On computing subfields. A detailed description of the algorithm

J. Klüners, Journal de Theorie Des Nombres de Bordeaux 10 (1998) 243–271.

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Journal Article | Published | English
Abstract
Let ℚ(α) be an algebraic number field given by the minimal polynomial f of α. We want to determine all subfields ℚ(β) ⊂ Q(α) of given degree. It is convenient to describe each subfield by a pair (g, h) ∈ Z [t] x ℚ[t] such that g is the minimal polynomial of β = h(α) . There is a bijection between the block systems of the Galois group of f and the subfields of ℚ(α). These block systems are computed using cyclic subgroups of the Galois group which we get from the Dedekind criterion. When a block system is known we compute the corresponding subfield using p- adic methods. We give a detailed description for all parts of the algorithm.
Publishing Year
Journal Title
Journal de Theorie des Nombres de Bordeaux
Volume
10
Issue
2
Page
243-271
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Klüners J. On computing subfields. A detailed description of the algorithm . Journal de Theorie des Nombres de Bordeaux. 1998;10(2):243-271. doi:https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0
Klüners, J. (1998). On computing subfields. A detailed description of the algorithm . Journal de Theorie Des Nombres de Bordeaux, 10(2), 243–271. https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0
@article{Klüners_1998, title={On computing subfields. A detailed description of the algorithm }, volume={10}, DOI={https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0}, number={2}, journal={Journal de Theorie des Nombres de Bordeaux}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={1998}, pages={243–271} }
Klüners, Jürgen. “On Computing Subfields. A Detailed Description of the Algorithm .” Journal de Theorie Des Nombres de Bordeaux 10, no. 2 (1998): 243–71. https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0.
J. Klüners, “On computing subfields. A detailed description of the algorithm ,” Journal de Theorie des Nombres de Bordeaux, vol. 10, no. 2, pp. 243–271, 1998, doi: https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0.
Klüners, Jürgen. “On Computing Subfields. A Detailed Description of the Algorithm .” Journal de Theorie Des Nombres de Bordeaux, vol. 10, no. 2, Elsevier BV, 1998, pp. 243–71, doi:https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0.
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