Division and Slope Factorization of p-Adic Polynomials
Number Theory
2016-02-04 v1 Symbolic Computation
Abstract
We study two important operations on polynomials defined over complete discrete valuation fields: Euclidean division and factorization. In particular, we design a simple and efficient algorithm for computing slope factorizations, based on Newton iteration. One of its main features is that we avoid working with fractional exponents. We pay particular attention to stability, and analyze the behavior of the algorithm using several precision models.
Cite
@article{arxiv.1602.01303,
title = {Division and Slope Factorization of p-Adic Polynomials},
author = {Xavier Caruso and David Roe and Tristan Vaccon},
journal= {arXiv preprint arXiv:1602.01303},
year = {2016}
}