Simultaneous elimination by using several tools from real algebraic geometry
type: Item
instance of: scholarly article
title: Simultaneous elimination by using several tools from real algebraic geometry
zbMATH Open document ID: 0952.14043
author: Laureano Gonzalez-Vega
author: Neila González-Campos
published in: Journal of Symbolic Computation
publication date: 2001-01-10T00:00:00Z
review text: There are several methods in computer algebra to eliminate variables: Gröbner bases, resultants, Ritt-characteristic sets, etc. This paper presents two new elimination procedures for two particular problems: The simultaneous elimination of one variable from several polynomial that is based in a linear-algebra method to compute the degree of the gcd of several univariate polynomials over an integral domain, called \textit{S. Barnett}'s method [Proc. Camb. Philos. Soc. 70, 263-268 (1971; Zbl 0224.15018)], and the simultaneous elimination of several variables in several equations containing a Pham system (a zero-dimensional polynomial system with very good parameter specialization properties) that is based on Hermite's method. The extension of the technique above to more general systems is difficult because it depends on the existence of the universal base for a quotient ring.
reviewed by: M. Ladra
Mathematics Subject Classification ID: 14Q20
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 14P99
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 1369540
zbMATH Keywords: elimination
zbMATH Keywords: greatest common divisor of polynomials
zbMATH Keywords: Hermite's method
zbMATH Keywords: real algebraic geometry
zbMATH Keywords: computer aided geometric design
MaRDI profile type: Publication
full work available at URL: jsco.1998.0268
OpenAlex ID: W2152080657
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DOI: 10.1006/JSCO.1998.0268
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description: scientific article; zbMATH DE number 1369540