On the simplification of the coefficients of a parametrization

Authors:
Carlos Andradas;Tomas Recio;J. Rafael Sendra;Luis Felipe Tabera
Affiliations:
Departamento de Álgebra, Universidad Complutense de Madrid, 28040, Madrid, Spain;Departamento de Matemáticas, Universidad de Cantabria, 39071, Santander, Spain;Departamento de Matemáticas, Universidad de Alcalá, 28871, Alcalá de Henares, Spain;IMDEA Mathematics Foundation, Módulo C-IX 3th floor Facultad de Ciencias - UAM Ciudad Universitaria de Cantoblanco E-28049, Madrid, Spain
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

This paper deals with the problem of finding, for a given parametrization of an algebraic variety V of arbitrary dimension, another parametrization with coefficients over a smaller field. We proceed adapting, to the parametric case, a construction introduced by A. Weil for implicitly given varieties. We find that this process leads to the consideration of new varieties of a particular kind (ultraquadrics, in the terminology of this paper) in order to check, algorithmically, several interesting properties of the given variety V, such as the property of being reparametrizable over the smaller field.