12 Nov 18:58 2012

## Re: analytic_rank() discussed on mathoverflow

Nils Bruin <nbruin <at> sfu.ca>

2012-11-12 17:58:51 GMT

2012-11-12 17:58:51 GMT

On Nov 12, 9:46 am, Dima Pasechnik <dimp... <at> gmail.com> wrote: > please have a look (and perhaps reply - I am not an expert on this > stuff): It has to check that a certain analytic function vanishes to 8th order at a particular point. That involves proving that all its derivatives up to 7th order vanish at the point. It's the*proving*that's hard. However, proving that they're not 0 is straightforward: Just approximate to sufficient precision. Thus, if sage gets it wrong and pari and magma get it right then it looks like sage gets a precision bound wrong somewhere. One would normally expect that a routine like this will err by*overestimating*the order of vanishing, since underestimating involves saying "I cannot really distinguish this approximated value from zero, but I bet it's nonzero". That, or sage is correct and we're looking at a counterexample of the Birch--Swinnerton-Dyer conjecture. -- -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel <at> googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscribe <at> googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.