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P-adic precision of the characteristic polynomial

Hold Date
2017-10-27 15:00〜2017-10-27 16:00
Seminar Room W1-C-716, West Zone 1, Ito campus, Kyushu University
Object person
Tristan Vaccon (Université de Limoges, France)

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.