Higher Newton polygons and integral bases

Let A be a Dedekind domain whose field of fractions K   is a global field. Let pp be a non-zero prime ideal of A  , and KpKp the completion of K   at pp. The Montes algorithm factorizes a monic irreducible polynomial f∈A[x]f∈A[x] over KpKp, and provides essential arithmetic information about the finite extensions of KpKp determined by the different irreducible factors. In particular, it can be used to compute a pp-integral basis of the extension of K determined by f  . In this paper we present a new and faster method to compute pp-integral bases, based on the use of the quotients of certain divisions with remainder of f that occur along the flow of the Montes algorithm.