A complete discrimination system for polynomials with complex coefficients and its automatic generation
type: Item
instance of: scholarly article
title: A complete discrimination system for polynomials with complex coefficients and its automatic generation
zbMATH Open document ID: 0949.12002
DOI: 10.1007/BF02917106
author: Songxin Liang
author: Jingzhong Zhang
published in: Science in China. Series E
publication date: 2000-12-05T00:00:00Z
review text: Write the polynomial \(f(x)\) as \(f_1(x)+ if_2(x)\), where \(f_1\) and \(f_2\) have real coefficients. The authors give a method of determining the numbers of real zeros, pairs of complex conjugate zeros, and complex zeros with no conjugate (which can arise if \(f_2\) has some non-zero coefficients) of \(f\). The method is based on constructing sequences of numbers starting from the signs of determinants of subresultants of various polynomials and their derivatives. It has been implemented in Maple, and some run times are given. The authors also consider dealing with polynomials with literal coefficients and the problem of investigating the positive definiteness of polynomials in two variables. Proofs are not given, but are referred to from papers inaccessible to this reviewer. Examples, for reasons of space, are not given in full.
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1342527
zbMATH Keywords: numbers of real zeros
zbMATH Keywords: pairs of complex conjugate zeros
zbMATH Keywords: complex zeros with no conjugate
zbMATH Keywords: subresultants
zbMATH Keywords: polynomials
zbMATH Keywords: Maple
zbMATH Keywords: positive definiteness
zbMATH Keywords: polynomials in two variables
describes a project that uses: Maple
describes a project that uses: QEPCAD
MaRDI profile type: Publication
cites work: A complete discrimination system for polynomials
cites work: Q4848888
cites work: Q3136296
cites work: Q4079605
cites work: Polynomial algorithms in computer algebra
description: scientific article; zbMATH DE number 1342527