GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "RingsForHomalg" ); R := HomalgFieldOfRationalsInSingular( ) * "x,y"; LoadPackage( "Modules" ); I := LeftSubmodule( "x", R ); J := LeftSubmodule( "x,y", R ); K := I * J; pp := PrimaryDecomposition( K );