Practical improvements to class group and regulator computation of real quadratic fields

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Abstract

We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying the double large prime strategy, an improved structured Gaussian elimination strategy, and the use of Bernstein's batch smoothness algorithm. We achieve a significant speed-up and are able to compute the ideal class group structure and the regulator corresponding to a number field with a 110-decimal digit discriminant. © 2010 Springer-Verlag Berlin Heidelberg.

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APA

Biasse, J. F., & Jacobson, M. J. (2010). Practical improvements to class group and regulator computation of real quadratic fields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 50–65). https://doi.org/10.1007/978-3-642-14518-6_8

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