Computation of generalized discriminant of a real polynomial

Abstract:

We consider a certain generalization of discriminant of a real polynomial, defined by the linear Hahn operator decreasing degree of the polynomial by one. We study the structure of the generalized discriminant set of the real polynomial i.e. the set of all the values of the polynomial coefficients at which the polynomial and its image of Hahn operator have common root. The structure of the generalized discriminant set of the polynomial of degree n is described by means of partitions of integer number $n$. Some algorithms of computation of polynomial parametrization of the generalized discriminant set in the coefficient space are proposed. Main steps of described algorithms are implemented as a software library in the computer algebra system Maple. Some examples of computations are proposed.