GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "RingsForHomalg" ); R := HomalgFieldOfRationalsInDefaultCAS( ) * "x0,x1"; LoadPackage( "GradedRingForHomalg" ); R := GradedRing( R ); A := KoszulDualRing( R ); m := HomalgMatrix( "[ e0, e1, 0, 0, e0, e1 ]", 2, 3, A );