## 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

### Citations:

Zbl 0709.11056; Zbl 0726.11081
Full Text:

### References:

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