Displaying similar documents to “Root separation for reducible integer polynomials”

Reciprocal Stern Polynomials

A. Schinzel (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

A partial answer is given to a problem of Ulas (2011), asking when the nth Stern polynomial is reciprocal.

On Roots of Polynomials and Algebraically Closed Fields

Christoph Schwarzweller (2017)

Formalized Mathematics

Similarity:

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].

Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4

Souad El Otmani, Armand Maul, Georges Rhin, Jean-Marc Sac-Épée (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots....