GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "ModulePresentationsForCAP" ); ZZ := HOMALG_MATRICES.ZZ; LeftPresentations( ZZ ); RightPresentations( ZZ ); A := HomalgMatrix( [ [ 1, 2 ], [ 2, 3 ] ], ZZ ); Aleft := AsLeftPresentation( A ); Aright := AsRightPresentation( A ); B := HomalgMatrix( [ [ 1, 2 ] ], ZZ ); Bleft := AsLeftPresentation( B ); Bright := AsRightPresentation( B ); tau := HomalgMatrix( [ [ 1, 0 ], [ 0, 1 ] ], ZZ ); ######################### ## ## Cokernel ## ######################### A := AsLeftPresentation( HomalgZeroMatrix( 0, 1, ZZ ) ); phi := HomalgMatrix( [ [ 4 ] ], ZZ ); phi := PresentationMorphism( A, phi, A ); epsilon := CokernelProjection( phi ); tau := HomalgMatrix( [ [ 2 ] ], ZZ ); B := AsLeftPresentation( HomalgMatrix( [ [ 8 ] ], ZZ ) ); tau := PresentationMorphism( A, tau, B );