Genetics of polynomials over local fields
Jordi Guàrdia, Enric Nart · Contemporary mathematics - American Mathematical Society · 2015
Let ( K , v ) (K,v) be a discrete valued field with valuation ring O \mathcal {O} , and let O v \mathcal {O}_v be the completion of O \mathcal {O} Wit respect to the v v -adic topology. In this paper we discuss the advantages of manipulating polynomials in O v [ x ] \mathcal {O}_v[x] on a computer by means of OM representations of prime (monic and irreducible) polynomials. An OM representation supports discrete data characterizing the Okutsu equivalence class of the prime polynomial. These discrete parameters are a kind of DNA sequence common to all individuals in the same Okutsu class, and they contain relevant arithmetic information about the polynomial and the extension of K v K_v that it determines.