#### Vol. 16, No. 6, 2022

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Square-free OM computation of global integral bases

### Jordi Guàrdia and Enric Nart

Vol. 16 (2022), No. 6, 1327–1376
##### Abstract

For a prime $p$, the OM algorithm finds the $p$-adic factorization of an irreducible polynomial $f\in ℤ\left[x\right]$ in polynomial time. This may be applied to construct $p$-integral bases in the number field $K$ defined by $f$. In this paper, we adapt the OM techniques to work with a positive integer $N$ instead of $p$. As an application, we obtain an algorithm to compute global integral bases in $K$, which does not require a previous factorization of the discriminant of $f$.

##### Keywords
integral basis, Newton polygons, OM algorithm
Primary: 11R04
Secondary: 11Y40