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

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.

preprint2010arXivOpen access
Jean-François BiasseJacobson John Michael
math.NT
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Open access2 authors1 topic
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Jean-François BiasseJacobson John Michael

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