ИСТИНА

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 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 algorithm for computation of parametric representation of the resonance set is implemented as a library of the CAS Maple. Obtained results are used for solving the problem of formal stability of a stationary point of a multiparametric Hamiltonian problem with three degrees of freedom.