Computation of integral bases

Let A be a Dedekind domain, K the fraction field of A  , and f∈A[x]f∈A[x] a monic irreducible separable polynomial. For a given non-zero prime ideal pp of A   we present in this paper a new characterization of a pp-integral basis of the extension of K determined by f  . This characterization yields in an algorithm to compute pp-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 pp-integral basis is significantly faster than the similar approach from [8] and provides in many cases a priori a triangular basis.