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AAA68: Workshop on General Algebra (68. Arbeitstagung Allgemeine Algebra)
June 10-13, 2004
Technische Universität Dresden
Dresden, Germany |
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Organizers
Reinhard Pöschel, Bernhard Ganter
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Discriminant-Resultant Families and Root Multiplicity Analysis
by
Armenak S. Gasparyan
Program System Institute of RAS, Pereslavl-Zalesskii, Russia
We introduce discriminants and resultants associated with graphs and observe
how certain families of these functions can give rich information about the
root multiplicities of univariate real polynomials. Some appropriately chosen
discriminant (resultant) sequences serve as exact criteria for polynomials to
have given multiplicities of roots (common roots). Moreover, from
correspondence between sign vectors of discriminants (resultants) and root
multiplicity vectors we derive several theorems about polynomials with given
properties of the root multiplicities. Based in such consideration, we explain
algorithms for determining multiplicity vectors and other related properties
of roots (or common roots) of the polynomials. Finally, the sign tables of
discriminant families furnish several new series of general inequalities over
the coefficients of real polynomials with not necessarily real roots.
Date received: May 19, 2004
Copyright © 2004 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Mathematical Conference Abstracts.
Document # canq-72.