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Séminaire Calcul Formel

Sur la précision p-adique du polynôme caractéristique

by Tristan Vaccon (XLIM - MATHIS)

jeudi 15 juin 2017 de au (Europe/Paris)
at Bâtiment XLIM ( Salle XR203 )
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.