#### Conference abstracts

Session A3 - Computational Number Theory

July 12, 17:40 ~ 18:20 - Room B6

## Genetics of polynomials over local fields

### Guàrdia Jordi

### Universitat Politècnica de Catalunya, Catalunya - jordi.guardia-rubies@upc.edu

Let $(K,v)$ be a discrete valued field with valuation ring $\mathcal{O}$, and let $\mathcal{O}_v$ be the completion of $\mathcal{O}$ with respect to the $v$-adic topology. In our talk we will discuss the advantages of manipulating polynomials in $\mathcal{O}_v[x]$ in a computer by means of OM representations of prime polynomials. An OM representation supports discrete data that are a kind of DNA sequence common to all individuals in the Okutsu equivalence class of the prime polynomial. These discrete parameters contain relevant arithmetic information about the polynomial and the extension of $K_v$ it determines.

Joint work with Enric Nart (Universitat Autònoma de Barcelona, Catalonia).