Abstract

We describe improvements to the subexponential methods 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. These improvements are particularly efficient for number fields of small degree for which a speedup of an order of magnitude is achieved with respect to the standard methods.

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Mathematical Subject Classification 2000

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