Iterated discriminants

Daniel Lazard*, Scott McCallum

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

It is shown that the discriminant of the discriminant of a multivariate polynomial has the same irreducible factors as the product of seven polynomials each of which is defined as the GCD of the generators of an elimination ideal. Under relatively mild conditions of genericity, three of these polynomials are irreducible and generate the corresponding elimination ideals, while the other four are equal to one. Moreover the irreducible factors of two of these polynomials have multiplicity at least two in the iterated discriminant and the irreducible factors of two others of the seven polynomials have multiplicity at least three. The proof involves an extended use of the notion of generic point of an algebraic variety and a careful study of the singularities of the hypersurface defined by a discriminant, which may be interesting by themselves.

Original languageEnglish
Pages (from-to)1176-1193
Number of pages18
JournalJournal of Symbolic Computation
Volume44
Issue number9
DOIs
Publication statusPublished - Sep 2009

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