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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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LoadPackage( "LinearAlgebraForCAP" );

Q := HomalgFieldOfRationals( );

a := VectorSpaceObject( 3, Q );

b := VectorSpaceObject( 4, Q );

homalg_matrix := HomalgMatrix( [ [ 1, 0, 0, 0 ], [ 0, 1, 0, -1 ], [ -1, 0, 2, 1 ] ], 3, 4, Q );

alpha := VectorSpaceMorphism( a, homalg_matrix, b );

homalg_matrix := HomalgMatrix( [ [ 1, 1, 0, 0 ], [ 0, 1, 0, -1 ], [ -1, 0, 2, 1 ] ], 3, 4, Q );

beta := VectorSpaceMorphism( a, homalg_matrix, b );