GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "RingsForHomalg" ); R := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z" / "x^2+y^2+z^2-1"; m := HomalgMatrix( "[ x, y, z ]", 1, 3, R ); LoadPackage( "Modules" ); M := LeftPresentation( m ); IsStablyFree( M ); ## also figures out the rank