  Recently, a method to compute the implicit equation of a parametrized
hypersurface has been developed by the authors. We address here some questions
related to this method. First, we prove that the degree estimate for the
stabilization of the MacRae's invariant of a graded part of the symmetric
algebra is optimal. Then we show that the extraneous factor that may appear in
the process splits into a product a linear forms in the algebraic closure of
the base field, each linear form being associated to a non complete
intersection base point. Finally, we make a link between this method and a
resultant computation for the case of rational plane curves and space surfaces.
