Relations between polynomial roots

Michael Drmota; Mariusz Skałba

Displaying similar documents to “Relations between polynomial roots”

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Computation of the Galois group of a polynomial with rational coefficients.

Durov, N.V. (2004)

Zapiski Nauchnykh Seminarov POMI

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Computation of the Galois group of a polynomial with rational coefficients. II.

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An extension of the root perturbation $m$ -dimensional polynomial factorization method

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The maximum number of real roots of a multihomogeneous system of polynomial equations.

McLennan, Andrew (1999)

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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].

Abelian varieties over finite fields with a specified characteristic polynomial modulo $ℓ$

Joshua Holden (2004)

Journal de Théorie des Nombres de Bordeaux

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We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial $P (T)$ modulo $ℓ$ . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order $ℓ$ .