Division and Slope Factorization of p-Adic Polynomials

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.