分野別セミナー

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.