This article is cited in 1 scientific paper (total in 1 paper)
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
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.
elimination theory, subresultant, subdiscriminant, resonance set, computer algebra.
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A. B. Batkhin, “On the structure of the resonance set of a real polynomial”, Chebyshevskii Sb., 17:3 (2016), 5–17
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\paper On the structure of the resonance set of a real polynomial
\jour Chebyshevskii Sb.
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This publication is cited in the following articles:
A. B. Batkhin, “Vychislenie obobschënnogo diskriminanta veschestvennogo mnogochlena”, Preprinty IPM im. M. V. Keldysha, 2017, 088, 40 pp.
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