论文标题
计算在$ p $ - adic字段上的多项式的Galois组
Computing the Galois group of a polynomial over a $p$-adic field
论文作者
论文摘要
我们介绍了一种用于计算在$ p $ - adiC领域定义的多项式的算法系列。除了“幼稚”算法之外，这些是该任务的第一个一般算法。作为一个应用程序，我们计算了所有完全分支的扩展名的Galois组，该扩展名为$ \ mathbb {q} _2 _2 $ 18、20和22的学位，其表格可在线提供。
We present a family of algorithms for computing the Galois group of a polynomial defined over a $p$-adic field. Apart from the "naive" algorithm, these are the first general algorithms for this task. As an application, we compute the Galois groups of all totally ramified extensions of $\mathbb{Q}_2$ of degrees 18, 20 and 22, tables of which are available online.
