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

  • Andreas Stein
  • Hugh C. Williams
Conference paper

DOI: 10.1007/BFb0054896

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

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(q2/5g) 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(q2/5) polynomial operations. We show how we increased the speed of the O(q2/5g)-algorithm such that we are able to large values of regulators of real quadratic congruence function fields of small genus.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Andreas Stein
    • 1
  • Hugh C. Williams
    • 1
  1. 1.University of ManitobaWinnipegCanada

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