On 2012-11-12, Nils Bruin <nbr...@sfu.ca> wrote: > On Nov 12, 9:46 am, Dima Pasechnik <dimp...@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. sage: e.cremona_label() '457532830151317a1' sage: e.analytic_rank(leading_coefficient=True) (4, -2.50337480324368498e-9)
here is what I got after some hours of running. e-9 does not look as suspiciosuly small to me... and if I try algorithm='rubinstein' I see the following repeating ad nauseum: *** bug in PARI/GP (Segmentation Fault), please report *** bug in PARI/GP (Segmentation Fault), please report *** bug in PARI/GP (Segmentation Fault), please report -- 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@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
