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Iterated discriminants

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Title: Iterated discriminants
Related: Journal of symbolic computation, Vol. 44, Issue 9, (2009), p.1176-1193
DOI: 10.1016/j.jsc.2008.05.006
Publisher: Academic Press / Elsevier
Date: 2009
FoR/RFCD Code(s): 010200 Applied Mathematics 080200 Computation Theory and Mathematics 010300 Numerical and Computational Mathematics
Author/Creator: Lazard, Daniel
Author/Creator: McCallum, Scott
Description: 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.
Description: 18 page(s)
Subject Keyword: 010200 Applied Mathematics
Subject Keyword: 080200 Computation Theory and Mathematics
Subject Keyword: 010300 Numerical and Computational Mathematics
Subject Keyword: Multivariate polynomial
Subject Keyword: Discriminant
Subject Keyword: Generic point
Subject Keyword: Singularities of discriminant hypersurface
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

Identifier: http://hdl.handle.net/1959.14/146736
Identifier: ISSN:0747-7171
Identifier: mq-rm-2009004138
Language: eng
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