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#! @Chapter Examples and Tests
#! @Section Closed Monoidal Structure
LoadPackage( "ModulePresentationsForCAP" );
LoadPackage( "RingsForHomalg" );
#! @Example
R := HomalgRingOfIntegers( );;
fpres := LeftPresentations( R );;
M := AsLeftPresentation( fpres, HomalgMatrix( [ [ 2 ] ], 1, 1, R ) );
#! <An object in Category of left presentations of Z>
N := AsLeftPresentation( fpres, HomalgMatrix( [ [ 3 ] ], 1, 1, R ) );
#! <An object in Category of left presentations of Z>
T := TensorProductOnObjects( M, N );
#! <An object in Category of left presentations of Z>
Display( T );
#! [ [ 3 ],
#! [ 2 ] ]
#!
#! An object in Category of left presentations of Z
IsZero( T );
#! true
H := InternalHomOnObjects( DirectSum( M, M ), DirectSum( M, N ) );
#! <An object in Category of left presentations of Z>
Display( H );
#! [ [ 0, 0, 0, -2 ],
#! [ 1, 2, 0, 0 ],
#! [ 0, 2, 2, 0 ],
#! [ 2, 3, 0, 2 ] ]
#!
#! An object in Category of left presentations of Z
alpha := StandardGeneratorMorphism( H, 3 );
#! <A morphism in Category of left presentations of Z>
l := LambdaElimination( DirectSum( M, M ), DirectSum( M, N ), alpha );
#! <A morphism in Category of left presentations of Z>
IsZero( l );
#! false
Display( l );
#! [ [ -2, 6 ],
#! [ -1, -3 ] ]
#!
#! A morphism in Category of left presentations of Z
#! @EndExample
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