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固有多項式のp進精度 (p-adic precision of the characteristic polynomial)


開催時期 2017-10-27 15:00~2017-10-27 16:00

場所 九州大学 伊都キャンパス ウエスト1号館 中セミナー室 W1-C-716

受講対象  

講師 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.