On the computation of unit groups and class groups of totally real quartic fields

Buchmann, J.; Pohst, M.; von Schmettow, J.

doi:10.1090/S0025-5718-1989-0970698-1

On the computation of unit groups and class groups of totally real quartic fields
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by J. Buchmann, M. Pohst and J. von Schmettow PDF

Math. Comp. 53 (1989), 387-397 Request permission

Abstract:

In this paper we describe the computation of a system of fundamental units and of the class group for each totally real quartic field $\mathcal {F}$ of discriminant less than ${10^6}$. Generating equations, integral bases, and the Galois groups for all those fields were recently given by Buchmann and Ford.

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Über die Berechnung von Klassengruppen algebraischer Zahlkörper