Automatic computation of the complete root classification for a parametric polynomial
type: Item
instance of: scholarly article
title: Automatic computation of the complete root classification for a parametric polynomial
zbMATH Open document ID: 1186.12003
author: Songxin Liang
author: D. J. Jeffrey
published in: Journal of Symbolic Computation
publication date: 2009-09-14T00:00:00Z
review text: The authors present an improvement of their algorithm to compute complete root classifications (CRC) of univariate polynomials with real parametric coefficients [An algorithm for computing the complete root classification of a parametric polynomial. Artificial intelligence and symbolic computation. 8th international conference, AISC 2006, Beijing, China, September 20--22, 2006. Proceedings. Berlin: Springer. Lecture Notes in Artificial Intelligence, Lecture Notes Comput. Sci. 4120, 116--130 (2006; Zbl 1156.68632)]. This improvement consists mainly on working directly with 'sign lists' rather than 'revised sign lists'. A second improvement is to simplify the set of generated conditions, by means of a test for extraneous cases (empty conditions). The authors discuss the equivalence of discriminant sequences, principal Sturm-Habicht coefficient sequences, and principal and signed subresultant coefficient sequences for CRC computations. They also review some previous algorithms by different authors and present some sparse examples.
reviewed by: David Sevilla
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 5603618
zbMATH Keywords: complete root classification
zbMATH Keywords: parametric polynomial
zbMATH Keywords: real quantifier elimination
zbMATH Keywords: real root
zbMATH Keywords: subresultant polynomial
describes a project that uses: QEPCAD
MaRDI profile type: Publication
full work available at URL: j.jsc.2009.05.003
OpenAlex ID: W2145025251
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DOI: 10.1016/J.JSC.2009.05.003
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description: scientific article; zbMATH DE number 5603618