We present a new method to propagate p-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy application to the stableâ€¦ (More)

In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division andâ€¦ (More)

We design an algorithm for computing the <i>p</i>-curvature of a differential system in positive characteristic <i>p</i>. For a system of dimension <i>r</i> with coefficients of degree at mostâ€¦ (More)

Let R be a discrete valuation ring (DVR) and K be its fraction field. If M is a matrix over R admitting a LU decomposition, it could happen that the entries of the factors L and U do not lie in R,â€¦ (More)

Using the differential precision methods developed previously by the same authors, we study the p-adic stability of standard operations on matrices and vector spaces. We demonstrate thatâ€¦ (More)

Let R be a complete discrete valuation ring, S = R[[u]] and n a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection ofâ€¦ (More)

We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). Weâ€¦ (More)

We discuss theoretical and algorithmic questions related to the <i>p</i>-curvature of differential operators in characteristic <i>p</i>. Given such an operator <i>L</i>, and denoting by Îž(<i>L</i>)â€¦ (More)