Jordi Guàrdia, Enric Nart
Published 2015-10-07Version 1
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.
DISCRIMINANT and integral basis OF $\mathbb{Q}(\sqrt[12]{a})$
Discriminant and integral basis of pure nonic fields
Discriminant and Integral basis of sextic fields defined by x^6+ax+b
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