Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Friday, March, 8, 2013, at University of Western Ontario
Recent advances on the theory of regular chains
Changbo Chen, University of Western Ontario

Abstract: In this talk, two recent advances on the theory of regular chains will be discussed. We shall start with a theoretical question, summarized below and which is one of the facets of the so-called Ritt problem. A software presentation of the new support for Maple's solve command with semi-algebraic systems will conclude the talk. Given a regular chain R, we propose an algorithm which computes the non-trivial limit points of the quasi-component Q of R, that is, the points that belong to the Zariski closure of Q but not to Q. Our procedure relies on Puiseux series expansions and avoids the computation of a system of generators of the saturated ideal of R. We focus on the case where this saturated ideal has dimension one and we discuss extensions of this work in higher dimensions. This is a joint work with Parisa Alvandi and Marc Moreno Maza.


Last modified on Tuesday, 05 March 2013, at 12:47 hours.