For a prime $p$, the OM algorithm finds the $p$-adic factorization of an irreducible polynomial $f\in \mathbb{Z}[x]$ 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 $f$.

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全局积分基的无平方 OM 计算

对于一个素数$p$, OM 算法找到$p$-不可约多项式的进数因式分解$F\in \mathbb{Z}[X]$在多项式时间内。这可以应用于构建$p$- 数字字段中的整数碱基$ķ$被定义为$F$. 在本文中，我们采用 OM 技术来处理正整数$ñ$代替$p$. 作为一个应用程序，我们获得了一种计算全局积分基的算法$ķ$，这不需要事先对 的判别式进行因式分解$F$.