New techniques for computing the ideal class group and a system of fundamental units in number fields

Details New techniques for computing the ideal class group and a system of fundamental units in number fields New techniques for computing the ideal class group and a system of fundamental units in number fields

2012-04-05

arxiv.org/abs/1204.1294v1

Mathematics

Number Theory

17 pages

Scientific paper

We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use sieving techniques adapted from the number field sieve algorithm to derive relations between elements of the ideal class group, and $p$-adic approximations to manage the loss of precision during the computation of units. This new algorithm is particularily efficient for number fields of small degree for which a speed-up of an order of magnitude is achieved with respect to the standard methods.

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