Decomposing polynomial systems into simple systems
type: Item
instance of: scholarly article
title: Decomposing polynomial systems into simple systems
zbMATH Open document ID: 0913.12008
author: Dongming Wang
published in: Journal of Symbolic Computation
publication date: 1999-06-07T00:00:00Z
review text: A polynomial system \([P,Q]\) is a pair of multivariate polynomial sets \(P\) and \(Q\) and Zero \(([P,Q])\) is the set of all common zeros of the polynomials in \(P\) which are not zeros of any polynomial in \(Q\). Fixing an ordering to the variables, a simple system is a polynomial system ordered in triangular form, in which every polynomial is squarefree and has non-vanishing leading coefficient with respect to its leading variable. The author shows how to decompose any polynomial system into finitely many simple systems \([T_i,T_i']\) such that \[ \text{Zero} \bigl([P,Q]\bigr) =\bigcup \text{Zero} [T_i,T_i']. \] The method deals with top-down elimination and the construction of subresultant chains. The author also presents an algorithm (Sim Sys) that decomposes any polynomial system in the sense stated above. He shows how Sim Sys works in different examples and finally states several properties of simple systems.
reviewed by: Juan Sabia
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 13P05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1204277
zbMATH Keywords: polynomial orderings
zbMATH Keywords: polynomial system
zbMATH Keywords: simple system
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: jsco.1997.0177
OpenAlex ID: W2056521839
Wikidata QID: Q56602967
DOI: 10.1006/JSCO.1997.0177
description: scientific article; zbMATH DE number 1204277