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

@article{Otmani2013IntegerLP, title={Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4}, author={S. El Otmani and A. Maul and Georges Rhin and Jean-Marc Sac-{\'E}p{\'e}e}, journal={Journal de Theorie des Nombres de Bordeaux}, year={2013}, volume={25}, pages={71-78} }

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…

## 4 Citations

### Searching for Hyperbolic Polynomials with Span Less than 4

- MathematicsExp. Math.
- 2022

Abstract A monic, irreducible polynomial in one variable having integer coefficients and all real roots deserves particular interest if its roots lie in an interval of length 4 whose end-points are…

### Chebyshev coordinates and Salem numbers

- Mathematics
- 2018

By expressing polynomials in the basis of Chebyshev polynomials, certain families of hyperbolic polynomials appear naturally. Some of these families have all their roots in the interval $[-2,2]$. In…

### Finding Degree-16 Monic Irreducible Integer Polynomials of Minimal Trace by Optimization Methods

- MathematicsExp. Math.
- 2014

In this paper, we give a list of monic integer polynomials of smallest possible trace, irreducible, of degree 16, and having all roots real and positive. Moreover, we think that this list may be…

### On hyperbolic small-span CNS polynomials

- Mathematics
- 2018

We characterize hyperbolic small-span CNS polynomials of degree up to 4.

## References

SHOWING 1-9 OF 9 REFERENCES

### Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten.

- Mathematics
- 1857

L W enn die Wurzeln einer ganzzahligen Gleichung, in welcher der erste Coefficient Eins ist, alle imaginär und ihre analytischen Moduln sämmtlich gleich Eins sind, so müssen dieselben stets Wurzeln…

### Metz Cedex E-mail: jean-marc.sac-epee@univ-lorraine

### Intervals containing infinitely many sets of conjugate algebraic integers

- Studies in Mathematical Analysis and Related Topics: Essays in honor of George Pólya, Stanford Univ. Press, 1962, 305-315. MR0144892

### Message Passing Interface (MPI) Forum Home Page

- http://www.mpi-forum. org/
- 2009

### Metz Cedex E-mail: armand.maul@univ-lorraine

### The Totally Real Algebraic Integers with Diameter less than 4

- Moscow Journal of Combinatorics and Number Theory Vol. 1
- 2011