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Implicitization of parametric curves and surfaces by using symmetric functions

This paper is devoted to present a new algorithm to compute the implicit equation of a parametric plane curve and several classes of parametric surfaces in the three dimensional euclidean space. This algorithm does not require of the computation of any symbolic determinant or Gr6bner 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.