Computing the Galois group of a polynomial over a p-adic field

被引：1

作者：

Doris, Christopher ^{[1
]}

机构：

[1] Univ Bristol, Sch Math, Heilbronn Inst Math Res, Bristol BS8 1UG, Avon, England

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2020年 / 16卷 / 08期

关键词：

p-Adic fields; Galois theory; computation; EXTENSIONS;

D O I：

10.1142/S179304212050092X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Q(2) of degrees 18, 20 and 22, tables of which are available online.

引用

页码：1767 / 1801

页数：35

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