English

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 n×nn\times n 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 χ\chi(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).

Keywords

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}
}
R2 v1 2026-06-22T18:10:23.761Z