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.
\Bibitem{Bat17}
\by A.~B.~Batkhin
\paper Computation of generalized discriminant of a real polynomial
\jour Keldysh Institute preprints
\yr 2017
\papernumber 088
\totalpages 40
\mathnet{http://mi.mathnet.ru/ipmp2304}
\crossref{https://doi.org/10.20948/prepr-2017-88}
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https://www.mathnet.ru/eng/ipmp/y2017/p88
This publication is cited in the following 4 articles:
A. B. Batkhin, “Invariant Coordinate Subspaces of Normal Form of a System of Ordinary Differential Equations”, Program Comput Soft, 47:2 (2021), 99
A. B. Batkhin, “Invariantnye koordinatnye podprostranstva normalnoi formy sistemy obyknovennykh differentsialnykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2020, 072, 23 pp.
V. Shcherban, “Arithmetic Table as an Integral Part of all Computational Mathematics”, BSP, 6:6 (2020), 31
A. B. Batkhin, “Computation of the Resonance Set of a Polynomial under Constraints on Its Coefficients”, Program Comput Soft, 45:2 (2019), 27
Citation in format AMSBIB
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