number of partitions bench mark

[Max Alekseyev]

First,

I confirm that this bug is present in Maple 11 as well.

Also, my code for testing numbpart() values can be found in
http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=557
I used it to discover a bug in PARI's implementation of numbpart() a
year ago. But since this bug was fixed, I found PARI's implementation
quite reliable. In particular, I tested it on some random numbers up
to 10^7 and in all cases it computed correct results.

Regards,
Max

On Mon, May 12, 2008 at 1:48 PM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
>
>  One of the two PARI maintainers indicates that there are differences
>  between the Maple V10 number of partitions (combinat[numbpart])
>  and the current PARI-svn  (the latter based on the Ramanujan-Rademacher
>  formula see src/modules/part.c). It might be helpful if someone with Mma
>  could produce another suite of benchmarks for these n below as some
>  kind of "third party" counter check:
>
>  11269
>  11566
>  12376
>  12430
>  12700
>  12754
>  15013
>  17589
>  17797
>  18181
>  18421
>  18453
>  18549
>  18597
>  18885
>  18949
>  18997
>
>  I do not have access to Mma.
>
>  Richard, http://www.strw.leidenuniv.nl/~mathar
>
>  kb> I believe Maple is wrong in all cases. Quick check:
>  kb>
>  kb> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>  kb> %%
>  kb>
>  kb> ? default(seriesprecision, 12000);
>  kb> ? polcoeff(1/eta('x),11269)
>  kb> %2 = 2311391772313039755144117876494556289590601993601099725578515191051551761
>  kb> 80318215891795874905318274163248033071850
>  kb> ? numbpart(11269)
>  kb> %3 = 2311391772313039755144117876494556289590601993601099725578515191051551761
>  kb> 80318215891795874905318274163248033071850
>  kb>
>  kb> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>  kb> %%
>  kb>
>  kb>     |\^/|     Maple 10 (IBM INTEL LINUX)
>  kb> ._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005
>  kb>  \  MAPLE  /  All rights reserved. Maple is a trademark of
>  kb>  <____ ____>  Waterloo Maple Inc.
>  kb>       |       Type ? for help.
>  kb>
>  kb> > combinat[numbpart](11269);
>  kb> 231139177231303975514411787649455628959060199360109972557851519105155176180\
>  kb>     318215891795874905318274163248033071851
>  kb> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>  kb> %%
>  kb>
>  kb> Cheers,
>  kb>
>  kb>     K.B.
>
>