GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "RingsForHomalg" ); R := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z"; LoadPackage( "Modules" ); P1 := LeftSubmodule( "x*y+y*z+z*x", R ); P2 := LeftSubmodule( "x^2+y,y*z+2", R ); P3 := LeftSubmodule( "x*y-1,y+z", R ); I := Intersect( P1, P2, P3 ); W := 1 * R / I;