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 Chebyshevskii Sb., 2016, Volume 17, Issue 3, Pages 5–17 (Mi cheb493)

On the structure of the resonance set of a real polynomial

A. B. Batkhin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: We consider the resonance set of a real polynomial, i. e. the set of all the points of the coefficient space at which the polynomial has commensurable roots. The resonance set of a polynomial can be considered as a certain generalization of its discriminant set. The structure of the resonance set is useful for investigation of resonances near stationary point of a dynamical system.
The constructive algorithm of computation of polynomial parametrization of the resonance set is provided. The structure of the resonance set of a polynomial of degree $n$ is described in terms of partitions of the number $n$.
The main algorithms, described in the paper, are organized as a library of the computer algebra system Maple. The description of the resonance set of a cubic polynomial is given.
Bibliography: 12 titles.

Keywords: elimination theory, subresultant, subdiscriminant, resonance set, computer algebra.

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UDC: 512.6+004.421.6
Accepted:13.09.2016

Citation: A. B. Batkhin, “On the structure of the resonance set of a real polynomial”, Chebyshevskii Sb., 17:3 (2016), 5–17

Citation in format AMSBIB
\Bibitem{Bat16} \by A.~B.~Batkhin \paper On the structure of the resonance set of a real polynomial \jour Chebyshevskii Sb. \yr 2016 \vol 17 \issue 3 \pages 5--17 \mathnet{http://mi.mathnet.ru/cheb493} \elib{https://elibrary.ru/item.asp?id=27452078} 

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This publication is cited in the following articles:
1. A. B. Batkhin, “Vychislenie obobschënnogo diskriminanta veschestvennogo mnogochlena”, Preprinty IPM im. M. V. Keldysha, 2017, 088, 40 pp.
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