Parametrization of the discriminant set of a real polynomial

Abstract:

We consider the discriminant set of a real polynomial, i.e. the set of all the points of coefficient space at which the polynomial has multiple zeroes. The constructive algorithm of computation of polynomial representation of the discriminant set is provided. The structure of the discriminant set is linked with the problems of natural numbers partitions. Different algorithms of computation of subdiscriminants of the polynomial are discussed as well. The main algorithms, described in the preprint, are organized as a library for the computer algebra system Maple.