GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "RingsForHomalg" ); LoadPackage( "Modules" ); Qt := HomalgFieldOfRationalsInDefaultCAS( ) * "t"; A1 := RingOfDerivations( Qt, "D" ); M := HomalgMatrix( "[ \ t^2, 1-t*D, \ 2+t*D, -D^2 \ ]", 2, 2, A1 ); M := LeftPresentation( M ); d := Resolution( M ); d_short := ShortenResolution( M ); Assert( 0, IsIdenticalObj( Cokernel( FirstMorphismOfResolution( M ) ), M ) );