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