#17157: Improve formula for Bell numbers
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Reporter: jdemeyer | Owner:
Type: enhancement | Status: positive_review
Priority: minor | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers: Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/17157 | c93c4e92544c2cc2cca5119b95a31b0e62969797
Dependencies: #16428 | Stopgaps:
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Changes (by tscrim):
* status: needs_review => positive_review
* reviewer: => Travis Scrimshaw
Comment:
Some timings:
{{{
sage: %timeit bell_number(200)
1000 loops, best of 3: 612 µs per loop
sage: %timeit bell_number(200, algorithm='dobinski')
100 loops, best of 3: 2.2 ms per loop
sage: %timeit bell_number(200, algorithm='gap')
1 loops, best of 3: 21 ms per loop
sage: %timeit bell_number(200, algorithm='mpmath')
10 loops, best of 3: 21.2 ms per loop
sage: %timeit bell_number(1000)
10 loops, best of 3: 40.1 ms per loop
sage: %timeit bell_number(1000, algorithm='dobinski')
10 loops, best of 3: 49.5 ms per loop
sage: %timeit bell_number(1000, algorithm='gap')
1 loops, best of 3: 1.58 s per loop
sage: %timeit bell_number(1000, algorithm='mpmath')
1 loops, best of 3: 737 ms per loop
sage: %timeit bell_number(10000, algorithm='flint')
1 loops, best of 3: 3.57 s per loop
sage: %timeit bell_number(10000, algorithm='dobinski')
1 loops, best of 3: 20 s per loop
}}}
So LGTM.
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Ticket URL: <http://trac.sagemath.org/ticket/17157#comment:16>
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