Séminaire Calcul Formel

Sur la précision p-adique du polynôme caractéristique

par Tristan Vaccon (XLIM - MATHIS)

Europe/Paris
Salle XR203 (Bâtiment XLIM)

Salle XR203

Bâtiment XLIM

Description
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.
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