New Elimination Tools based on Symmetric Functions for the Implicitization of Parametric

Curves and Surfaces

Laureano González-Vega Departamento de Matemáticas Univerisidad de Cantabria Santander 39071, Spain gvega@matsun1.unican.es

Abstract

This talk 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 requiere of the computation of any symbolic determinant or Gröbner Basis, being these tools replaced by the efficient computation of some symmetric functions, in particular the Newton Sums on the solution set of a well precised zero dimensional ideal.

keywords: parametric curves, surfaces, implicitization and symmetric functions.