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Square-free OM computation of global integral bases
Algebra & Number Theory ( IF 0.9 ) Pub Date : 2022-09-27 , DOI: 10.2140/ant.2022.16.1327
Jordi Guàrdia , Enric Nart

For a prime p, the OM algorithm finds the p-adic factorization of an irreducible polynomial f [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.



中文翻译:

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 [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.

更新日期:2022-09-28
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