Computing the Galois group of a polynomial over a p-adic field
نویسندگان
چکیده
منابع مشابه
Computing the Galois group of a polynomial
This article outlines techniques for computing the Galois group of a polynomial over the rationals, an important operation in computational algebraic number theory. In particular, the linear resolvent polynomial method of [6] will be described.
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An n-ary integral quadratic form is a formal expression Q(x1, · · · , xn) = ∑ 1≤i,j≤n aijxixj in nvariables x1, · · · , xn, where aij = aji ∈ Z. We present a randomized polynomial time algorithm that given a quadratic form Q(x1, · · · , xn), a prime p, and a positive integer k outputs a U ∈ GLn(Z/p Z) such that U transforms Q to its p-adic canonical form.
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2020
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304212050092x