Computation of the degree of rational surface parametrizations
IdentifiersPermanent link (URI): http://hdl.handle.net/10017/49505
Ministerio de Educación y Ciencia
Pérez Díaz, S. & Sendra, J.R. 2004, "Computation of the degree of rational surface parametrizations", Journal of Pure and Applied Algebra, vol. 193, no. 1-3, pp. 99-121.
Degree of a Rational Map
info:eu-repo/grantAgreement/EC/FP5-IST/IST-2001-35512/EU/INTERSECTION ALGORITHMS FOR GEOMETRY BASED IT-APPLICATIONS USING APPROXIMATE ALGEBRAIC METHODS/GAIA II
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2003 Elsevier
A rational affine parametrization of an algebraic surface establishes a rational correspondence of the affine plane with the surface. We consider the problem of computing the degree of such a rational map. In general, determining the degree of a rational map can be achieved by means of elimination theoretic methods. For curves, it is shown that the degree can be computed by gcd computations. In this paper, we show that the degree of a rational map induced by a surface parametrization can be computed by means of gcd and univariate resultant computations. The basic idea is to express the elements of a generic fibre as the finitely many intersection points of certain curves directly constructed from the parametrization, and defined over the algebraic closure of a field of rational functions.
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