On Wednesday, July 24, 2019 at 7:43:10 AM UTC-7, Michael Beeson wrote: > > SageMath has built-in functions to compute the regulator and the > fundamental unit of a quadratic field. The regulator of a quadratic field > is the log of the absolute value of the fundamental unit. > So, the following code should print out the same number on each line. > But, as you can check, it does so only some of the time. Try > checkRegulator(30) for example. I am using version 8.7. > I also wrote other code (not included here) based on the Dedekind zeta > function to compute the regulator. It agrees with SageMath's "regulator" > function rather than with log of the fundamental unit. > > def checkRegulator(N): > for d in range(3,N): > if not is_squarefree(d): > continue > K.<a> = QuadraticField(d) > G = K.unit_group() > u = G.gen(1).value(); > Rdirect = abs(n(log(u))) >
I think your problem is here: you need to take abs(u) before taking the log; otherwise you can get some funny complex number back. You also want to take the embedding into R that is larger than 1 in absolute value, but if you take the abs of the log afterwards it doesn't matter. > RSage = K.regulator() > print(d,RSage,Rdirect) > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/6caa4472-67ae-454e-8150-90c7148c61ad%40googlegroups.com.
