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illiam Stein wrote:
> John,
>  
> I'm upgrading SAGE to PARI-2.2.13-beta.  Your script bgc.gp
> doesn't load in the new version of PARI:
>  
> I get this error:
>  
> ? \rbgc
>   *** polcoeff: non existent component in truecoeff.
>  
> This is from the third line of this:
>  
> ellld_ll = -Euler*ellld_s + sum(n=2,30,(-1)^n * zeta(n) / n * ellld_s^n);
> ellld_mm = exp(ellld_ll);
> ellld_pn_coeffs=vector(25,i,polcoeff(ellld_mm,i-1));
>                       ^^^^
>  
> If I print ellld_mm it has precision 17.  If i change the 25
> above to 17, then the file loads fine, and on a (very small)
> bunch of test curves it gives the right answer.
>  
> Thoughts?
>  
> William
>  

Date: Thu, 18 May 2006 13:34:16 +0100
From: "Prof. J. E. Cremona" <John.Cremona@nottingham.ac.uk>
To: wstein@gmail.com
Subject: Re: bgc.gp

I had noticed that too but I did not realise that SAGE was using these
scripts.  I have not worked on this for over a year, since all my
Heegner-point computations shifted to Magma where the huge improvements
by Delaunay and Mark W make mine seem very bad.  It would be good to
improve my gp scripts some time, but there's not time!
 
Your suggested change is fine.  This parameter is in effect an uppoer
bound for the ranks which can be dealt with;  but curves of rank greater
than (say) 10 have such a huge conductor that these series will not
converge sufficiently, so reducing from 25 to 17 will not cause any
problems.
 
John
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