On the computation of totally real quartic fields of small discriminant

Buchmann, Johannes; Ford, David

doi:10.1090/S0025-5718-1989-0946599-1

On the computation of totally real quartic fields of small discriminant
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by Johannes Buchmann and David Ford PDF

Math. Comp. 52 (1989), 161-174 Request permission

Abstract:

All totally real quartic fields of discriminant less than ${10^6}$ are computed. The method used to generate the fields is derived from Delone and Faddeev, with corrections and improvements. A new method for deciding field isomorphism is used to eliminate redundant examples. Integral bases and Galois groups are given for each field.

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