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Enumeration of quartic fields of small discriminant. (English) Zbl 0788.11060
Summary: We have previously enumerated totally real (signature 4) [J. Buchmann and D. Ford, Math. Comput. 52, 161-174 (1989; Zbl 0668.12001)] and totally complex (signature 0) [D. Ford, Computational Number Theory, Debrecen 1989, 129-138 (1991; Zbl 0729.11051)] fields.
With the mixed-type case now completed, all algebraic number fields of degree 4 with absolute discriminant $$<10^ 6$$ have been enumerated. Methods from the totally real and totally complex cases were used without major modification. Isomorphism of fields was determined by a method similar to one of Lenstra. The $$T_ 2$$ criterion of Pohst was applied to reduce the number of redundant examples.

##### MSC:
 11Y40 Algebraic number theory computations 11-04 Software, source code, etc. for problems pertaining to number theory 11R16 Cubic and quartic extensions
##### Keywords:
quartic fields; small discriminant
Full Text:
##### References:
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