Abstract
Computing the class group and regulator of an algebraic number field K are two major tasks of algorithmic algebraic number theory. The asymptotically fastest method known has conjectured sub-exponential running time and was proposed in [5]. In this paper we show how sieving methods developed for factoring algorithms can be used to speed up this algorithm in practice. We present numerical experiments which demonstrate the efficiency of our new strategy. For example, we are able to compute the class group of an imaginary quadratic field with a discriminant of 55 digits 20 times as fast as S. Düllmann in an earlier record-setting implementation ([1]) which did not use sieving techniques. We also present class numbers of large cubic fields.
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Buchmann, J., Jacobson, M.J., Neis, S., Theobald, P., Weber, D. (1999). Sieving Methods for Class Group Computation. In: Matzat, B.H., Greuel, GM., Hiss, G. (eds) Algorithmic Algebra and Number Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59932-3_1
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DOI: https://doi.org/10.1007/978-3-642-59932-3_1
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