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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.

UDC: 512.6+004.421.6

Received: 04.06.2016
Accepted: 13.09.2016

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