On 7/24/07, Nick Alexander <[EMAIL PROTECTED]> wrote:
> "Alec Mihailovs" <[EMAIL PROTECTED]> writes:
>
> > May I suggest to add timing to the examples in the documentation - that
> > would be very useful.
> >
> > For example, in recent discussion about Bell numbers on the math-fun list,
> > it was noted that it takes a very long time to calculate bell(1000) in Maple
> > while BellB[1000] in Mathematica is much faster. I looked at the
> > corresponding section in SAGE Reference manual,
> >
> > http://modular.math.washington.edu/sage/doc/html/ref/module-sage.combinat.combinat.html
> >
> > and couldn't tell how much time it takes in SAGE (probably, rather long,
> > because it wraps GAP's Bell.)
>
> sage: sage.combinat.expnums.expnums(10, 1)
>  [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
>
> for computing Bell numbers quickly.  It's not asymptotically faster
> than Gap, but it is fairly tuned.

Nick,

On this topic, SAGE's bell_number command currently still *calls*
GAP.  It seems to me it should call your expnums function.  What
do you think?  Should it cache answers?  Thoughts?  Basically
I want to improve SAGE's bell_number command so it isn't so slow
by using your expnums function.  Also, I wonder what the memory
issues are.

 -- William

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