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This article is cited in 4 scientific papers (total in 5 papers)
Rational expressions for multiple roots of algebraic equations
I. A. Antipova, E. N. Mikhalkin, A. K. Tsikh Siberian Federal University, Krasnoyarsk
Abstract:
The general polynomial with variable coefficients is considered. In terms of the resultants of this polynomials and its derivatives simple rational expressions in the coefficients of the polynomial are found for its multiple zeros. Similar results are extended to systems of $n$ polynomial equations with $n$ unknowns. Justifications of the formulae for multiple roots thus obtained are based on the properties of the logarithmic Gauss map of the discriminant variety of a system of equations and on a linearization procedure for the system. The resulting formulae are of interest not only for theoretical aspects of the algebra of polynomials, but also for numerical mathematics and various areas of applied mathematics connected with finding critical points of polynomial maps.
Bibliography: 20 titles.
Keywords:
general algebraic equation, system of algebraic equations, discriminant variety, multiple root, logarithmic Gauss map.
Received: 29.03.2017 and 31.12.2017
Citation:
I. A. Antipova, E. N. Mikhalkin, A. K. Tsikh, “Rational expressions for multiple roots of algebraic equations”, Mat. Sb., 209:10 (2018), 3–30; Sb. Math., 209:10 (2018), 1419–1444
Linking options:
https://www.mathnet.ru/eng/sm8950https://doi.org/10.1070/SM8950 https://www.mathnet.ru/eng/sm/v209/i10/p3
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Abstract page: | 942 | Russian version PDF: | 249 | English version PDF: | 32 | References: | 63 | First page: | 60 |
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