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# LinearAlgebraForCAP, single 9
#
# 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("linearalgebraforcap09.tst");
# doc/_Chapter_Examples_and_Tests.xml:415-486
gap> field := HomalgFieldOfRationals( );;
gap> vec := MatrixCategory( field );;
gap> A := MatrixCategoryObject( vec, 1 );;
gap> B := MatrixCategoryObject( vec, 2 );;
gap> C := MatrixCategoryObject( vec, 3 );;
gap> alpha := VectorSpaceMorphism( A, HomalgMatrix( [ [ 1, 0, 0 ] ], 1, 3, field ), C );;
gap> beta := VectorSpaceMorphism( C, HomalgMatrix( [ [ 1, 0 ], [ 1, 1 ], [ 1, 2 ] ], 3, 2, field ), B );;
gap> IsZeroForMorphisms( PreCompose( alpha, beta ) );
false
gap> IsCongruentForMorphisms(
> IdentityMorphism( HomologyObject( alpha, beta ) ),
> HomologyObjectFunctorial( alpha, beta, IdentityMorphism( C ), alpha, beta )
> );
true
gap> kernel_beta := KernelEmbedding( beta );;
gap> K := Source( kernel_beta );;
gap> IsIsomorphism(
> HomologyObjectFunctorial(
> MorphismFromZeroObject( K ),
> MorphismIntoZeroObject( K ),
> kernel_beta,
> MorphismFromZeroObject( Source( beta ) ),
> beta
> )
> );
true
gap> cokernel_alpha := CokernelProjection( alpha );;
gap> Co := Range( cokernel_alpha );;
gap> IsIsomorphism(
> HomologyObjectFunctorial(
> alpha,
> MorphismIntoZeroObject( Range( alpha ) ),
> cokernel_alpha,
> MorphismFromZeroObject( Co ),
> MorphismIntoZeroObject( Co )
> )
> );
true
gap> op := Opposite( vec );;
gap> alpha_op := Opposite( op, alpha );;
gap> beta_op := Opposite( op, beta );;
gap> IsCongruentForMorphisms(
> IdentityMorphism( HomologyObject( beta_op, alpha_op ) ),
> HomologyObjectFunctorial( beta_op, alpha_op, IdentityMorphism( Opposite( C ) ), beta_op, alpha_op )
> );
true
gap> kernel_beta := KernelEmbedding( beta_op );;
gap> K := Source( kernel_beta );;
gap> IsIsomorphism(
> HomologyObjectFunctorial(
> MorphismFromZeroObject( K ),
> MorphismIntoZeroObject( K ),
> kernel_beta,
> MorphismFromZeroObject( Source( beta_op ) ),
> beta_op
> )
> );
true
gap> cokernel_alpha := CokernelProjection( alpha_op );;
gap> Co := Range( cokernel_alpha );;
gap> IsIsomorphism(
> HomologyObjectFunctorial(
> alpha_op,
> MorphismIntoZeroObject( Range( alpha_op ) ),
> cokernel_alpha,
> MorphismFromZeroObject( Co ),
> MorphismIntoZeroObject( Co )
> )
> );
true
#
gap> STOP_TEST("linearalgebraforcap09.tst", 1);
[ Dauer der Verarbeitung: 0.20 Sekunden
(vorverarbeitet)
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