The default is FineGrading => false. If the option FineGrading=>true is given, then the ideal returned has the natural $\ZZ^4$ grading, where x_i has degree \{1,0,i,a-i\}\ and y_i has degree \{0,1,i,b-i\}. (Note that after the call carpet(a1,a2) we have a = min(a1,a2), b = max(a1,a2).)
The object FineGrading is a symbol.