【报告摘要】We consider a zero-dimensional polynomial system in n variables defined over a field K. In the context of computing a Rational Univariate Representation (RUR) of its solutions, say a parameterization of the solutions, we address the problem of certifying a separating linear form and, once certified, calculating the RUR that comes from it, without any condition on the ideal else than being zero-dimensional. In a first part, many knowns facts will be recall about historical ways of computing such parameterizations as well as results on the size of such objects. In the second part it will be shown that such a  parameterization can be read (closed formula) from lexicographic Gröebner bases of bivariate elimination ideals, even in the case where the original ideal that is not in shape position, so that one can use the same core as the well known FGLM method to propose a simple algorithm.

 

【报告人简介】Fabrice Rouillier，senior researcher (Research Director) at Institut national de recherche en informatique et en automatique (INRIA). He is the head of the OURAGAN Inria project-team (http://team.inria.fr/ouragan) which is a joint team with Sorbonne Université, Université Paris Cité and CNRS located at Institut de Mathématiques de Jussieu and the chairman of the association Animath (http://animath.fr) for the promotion of mathematics.