Applications of the Newton Index to the Construction of Irreducible Polynomials

摘要

We use properties of the Newton index associated to a polynomial with coefficients in a discrete valuation domain for generating classes of irreducible polynomials. We obtain factorization properties similar to the case of bivariate polynomials and we give new applications to the construction of families of irreducible polynomials over various discrete valuation domains. The examples are obtained using the package gp-pari.