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… 

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References

SHOWING 1-9 OF 9 REFERENCES

Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten.

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

Algebraic equations with span less than 4

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

      Metz Cedex E-mail: georges.rhin@univ-lorraine