Geodesic
On the structure of the resonance set of a real polynomial
Čebyševskij sbornik, Tome 17 (2016) no. 3, pp. 5-17

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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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     title = {On the structure of the resonance set of a real polynomial},
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A. B. Batkhin. On the structure of the resonance set of a real polynomial. Čebyševskij sbornik, Tome 17 (2016) no. 3, pp. 5-17. http://geodesic.mathdoc.fr/item/CHEB_2016_17_3_a0/