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Международная конференция по комплексному анализу, посвященная 75-летию Е. М. Чирки
December 4, 2017 14:00, Moscow, Steklov Mathematical Institute, Conference hall, 9th floor
 


Multiple roots of polynomial systems

A. K. Tsikh

Siberian Federal University, Krasnoyarsk
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A. K. Tsikh
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Abstract: We consider a general polynomial with variable coefficients. The main result involves rational expressions in coefficients for multiple roots of the polynomial which are given in terms of resultants of the polynomial and its derivatives. We also prove similar results for a system of $n$ polynomial equations in $n$ unknowns. Basic tools we use in the proof are properties of the logarithmic Gauss mapping for discriminant set of the system and the linearization procedure. Formulas we present can be applied both in the algebra of polynomials and in problems of applied mathematics concerned with analysis of critical points of the polynomial mappings.++

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