RT info:eu-repo/semantics/article
T1 Computation of the degree of rational surface parametrizations
A1 Pérez Díaz, Sonia
A1 Sendra Pons, Juan Rafael
K1 Rational Parametrization
K1 Algebraic Surface
K1 Degree of a Rational Map
K1 Matemáticas
K1 Mathematics
AB 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.
PB Elsevier
SN 0022-4049
YR 2004
FD 2004-10-01
LK http://hdl.handle.net/10017/49505
UL http://hdl.handle.net/10017/49505
LA eng
NO European Commission
DS MINDS@UW
RD 18-abr-2024