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############################################################################
##
#W cat1-more.g XMODALG example files Zekeriya Arvasi
#W & Alper Odabas
#Y Copyright (C) 2014-2024, Zekeriya Arvasi & Alper Odabas,
##
Print("\nXModAlg test file cat1-more.g :-");
Print("\ntesting constructions of cat1-algebras\n\n");
LoadPackage( "xmodalg" );
A := GroupRing( GF(2), Group((1,2,3)(4,5)) );
SetName( A, "GF(2)[c6]" );
R := GroupRing( GF(2), Group( (1,2,3) ) );
SetName( R, "GF(2)[c3]" );
f := AllAlgebraHomomorphisms( A, R );
g := AllAlgebraHomomorphisms( R, A );
C4 := PreCat1AlgebraObj( f[6], f[6], g[8] );
IsCat1Algebra( C4 );
Size2d( C4 );
Dimension( C4 );
Display( C4 );
C2 := Cat1AlgebraSelect( 4, 6, 2, 2 );
Size2d( C2 );
Dimension(C2);
Display( C2 );
C := Cat1AlgebraSelect(11);
C := Cat1AlgebraSelect(4,12);
C := Cat1AlgebraSelect(2,6,3);
C := Cat1AlgebraSelect(2,6,2);
C3 := Cat1AlgebraSelect( 2, 6, 2, 4 );;
A3 := Source( C3 );
B3 := Range( C3 );
eA3 := Elements( A3 );;
eB3 := Elements( B3 );;
AA3 := Subalgebra( A3, [ eA3[1], eA3[2], eA3[3] ] );
[ Size(A3), Size(AA3) ];
BB3 := Subalgebra( B3, [ eB3[1], eB3[2] ] );
[ Size(B3), Size(BB3) ];
CC3 := SubCat1Algebra( C3, AA3, BB3 );
Display( CC3 );
C4 := Cat1AlgebraSelect( 2, 1, 1, 1 );
G := SmallGroup(4,2);
F := GaloisField(4);
R := GroupRing( F, G );
Size(R);
SetName( R, "GF(2^2)[k4]" );
e5 := Elements(R)[5];
S := Subalgebra( R, [e5] );
SetName( S, "<e5>" );
## the following may be included once AlgebraAction2 has been fixed
## RS := Cartesian( R, S );;
## SetName( RS, "GF(2^2)[k4] x <e5>" );
## act := AlgebraAction( R, RS, S );;
## bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );
## IsAlgebraAction( act );
## IsAlgebraHomomorphism( bdy );
## XM := PreXModAlgebraByBoundaryAndAction( bdy, act );
## CXM := Cat1AlgebraByXModAlgebra( XM );
## Display(CXM);
## X3 := XModAlgebraByCat1Algebra( C3 );
## Display( X3 );
#############################################################################
##
#E cat1-more.g . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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