Re: intnum() unfortunate events

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

On Thu, Aug 06, 2009 at 03:18:57PM -0700, Ilya Zakharevich wrote:
> ? f(N)=intnum(X=-N,N, erfc(X)*X) + erfc(-N)*N^2/2 - erfc(N)*N^2/2
> ? for(P=1,15, default(realprecision,10*P); print(10*P, " => ", f(100)))
> 10 => 3.662944319
> 20 => 0.92567475529080305843
> 
> Note that this is a very different situation than spikes in the
> integrant (which ARE very hard to detect).  THIS ("jumps" of a
> function sitting between grid points) would be detected by ANY minor
> shift in the integration grid...
> 
> Any thoughts?

I supopose this is with PARI 2.3
PARI 2.4.2 intnum does not use grid points anymore, however it has strong
regularity requirement on the complex plane.

With PARI svn and splitting the integral at 0, you get the correct result:

f(N)=intnum(X=-N,0, erfc(X)*X) + intnum(X=0,N, erfc(X)*X) +  erfc(-N)*N^2/2 - erfc(N)*N^2/2
for(P=1,15, default(realprecision,10*P); print(10*P, " => ", f(100)))
10 => 0.5000000000
20 => 0.50000000000000000000
30 => 0.500000000000000000000000000000
40 => 0.5000000000000000000000000000000000000000

Cheers,
Bill.