article
Computing Automorphisms of Abelian Number Fields
published
Jürgen
Klüners
author 21202
Vincenzo
Acciaro
author
102
department
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
eng
Mathematics of Computation
1088-6842
0025-5718
682271179-1186
https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf
@article{Klüners_Acciaro_1999, title={Computing Automorphisms of Abelian Number Fields}, volume={68}, number={227}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Acciaro, Vincenzo}, year={1999}, pages={1179–1186} }
Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i>, vol. 68, no. 227, American Mathematical Society (AMS), 1999, pp. 1179–86.
J. Klüners and V. Acciaro, “Computing Automorphisms of Abelian Number Fields,” <i>Mathematics of Computation</i>, vol. 68, no. 227, pp. 1179–1186, 1999.
Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i> 68, no. 227 (1999): 1179–86.
Klüners, J., & Acciaro, V. (1999). Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>, <i>68</i>(227), 1179–1186.
J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.
Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>. 1999;68(227):1179-1186.
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