Characteristic polynomials of p-adic matrices
Number Theory
2017-02-07 v1 Symbolic Computation
Abstract
We analyze the precision of the characteristic polynomial of an p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time O~(n^omega)) for (A) to have precision exactly O(p^N). We also give a O~(n^3) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p^N).
Cite
@article{arxiv.1702.01653,
title = {Characteristic polynomials of p-adic matrices},
author = {Xavier Caruso and David Roe and Tristan Vaccon},
journal= {arXiv preprint arXiv:1702.01653},
year = {2017}
}