley
University of Wales at Bangor
Email: mas023@bangor.ac.uk

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