Sur la précision p-adique du polynôme caractéristique

par Tristan Vaccon (XLIM - MATHIS)

jeudi 15 juin 2017, 11:00 → 11:30 Europe/Paris

Salle XR203 (Bâtiment XLIM)

Characteristic polynomial is one of the most fundamental tools in linear algebra. Its effective computation has been heavily studied, resulting in near-optimal fast algorithm. The computation of characteristic polynomial of a p-adic matrix is used in Kedlaya's celebrated counting-point on hyperelliptic curves algorithm. As p-adic numbers can only be processed on a computer at finite precision, this raises the issue of the behaviour of precision on the computation of characteristic polynomials over matrices with p-adic coefficients. In this talk, we will introduce the method of differential precision to track p-adic precision, and apply it to the computation of characteristic polynomials. This is joint work with Xavier Caruso and David Roe.