Faculty of Physics - University of Bucharest

UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

Guest
2024-11-23 17:54

HOME CONFERENCES SEARCH LOGIN NEW USER IMAGES

Conference: Bucharest University Faculty of Physics 2014 Meeting

Section: Theoretical Physics and Applied Mathematics

Title:

Applications of the Newton polygon to irreducibility criteria

Authors:

D. STEFANESCU (1),V. GERDT (2)

Affiliation:

1) Faculty of Physics, University of Bucharest

2) Joint Institute for Nuclear Reasearch (Dubna), Laboratory for Inofrmation Technolgy

E-mail

doru.stefanescu@gmail.com

Keywords:

Newton polygon, irreducible polynomials

Abstract:

We consider properties of the Newton polygon associated with a univariate polynomials with the coefficients in a valuation domain (A,v). We compute the Newton index of such a polynomial and give factorization conditions in the case in which the hypotheses in G. Dumas' theorem are not satisfied. This allow us to construct new classes of irreducible polynomials, using computations with the gp=pari package. In particular there are extended criteria for polynomials over the integers and for bivariate polynomials over an agebraically closed field of cahracteristic zero.