On the structure of the resonance set of a real polynomial

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.