Displaying similar documents to “Overdetermined Strata in General Families of Polynomials”

On Root Arrangements of Polynomial-Like Functions and their Derivatives

Kostov, Vladimir (2005)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12D10. We show that for n = 4 they are realizable either by hyperbolic polynomials of degree 4 or by non-hyperbolic polynomials of degree 6 whose fourth derivatives never vanish (these are a particular case of the so-called hyperbolic polynomial-like functions of degree 4).

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

Ezzaldine, Hayssam, Kostov, Vladimir Petrov (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12D10. In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs. Research partially supported...

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

Kostov, Vladimir (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12D10. We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realized by real polynomials.

On Roots of Polynomials and Algebraically Closed Fields

Christoph Schwarzweller (2017)

Formalized Mathematics

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In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].