Pari source seems to be part in english and some comments and things
are written in french. They seem to have a great zeta function
implementation but the source code is really hard to understand, and
not just because some parts may be in french. It is very complicated
and they also use internal data types a lot. I'd have to get more
familiar with the code in general to understand it.
The zeta function I wrote is pretty much a first draft implementation.
It is not much good when the imaginary part is larger than about 100
I'd think. I'll see if I can improve it. If I can understand the pari
source I'll possibly rewrite some of that since it does appear to work
well.
Regards,
Ruben
On 21/06/2008, at 3:53 AM, Jordi Gutiérrez Hermoso wrote:
On 19/06/2008, Ruben Henner Zilibowitz <[EMAIL PROTECTED]>
wrote:
Ok source code is attached to this email.
Thank you. One comment: you used C complexes, which don't work in C++.
Funny, did you know that C and C++ have mutually incompatible
implementations of complex numbers, at least with gcc?
For inclusion into the GSL, the code should use gsl_complex.h so that
we don't run afoul of this C/C++ silliness. It's a trivial fix; I can
do this myself.
No I didn't rely on the Pari source partly because the author seems
to have
used french names for everything which I couldn't really understand.
Hm, I speak French, but I don't really know much about zeta (I plan to
fix the latter soon). Would it help if I translated the code into
English? Would you able to implement a better complex zeta algorithm
this way?
One caveat though: my implementation of the zeta function seems to
work
well provided the argument isn't far up the "critical strip". In
such cases
a different algorithm will need to be used and I haven't managed to
figure
out how to do that yet.
Well, here's a view of the critical strip from -100 to 100 on the
imaginary axis and 0.4 to 0.6 on the real, the absolute value of zeta
on that strip. It's with rainbow colours, so violet is small (zero)
and red is big.
http://www.cimat.mx/~jordi/piccies/critical-line.jpg
Thank you so much for this,
- Jordi G. H.
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