Computations with p-adic numbers

Xavier Caruso (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LFANT - Lithe and fast algorithmic number theory

This document contains the notes of a lecture I gave at the "Journées Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts: first, we present various implementations of p-adic numbers and compare them and second, we introduce a general framework for studying precision issues and apply it in several concrete situations.

Mots clés: p-adic numbers

Domaines: Théorie des nombres [math.NT]; Calcul formel [cs.SC]; Analyse numérique [cs.NA]

Xavier Caruso. Computations with p-adic numbers. Journées Nationales de Calcul Formel, In press, Les cours du CIRM. ⟨hal-01444183⟩