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# LinearAlgebraForCAP, single 7
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("linearalgebraforcap07.tst");
# doc/_Chapter_Examples_and_Tests.xml:281-322
gap> LoadPackage( "LinearAlgebraForCAP", false );
true
gap> ring := HomalgFieldOfRationals( );;
gap> vec := MatrixCategory( ring );;
gap> F := CapFunctor( "CohomForVec", [ vec, [ vec, true ] ], vec );;
gap> obj_func := function( A, B ) return TensorProductOnObjects( A, DualOnObjects( B ) ); end;;
gap> mor_func := function( source, alpha, beta, range ) return TensorProductOnMorphismsWithGivenTensorProducts( source, alpha, DualOnMorphisms( beta ), range ); end;;
gap> AddObjectFunction( F, obj_func );;
gap> AddMorphismFunction( F, mor_func );;
gap> Display( InputSignature( F ) );
[ [ Category of matrices over Q, false ], [ Category of matrices over Q, true ] ]
gap> V1 := TensorUnit( vec );;
gap> V3 := DirectSum( V1, V1, V1 );;
gap> pi1 := ProjectionInFactorOfDirectSum( [ V1, V1 ], 1 );;
gap> pi2 := ProjectionInFactorOfDirectSum( [ V3, V1 ], 1 );;
gap> value1 := ApplyFunctor( F, pi1, pi2 );;
gap> input := ProductCategoryMorphism( SourceOfFunctor( F ), [ pi1, Opposite( pi2 ) ] );;
gap> value2 := ApplyFunctor( F, input );;
gap> IsCongruentForMorphisms( value1, value2 );
true
gap> InstallFunctor( F, "F_installation" );;
gap> F_installation( pi1, pi2 );;
gap> F_installation( input );;
gap> F_installationOnObjects( V1, V1 );;
gap> F_installationOnObjects( ProductCategoryObject( SourceOfFunctor( F ), [ V1, Opposite( V1 ) ] ) );;
gap> F_installationOnMorphisms( pi1, pi2 );;
gap> F_installationOnMorphisms( input );;
gap> F2 := CapFunctor( "CohomForVec2", ProductCategory( [ vec, Opposite( vec ) ] ), vec );;
gap> AddObjectFunction( F2, a -> obj_func( a[1], Opposite( a[2] ) ) );;
gap> AddMorphismFunction( F2, function( source, datum, range ) return mor_func( source, datum[1], Opposite( datum[2] ), range ); end );;
gap> input := ProductCategoryMorphism( SourceOfFunctor( F2 ), [ pi1, Opposite( pi2 ) ] );;
gap> value3 := ApplyFunctor( F2, input );;
gap> IsCongruentForMorphisms( value1, value3 );
true
gap> Display( InputSignature( F2 ) );
[ [ Product of: Category of matrices over Q, Opposite( Category of matrices over Q ), false ] ]
gap> InstallFunctor( F2, "F_installation2" );;
gap> F_installation2( input );;
gap> F_installation2OnObjects( ProductCategoryObject( SourceOfFunctor( F2 ), [ V1, Opposite( V1 ) ] ) );;
gap> F_installation2OnMorphisms( input );;
#
gap> STOP_TEST("linearalgebraforcap07.tst", 1);
[ Dauer der Verarbeitung: 0.4 Sekunden
(vorverarbeitet)
]
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