✦ LIBER ✦

Subexponential Algorithms for Class Group and Unit Computations

✍ Scribed by H. COHEN; F. DIAZ Y DIAZ; M. OLIVIER

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 351 KB
Volume: 24
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1996.0143

No coin nor oath required. For personal study only.

✦ Synopsis

We describe in detail the implementation of an algorithm which computes the class group and the unit group of a general number field, and solves the principal ideal problem. The basic ideas of this algorithm are due to J. Buchmann. New ideas are the use of LLL-reduction of an ideal in a given direction which replaces the notion of neighbour, and the use of complex logarithmic embeddings of elements which plays a crucial role. Heuristically the algorithm performs in sub-exponential time with respect to the discriminant for fixed degree, and performs well in practice.

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