Local-to-global computation of integral bases without a previous factorization of the discriminant

We adapt an old local-to-global technique of Ore to compute, under certain mild assumptions, an integral basis of a number field without a previous factorization of the discriminant of the defining polynomial. In a first phase, the method yields as a by-product successive splittings of the discriminant. When this phase concludes, it requires a squarefree factorization of some base factors of the discriminant to terminate.