Institute of Mathematics for Industry

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P-adic precision of the characteristic polynomial


Hold Date 2017-10-27 15:00~2017-10-27 16:00

Place Seminar Room W1-C-716, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Tristan Vaccon (Université de Limoges, France)

Abstract:
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.