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The computation of sextic fields with a cubic subfield and no quadratic subfield. (English) Zbl 0746.11041

The author refines known methods for computing large tables of relative quadratic extensions \(K\) of cubic fields \(k\) for all possible signatures. This is under the assumption that \(K\) does not contain a quadratic subfield since the latter case was already considered in [A. M. Bergé, J. Martinet and the author, Math. Comput. 54, 869-884 (1990; Zbl 0709.11056)]. The resulting tables contain lots of useful information. For example, a generating polynomial over the cubic subfield \(k\) and the Galois group of the normal closure are listed. — The first 200 fields (with respect to the size of the absolute value of the discriminant) for each potential signature of \(K/k\) appeared in [the author, Sémin. Théor. Nombres Bordx., Ser. II 3, No. 1, 201-245 (1991; Zbl 0726.11081)]. The data can be requested from the author.

MSC:

11R11 Quadratic extensions
11R32 Galois theory
11Y40 Algebraic number theory computations
11-04 Software, source code, etc. for problems pertaining to number theory
11R21 Other number fields
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References:

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