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An improved method of computing the regulator of a real quadratic function field

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Book cover Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

There exists an effective algorithm for computing the regulator of a real quadratic congruence function field K=k(X)(√D) of genus g=deg(D)/2−1 in O(q 2/5g) polynomial operations. In those cases where the regulator exceeds 108, this algorithm tends to be far better than the Baby step-Giant step algorithm which performs O(q 2/5) polynomial operations. We show how we increased the speed of the O(q 2/5g)-algorithm such that we are able to large values of regulators of real quadratic congruence function fields of small genus.

Research supported by NSERC of Canada Grant #A7649

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Authors and Affiliations

  1. University of Manitoba, R3T 2N2, Winnipeg, MB, Canada

    Andreas Stein & Hugh C. Williams

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  1. Andreas Stein
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  2. Hugh C. Williams
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Stein, A., Williams, H.C. (1998). An improved method of computing the regulator of a real quadratic function field. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054896

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  • DOI: https://doi.org/10.1007/BFb0054896

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

  • eBook Packages: Springer Book Archive

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