On Jul 31, 2007, at 18:36 , William Stein wrote:
>
> Hi,
>
> Just to extend this thread some more, a few remarks.
While we're extending this, here's my $0.02 canadian (:-})
> On sage.math:
> SAGE:
> sage: time n = number_of_partitions(10^7)
> CPU times: user 0.73 s, sys: 0.00 s, total: 0.73 s
> Wall time: 0.73
> sage: time n = number_of_partitions(10^8)
> CPU times: user 8.42 s, sys: 0.00 s, total: 8.42 s
> Wall time: 8.42
> sage: time n = number_of_partitions(10^9)
> CPU times: user 105.82 s, sys: 0.00 s, total: 105.82 s
> Wall time: 105.81
>
> Mathematica:
> sage: time s=mathematica.eval('PartitionsP[10^7]')
> CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
> Wall time: 1.90
> sage: time s=mathematica.eval('PartitionsP[10^8]')
> CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
> Wall time: 9.91
> sage: time s=mathematica.eval('PartitionsP[10^9]')
> CPU times: user 0.03 s, sys: 0.01 s, total: 0.04 s
> Wall time: 70.43
>
> Interesting, SAGE seems better at Mathematica for
> smaller input.)
>
>
> On my OS X core 2 duo 2.33Ghz laptop:
>
> SAGE:
> sage: time n=number_of_partitions(10^7)
> CPU times: user 0.62 s, sys: 0.00 s, total: 0.62 s
> Wall time: 0.62
> sage: time n=number_of_partitions(10^8)
> CPU times: user 6.99 s, sys: 0.02 s, total: 7.00 s
> Wall time: 7.03
> sage: time n=number_of_partitions(10^9)
> CPU times: user 94.71 s, sys: 0.28 s, total: 94.99 s
> Wall time: 95.56
>
> MATHEMATICA:
> sage: time s=mathematica.eval('PartitionsP[10^7]')
> CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
> Wall time: 8.65
> sage: time s=mathematica.eval('PartitionsP[10^8]')
> CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
> Wall time: 48.08
> sage: time s=mathematica.eval('PartitionsP[10^9]')
> CPU times: user 0.04 s, sys: 0.00 s, total: 0.05 s
> Wall time: 350.30
>
> Yep -- Mathematica 5.2 interestingly totally sucks at
> computing the number of partitions on an Intel OSX
> machine... and SAGE rocks.
Checking partition count computation:
On a Core 2 Duo 2.33 Mhz, computing the number of partitions of 10^9:
Mathematica 5.2 (PartitionsP[10^9]: 95.5115 s
Sage 2.7.2.1 (number_of_partitions(10^9): 125.2 s
Jon Bober's code (i386: 'jb 1000000000'): 160 s
I wonder why our Core 2 Duo timings are so different?
All of the executables are "i386" binaries (32-bit x86).
One oddity: Jon Bober's code produced a value ending in
'30457526857797923685688339', while Mathematica and SAGE produced one
ending in '30457526831036667979062760', so they differ.
Justin
--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
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If it weren't for carbon-14, I wouldn't date at all.
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