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

Souad El Otmani^{[1]}; Armand Maul^{[2]}; Georges Rhin^{[2]}; Jean-Marc Sac-Épée^{[2]}

- [1] Université de Lorraine, site de Metz Ile du Saulcy 57045 Metz Cedex
- [2] Université de Lorraine, site de Metz Ile du Saulcy 57050 Metz Cedex

Journal de Théorie des Nombres de Bordeaux (2013)

- Volume: 25, Issue: 1, page 71-78
- ISSN: 1246-7405

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topEl Otmani, Souad, et al. "Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4." Journal de Théorie des Nombres de Bordeaux 25.1 (2013): 71-78. <http://eudml.org/doc/275691>.

@article{ElOtmani2013,

abstract = {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. These properties can be inferred from those of polynomials already treated in the literature on this topic.},

affiliation = {Université de Lorraine, site de Metz Ile du Saulcy 57045 Metz Cedex; Université de Lorraine, site de Metz Ile du Saulcy 57050 Metz Cedex; Université de Lorraine, site de Metz Ile du Saulcy 57050 Metz Cedex; Université de Lorraine, site de Metz Ile du Saulcy 57050 Metz Cedex},

author = {El Otmani, Souad, Maul, Armand, Rhin, Georges, Sac-Épée, Jean-Marc},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {inequality constraints; roots},

language = {eng},

month = {4},

number = {1},

pages = {71-78},

publisher = {Société Arithmétique de Bordeaux},

title = {Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4},

url = {http://eudml.org/doc/275691},

volume = {25},

year = {2013},

}

TY - JOUR

AU - El Otmani, Souad

AU - Maul, Armand

AU - Rhin, Georges

AU - Sac-Épée, Jean-Marc

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

JO - Journal de Théorie des Nombres de Bordeaux

DA - 2013/4//

PB - Société Arithmétique de Bordeaux

VL - 25

IS - 1

SP - 71

EP - 78

AB - 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. These properties can be inferred from those of polynomials already treated in the literature on this topic.

LA - eng

KW - inequality constraints; roots

UR - http://eudml.org/doc/275691

ER -

## References

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- I. Schur, Über die Verteilung der Würzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten. Math. Z. 1 (1918), 377–402. MR1544303. Zbl46.0128.03MR1544303
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