Computation of integral bases

Let A be a Dedekind domain, K the fraction field of A, and f∈. A[. x] a monic irreducible separable polynomial. For a given non-zero prime ideal p of A we present in this paper a new characterization of a p-integral basis of the extension of K determined by f. This characterization yields in an algorithm to compute p-integral bases, which is based on the use of simple multipliers that can be constructed with the data that occurs along the flow of the Montes Algorithm. Our construction of a p-integral basis is significantly faster than the similar approach from [8] and provides in many cases a priori a triangular basis.