Western University Computer ScienceWestern Science

MSc Thesis Defense

 

Masoud Ataei Jaliseh

ON THE EXTENDED HENSEL CONSTRUCTION AND ITS APPLICATION TO THE COMPUTATION OF REAL LIMIT

 

Date:
Time:
Place:
Supervisor:
Thesis Examiners:

Extra-Departmental
Examiner:
Chair:
Wednesday, December 20, 2017
9:30 a.m.
Middlesex College, Room 320
Dr. Marc Moreno Maza
Dr. Lucian Ilie
Dr. Rob Corless

Dr. David Jeffrey (Applied Math)
Dr. Robert Webber

 

Abstract:

The Extended Hensel Construction (EHC) is a procedure which, for an input bivariate polyno- mial with complex coefficients, can serve the same purpose as the Newton- Puiseux algorithm. We show that the EHC requires only linear algebra and univariate polynomial arithmetic. We deduce complexity estimates and report on a software implementation together with experi- mental results. This work is motivated and illustrated by two applications. The first one is the computation of real branches of space curves. The second one is the computation of limits of real multivariate rational function. For the latter, we present an algorithm for determining the existence of the limit of a real multivariate rational function q at a given point p which is an isolated zero of the denominator of q. When the limit exists, the algorithm computes it, without making any assumption on the number of variables.