Iterated discriminants
type: Item
instance of: scholarly article
title: Iterated discriminants
zbMATH Open document ID: 1206.13030
author: D. Lazard
author: Scott McCallum
published in: Journal of Symbolic Computation
publication date: 2009-07-01T00:00:00Z
review text: In this paper the authors prove that the discriminant of the discriminant of a multivariate polynomial has the same irreducible factors of the product of seven polynomials. These seven polynomials are obtained as the GCD of the generators of an elimination ideal. This result is similar to the one by \textit{L. Busé} and \textit{B. Mourrain} [Math. Comput. 78, No. 265, 345--386 (2009; Zbl 1200.13042)] for bivariate polynomials. In this paper the authors study the factors of the discriminant of the discriminant of a multivariate polynomial using an elimination ideal instead of resultants; in this way they can avoid degree hypotheses, however they do not get complete information on the multiplicity of the factors. The main result is obtained studying the order at a point of a polynomial and its discriminant, the singularities of the hypersurface defined by a discriminant and the use of the notion of ``generic point'' of an irreducible variety in the sense of Weil. As an application, the authors directly compute the factors of an iterated discriminant in a problem of quantifier elimination.
reviewed by: Cristina Bertone
Mathematics Subject Classification ID: 13P05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 5573847
zbMATH Keywords: multivariate polynomial
zbMATH Keywords: discriminant
zbMATH Keywords: generic point
zbMATH Keywords: singularities of discriminant hypersurface
MaRDI profile type: Publication
full work available at URL: j.jsc.2008.05.006
OpenAlex ID: W2911724704
cites work: Q3462466
cites work: Algorithms in real algebraic geometry
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cites work: Q4079605
cites work: Q5690494
cites work: Quantifier elimination: Optimal solution for two classical examples
cites work: Factors of iterated resultants and discriminants
cites work: Q4047653
cites work: Q5846813
DOI: 10.1016/J.JSC.2008.05.006
description: scientific article; zbMATH DE number 5573847