Tom Womack on Wed, 7 Jun 2000 15:38:04 +0100 |
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Computing analytic ranks |
I've written some code for computing analytic ranks of elliptic curves using the Buhler-Gross recursive method for computing sums of multiplicative functions. You can download it from http://tom.womack.net/maths/BG.gp and there's some test code in http://tom.womack.net/maths/test-bg.gp I hope the comments are enough to make it self-explanatory: it implements the functions ellanalyticrank(e) = [rank, L^(rank)(1), regulator*sha from BSD-conjecture] ellRegSha(e,r) [where r is the rank of e] = regulator*sha from BSD-conjecture ellSha(e, [pts]) takes a set of points supposed to generate e, and computes the analytic value of sha. I've been fairly careful that my global variables have peculiar names, so this should co-exist reasonably with other packages. Tom