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#############################################################################
##
#W convert.g XModAlg example files Z. Arvasi - A. Odabas
##
LoadPackage( "xmodalg" );
START_TEST( "XModAlg package: convert.tst" );
saved_infolevel_xmodalg := InfoLevel( InfoXModAlg );;
SetInfoLevel( InfoXModAlg, 0 );
## make convert.g independent of module.g, cat1.g and xmod.g
m3 := [ [0,1,0], [0,0,1], [1,0,0] ];;
A3 := Algebra( Rationals, [m3] );;
SetName( A3, "A3" );;
c3 := Group( (1,2,3) );;
Rc3 := GroupRing( Rationals, c3 );;
SetName( Rc3, "GR(c3)" );
g3 := GeneratorsOfAlgebra( Rc3 )[2];;
mg3 := RegularAlgebraMultiplier( Rc3, Rc3, g3 );;
Amg3 := AlgebraByGenerators( Rationals, [ mg3 ] );;
homg3 := AlgebraHomomorphismByImages( A3, Amg3, [ m3 ], [ mg3 ] );;
actg3 := AlgebraActionByHomomorphism( homg3, Rc3 );;
F5 := GF(5);;
id5 := One( F5 );;
two := Z(5);;
z5 := Zero( F5 );;
n0 := [ [id5,z5,z5], [z5,id5,z5], [z5,z5,id5] ];;
n1 := [ [z5,id5,two^3], [z5,z5,id5], [z5,z5,z5] ];;
n2 := [ [z5,z5,id5], [z5,z5,z5], [z5,z5,z5] ];;
An := Algebra( F5, [ n0, n1 ] );;
SetName( An, "An" );
Bn := Subalgebra( An, [ n1 ] );;
SetName( Bn, "Bn" );
Print( "IsIdeal( An, Bn )? ", IsIdeal( An, Bn ), "\n" );
actn := AlgebraActionByMultipliers( An, Bn, An );;
Xn := XModAlgebraByIdeal( An, Bn );
Display( Xn );
SetName( Xn, "Xn" );
############################
## Chapter 5, Section 5.1.1
Cn := Cat1AlgebraOfXModAlgebra( Xn );
Print( "Cn = Cat1AlgebraOfXModAlgebra( Xn ): ", Cn, "\n" );
Display( Cn );
bdy3 := AlgebraHomomorphismByImages( Rc3, A3, [ g3 ], [ m3 ] );;
X3 := XModAlgebraByBoundaryAndAction( bdy3, actg3 );;
C3 := Cat1AlgebraOfXModAlgebra( X3 );
Print( "\nC3 = Cat1AlgebraOfXModAlgebra( X3 ): ", C3, "\n" );
Display( C3 );
C6 := Cat1AlgebraSelect( 2, 6, 2, 4 );;
X6 := XModAlgebraOfCat1Algebra( C6 );
Print( "\nX6 = XModAlgebraOfCat1Algebra( C6 ):\n", X6, "\n" );
Display( X6 );
SetInfoLevel( InfoXModAlg, saved_infolevel_xmodalg );;
STOP_TEST( "convert.tst", 10000 );
############################################################################
##
#E convert.g . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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