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Mathematics of Computation

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On integral bases in relative quadratic extensions

Authors: M. Daberkow and M. Pohst
Journal: Math. Comp. 65 (1996), 319-329
MSC (1991): Primary 11R04, 11R20, 11Y40
MathSciNet review: 1325866
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Abstract: Let $\mathcal F$ be an algebraic number field and $\mathcal E$ a quadratic extension with $\mathcal E=\mathcal F(\sqrt {\mu})$. We describe a minimal set of elements for generating the integral elements $o_{\mathcal E}$ of $\mathcal E$ as an $o_{\mathcal F}$ module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of $\mathcal E$ as well. In the last section, we present examples of relative integral bases which were computed with the new algorithm and also give some running times.

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Additional Information

M. Daberkow
Affiliation: Technische Universität Berlin, Fachbereich 3, Sekr. Ma8-1, Straße des 17. Juni 136, 10623 Berlin, Germany

M. Pohst
Affiliation: Technische Universität Berlin, Fachbereich 3, Sekr. Ma8-1, Straße des 17. Juni 136, 10623 Berlin, Germany

Received by editor(s): June 17, 1994
Received by editor(s) in revised form: November 29, 1994
Article copyright: © Copyright 1996 American Mathematical Society