Zero–nonzero and real–nonreal sign determination

We consider first the zero–nonzero determination problem, which consists in determining the list of zero–nonzero conditions realized by a finite list of polynomials on a finite set Z⊂Ck with C an algebraic closed field. We describe an algorithm to solve the zero–nonzero determination problem and we...

Full description

Saved in:
Bibliographic Details
Published inLinear algebra and its applications Vol. 439; no. 10; pp. 3016 - 3030
Main Authors Perrucci, Daniel, Roy, Marie-Françoise
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.11.2013
Elsevier
Subjects
Algebraic Geometry
Complexity
Computer Science
Mathematics
Polynomial equations and inequations systems
Sign determination
Symbolic Computation
Sign determination
Polynomial equations and inequations systems
14P10
14Q20
Complexity
Online AccessGet full text

Cover

More Information
Summary:We consider first the zero–nonzero determination problem, which consists in determining the list of zero–nonzero conditions realized by a finite list of polynomials on a finite set Z⊂Ck with C an algebraic closed field. We describe an algorithm to solve the zero–nonzero determination problem and we perform its bit complexity analysis. This algorithm, which is in many ways an adaptation of the methods used to solve the more classical sign determination problem, presents also new ideas which can be used to improve sign determination. Then, we consider the real–nonreal sign determination problem, which deals with both the sign determination and the zero–nonzero determination problem. We describe an algorithm to solve the real–nonreal sign determination problem, we perform its bit complexity analysis and we discuss this problem in a parametric context.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2013.09.010