Implicitization of Parametric Curves and Surfaces by using Multidimensional Newton Formulae

This paper is devoted to present new algorithms computing the implicit equation of a parametric plane curve and several classes of parametric surfaces in the three dimensional euclidean space. These algorithms do not require the computation of any symbolic determinant or Gröbner Basis, being these tools replaced by the computation of some symmetric functions, in particular the Newton Sums, on the solution set of a well precised zero dimensional ideal.