---
res:
bibo_abstract:
- "Let L = ℚ(α) be an abelian number field of degree n. Most\r\nalgorithms for computing
the lattice of subfields of L require the computation\r\nof all the conjugates
of α. This is usually achieved by factoring the minimal\r\npolynomial mα(x) of
α over L. In practice, the existing algorithms for factoring\r\npolynomials over
algebraic number fields can handle only problems of moderate\r\nsize. In this
paper we describe a fast probabilistic algorithm for computing\r\nthe conjugates
of α, which is based on p-adic techniques. Given mα(x) and a\r\nrational prime
p which does not divide the discriminant disc(mα(x)) of mα(x),\r\nthe algorithm
computes the Frobenius automorphism of p in time polynomial\r\nin the size of
p and in the size of mα(x). By repeatedly applying the algorithm\r\nto randomly
chosen primes it is possible to compute all the conjugates of α.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Jürgen
foaf_name: Klüners, Jürgen
foaf_surname: Klüners
foaf_workInfoHomepage: http://www.librecat.org/personId=21202
- foaf_Person:
foaf_givenName: Vincenzo
foaf_name: Acciaro, Vincenzo
foaf_surname: Acciaro
bibo_issue: '227'
bibo_volume: 68
dct_date: 1999^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1088-6842
- http://id.crossref.org/issn/0025-5718
dct_language: eng
dct_publisher: American Mathematical Society (AMS)@
dct_title: Computing Automorphisms of Abelian Number Fields@
...