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#! @Chapter Examples and Tests
#! @Section PreComposeList and PostComposeList
LoadPackage( "LinearAlgebraForCAP" );
#! @Example
field := HomalgFieldOfRationals( );;
vec := MatrixCategory( field );;
A := MatrixCategoryObject( vec, 1 );;
B := MatrixCategoryObject( vec, 2 );;
C := MatrixCategoryObject( vec, 3 );;
alpha := VectorSpaceMorphism( A, HomalgMatrix( [ [ 1, 0, 0 ] ], 1, 3, field ), C );;
beta := VectorSpaceMorphism( C, HomalgMatrix( [ [ 1, 0 ], [ 1, 1 ], [ 1, 2 ] ], 3, 2, field ), B );;
IsCongruentForMorphisms( PreCompose( alpha, beta ), PostCompose( beta, alpha ) );
#! true
IsCongruentForMorphisms( PreComposeList( A, [ ], A ), IdentityMorphism( A ) );
#! true
IsCongruentForMorphisms( PreComposeList( A, [ alpha ], C ), alpha );
#! true
IsCongruentForMorphisms( PreComposeList( A, [ alpha, beta ], B ), PreCompose( alpha, beta ) );
#! true
IsCongruentForMorphisms( PostComposeList( A, [ ], A ), IdentityMorphism( A ) );
#! true
IsCongruentForMorphisms( PostComposeList( A, [ alpha ], C ), alpha );
#! true
IsCongruentForMorphisms( PostComposeList( A, [ beta, alpha ], B ), PostCompose( beta, alpha ) );
#! true
#! @EndExample
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