Computing Automorphisms of Abelian Number Fields
Klüners, Jürgen
Acciaro, Vincenzo
Let L = ℚ(α) be an abelian number field of degree n. Most
algorithms for computing the lattice of subfields of L require the computation
of all the conjugates of α. This is usually achieved by factoring the minimal
polynomial mα(x) of α over L. In practice, the existing algorithms for factoring
polynomials over algebraic number fields can handle only problems of moderate
size. In this paper we describe a fast probabilistic algorithm for computing
the conjugates of α, which is based on p-adic techniques. Given mα(x) and a
rational prime p which does not divide the discriminant disc(mα(x)) of mα(x),
the algorithm computes the Frobenius automorphism of p in time polynomial
in the size of p and in the size of mα(x). By repeatedly applying the algorithm
to randomly chosen primes it is possible to compute all the conjugates of α.
American Mathematical Society (AMS)
1999
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://ris.uni-paderborn.de/record/35941
Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>. 1999;68(227):1179-1186.
eng
info:eu-repo/semantics/altIdentifier/issn/1088-6842
info:eu-repo/semantics/altIdentifier/issn/0025-5718
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