Re: Functions elllderiv and ellanalyticrank

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sat, Dec 20, 2008 at 10:16:23AM +0100, Karim Belabas wrote:
> * Bill Allombert [2008-12-19 23:20]:
> > On Fri, Dec 19, 2008 at 07:20:53PM +0100, Karim Belabas wrote:
> > > > 2) I think elllderiv should be renamed ellL1 for consistency with bnrL1
> > > > (and maybe add a flag so that both functions have the same semantic).
> 
> Had forgotten to commit this one, sorry. No flag added: contrary to bnrL1, we
> compute the value at the center of the critical strip, so no symmetry
> in the special value here.

I'd like to clarify something:
Is it correct that bnrL1 returns L^(r)(0, chi)/r! and ellL1 returns L^(r)(1)?
The 1/r! missing factor is slighly inconsistent. However the functions
are already sufficiently differents so that it might not matter to much.

> > Also the DEBUG message should be improved to be more useful.
> 
> Done to some extent, I think. More specific suggestions (svn11475 and above) ?

I'd like timing of each ellL1 computation done by ellanalyticrank 
separately.

> > I just checked the first curves for each rank <=7, and it worked fine.
> > For the rank 7, and curve [0,1,0,-5945,583879], we get:
> > 
> > %3 = [7, 10410274.011880989226208667596394924308]
> >   ***   last result computed in 32mn, 22,973 ms.
> 
> Yes, point A) has recently been fixed.

Actually I think I ran it with 2GB of stack before this fix.

...

With \p38, ellanalytic rank fails on a large number (about 1/3 so far)
of rank 5 curve in Womack database (it reports rank 1 instead of 5).  

An example: [0, 0, 0, -5187, 176830]
? \p38
   realprecision = 38 significant digits
? ellanalyticrank(ellinit([0, 0, 0, -5187, 176830]))
%102 = [1, 1278372.8304848296806080373284485378614]
? ##
  ***   last result computed in 2,248 ms.
? \p100
   realprecision = 115 significant digits (100 digits displayed)
? ellanalyticrank(ellinit([0, 0, 0, -5187, 176830]))
%103 = [1, -5.325940321646741761873678862473973257966395825229515552647757138732472557105569149428617123587867198 E-5]
? ##
  ***   last result computed in 23,654 ms.
? \p300
   realprecision = 308 significant digits (300 digits displayed)
? ellanalyticrank(ellinit([0, 0, 0, -5187, 176830]))
%104 = [1, 1.03109774801654317703165538440292385425270140765489094906701694740003883225307680175789397957995636774656436968392004550456741982003305244178599175383191237909663561224188478459850675217896796053901785562987093216560935193453313209662350084597201356139829756733116552495511875367665860023212578851892 E-19]
? ##
  ***   last result computed in 6mn, 45,577 ms.

Clearly the value L'(1) is worng (independently of the rank of the
curve).

Cheers,
Bill.