#10170: Speed up the computation of Bell numbers
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Reporter: gerbicz | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone:
Component: combinatorics | Keywords: bell number
Author: Robert Gerbicz | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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For large n values use the formula:
bell(n)=exp(-1)*sum(k=0,infinity,k**n/k!)
Currently my code beats all known implementations, also sage's code which
wraps GAP's Bell is slow and using lots of memory, and unable to compute
bell_number(n) if n is large.
Some timings on Amd 2.1 GHz:
n time (Wall time)
300 0.01 sec.
1000 0.03 sec.
3000 0.18 sec.
10000 2.88 sec.
30000 46.79 sec.
100000 819.37 sec.
Compare these with another programs:
http://fredrik-j.blogspot.com/2009/03/computing-generalized-bell-
numbers.html
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10170>
Sage <http://www.sagemath.org>
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