Comments on the height reducing property

Shigeki Akiyama; Toufik Zaimi

Displaying similar documents to “Comments on the height reducing property”

On Roots of Polynomials with Positive Coefficients

Toufik Zaïmi (2011)

Publications de l'Institut Mathématique

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Root separation for reducible monic quartics

Andrej Dujella, Tomislav Pejković (2011)

Rendiconti del Seminario Matematico della Università di Padova

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Algebraic condition for decomposition of large-scale linear dynamic systems

Henryk Górecki (2009)

International Journal of Applied Mathematics and Computer Science

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The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization...

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].

Diophantine approximation in power series fields

Wolfgang Schmidt (1977)

Acta Arithmetica

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Simple polynomials

Miloš Kössler (1951)

Czechoslovak Mathematical Journal

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On Rolle's theorem for polynomials over the complex numbers.

Gallardo, Luis H. (2006)

Applied Mathematics E-Notes [electronic only]

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Polynomial squares of the form $a X^{m} + b {(1 - X)}^{n} + c$

Umberto Zannier (2004)

Rendiconti del Seminario Matematico della Università di Padova

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Solving quadratic equations over polynomial rings of characteristic two.

Jorgen Cherly, Luis Gallardo, Leonid Vaserstein, Ethel Wheland (1998)

Publicacions Matemàtiques

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We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation a_ntⁿ + ...+ a₀ = 0 with coefficients a_i in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction,...

Zhang-Zagier heights of perturbed polynomials

Christophe Doche (2001)

Journal de théorie des nombres de Bordeaux

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In a previous article we studied the spectrum of the Zhang-Zagier height [2]. The progress we made stood on an algorithm that produced polynomials with a small height. In this paper we describe a new algorithm that provides even smaller heights. It allows us to find a limit point less than $1.289735$ i.e. better than the previous one, namely $1.2916674$ . After some definitions we detail the principle of the algorithm, the results it gives and the construction that leads to this new limit point. ...