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# LinearAlgebraForCAP, single 6
#
# 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("linearalgebraforcap06.tst");
# doc/_Chapter_Examples_and_Tests.xml:227-272
gap> pre_compose := MonoidalPreComposeMorphism( a, b, c );
<A morphism in Category of matrices over Q>
gap> post_compose := MonoidalPostComposeMorphism( a, b, c );
<A morphism in Category of matrices over Q>
gap> pre_cocompose := MonoidalPreCoComposeMorphism( c, b, a );
<A morphism in Category of matrices over Q>
gap> post_cocompose := MonoidalPostCoComposeMorphism( c, b, a );
<A morphism in Category of matrices over Q>
gap> UnderlyingMatrix( pre_compose ) = TransposedMatrix( UnderlyingMatrix( pre_cocompose ) );
true
gap> UnderlyingMatrix( post_compose ) = TransposedMatrix( UnderlyingMatrix( post_cocompose ) );
true
gap> tp_hom_comp := TensorProductInternalHomCompatibilityMorphism( [ a, b, c, d ] );
<A morphism in Category of matrices over Q>
gap> cohom_tp_comp := InternalCoHomTensorProductCompatibilityMorphism( [ b, d, a, c ] );
<A morphism in Category of matrices over Q>
gap> UnderlyingMatrix( tp_hom_comp ) = TransposedMatrix( UnderlyingMatrix( cohom_tp_comp ) );
true
gap> lambda := LambdaIntroduction( alpha );
<A morphism in Category of matrices over Q>
gap> lambda_elim := LambdaElimination( a, b, lambda );
<A morphism in Category of matrices over Q>
gap> alpha = lambda_elim;
true
gap> alpha_op := VectorSpaceMorphism( b, TransposedMatrix( UnderlyingMatrix( alpha ) ), a );
<A morphism in Category of matrices over Q>
gap> colambda := CoLambdaIntroduction( alpha_op );
<A morphism in Category of matrices over Q>
gap> colambda_elim := CoLambdaElimination( b, a, colambda );
<A morphism in Category of matrices over Q>
gap> alpha_op = colambda_elim;
true
gap> UnderlyingMatrix( lambda ) = TransposedMatrix( UnderlyingMatrix( colambda ) );
true
gap> delta := PreCompose( colambda, lambda);
<A morphism in Category of matrices over Q>
gap> Display( EntriesOfHomalgMatrixAsListList( UnderlyingMatrix( TraceMap( delta ) ) ) );
[ [ 9 ] ]
gap> Display( EntriesOfHomalgMatrixAsListList( UnderlyingMatrix( CoTraceMap( delta ) ) ) );
[ [ 9 ] ]
gap> TraceMap( delta ) = CoTraceMap( delta );
true
gap> RankMorphism( a ) = CoRankMorphism( a );
true
#
gap> STOP_TEST("linearalgebraforcap06.tst", 1);
[ Dauer der Verarbeitung: 0.19 Sekunden
(vorverarbeitet)
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