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\title{New Elimination Tools based on Symmetric Functions for the Implicitization of Parametric Curves and Surfaces}
\author{Laureano Gonz\'alez-Vega \\
Departamento de Matem\'aticas \\
Univerisidad de Cantabria \\
Santander 39071, Spain \\
gvega@matsun1.unican.es}



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\begin{document}
\maketitle

\centerline{\bf Abstract}

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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 Gr\"obner 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.
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{\bf keywords:} parametric curves, surfaces, implicitization and symmetric 
functions. 
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