File: mgmring.tst

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#############################################################################
##
#W  mgmring.tst                 GAP library                     Thomas Breuer
##
#H  @(#)$Id: mgmring.tst,v 4.7.4.4 2005/08/29 14:50:35 gap Exp $
##
#Y  Copyright (C)  1997,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
##
##  To be listed in testall.g
##

gap> START_TEST("$Id: mgmring.tst,v 4.7.4.4 2005/08/29 14:50:35 gap Exp $");

gap> r:= GF(3);;
gap> m:= Group( (1,2,3), (1,2) );;
gap> rm:= FreeMagmaRing( r, m );
<algebra-with-one over GF(3), with 2 generators>

gap> ElementOfMagmaRing( ElementsFamily( FamilyObj( rm ) ), 0*Z(3),
>    [ 0, 1, 1, 1, -1, 1, -1 ]*Z(3)^0,
>    [ (), (2,3), (1,2,3), (2,3), (1,2), (1,2), (1,3,2) ] );
(Z(3))*(2,3)+(Z(3)^0)*(1,2,3)+(Z(3))*(1,3,2)

gap> IsGroupRing( rm );
true
gap> centre:= Centre( rm );
<algebra-with-one of dimension 3 over GF(3)>
gap> GeneratorsOfAlgebra( centre );
[ (Z(3)^0)*(), (Z(3)^0)*(), (Z(3)^0)*(2,3)+(Z(3)^0)*(1,2)+(Z(3)^0)*(1,3),
  (Z(3)^0)*(1,2,3)+(Z(3)^0)*(1,3,2) ]

gap> membrm:= Embedding( m, rm );;
gap> img:= Image( membrm, (1,2) );
(Z(3)^0)*(1,2)
gap> PreImagesRepresentative( membrm, img );
(1,2)
gap> rembrm:= Embedding( r, rm );;
gap> img:= Image( rembrm, Z(3) );
(Z(3))*()
gap> PreImagesRepresentative( rembrm, img );
Z(3)

gap> STOP_TEST( "mgmring.tst", 17400000 );


#############################################################################
##
#E