论文信息 - An Improved Method of Computing the Regulator of a Real Quadratic Function Field

An Improved Method of Computing the Regulator of a Real Quadratic Function Field

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.

Andreas Stein | Hugh C. Williams | A. Stein | H. Williams

[1] Marvin C. Wunderlich,et al. On the parallel generation of the residues for the continued fraction factoring algorithm , 1987 .

[2] Johannes Buchmann,et al. On the computation of the class number of an algebraic number field , 1989 .

[3] A. Stein. Equivalences between elliptic curves and real quadratic congruence function fields , 1997 .

[4] H. Lenstra. On the calculation of regulators and class numbers of quadratic fields , 1982 .

[5] Andreas Stein,et al. Some Methods for Evaluating the Regulator of a Real Quadratic Function Field , 1999, Exp. Math..

[6] Andreas Stein,et al. An algorithm for determining the regulator and the fundamental unit of hyperelliptic congruence function field , 1991, ISSAC '91.

[7] Friedrich Karl Schmidt,et al. Analytische Zahlentheorie in Körpern der Charakteristik p , 1931 .

[8] E. Artin,et al. Quadratische Körper im Gebiete der höheren Kongruenzen. I. , 1924 .

[9] Andreas Stein,et al. Key-exchange in real quadratic congruence function fields , 1996 .

[10] H. C. Williams,et al. Computation of real quadratic fields with class number one , 1988 .

[11] H. C. Williams,et al. Some computational results on a problem concerning powerful numbers , 1988 .