#17159: Stirling numbers at negative integers
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Reporter: pluschny | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.4
Component: combinatorics | Keywords: Stirling numbers
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Inconsistent behaviour of the Stirling numbers at negative integers
and insufficient documentation of these cases.
(1) stirling_number2(-3, -5) gives OverflowError.
(2) stirling_number2(-3, -5,"maxima") gives TypeError.
(3) stirling_number2(-3, -5, "gap") gives 35 which is correct but this
behaviour is not documented (doc says: n and k are nonnegative integers).
(4) stirling_number1(-3, -5) gives 25 which is correct but this
behaviour is not documented (doc implies that n and k are nonnegative
integers).
Proposal: Make GAP’s Stirling2 the default (as is GAP’s Stirling1)
and document the behaviour for negative integers. (Perhaps disregard
'maxima' and the native implementation altogether?)
Remark: The behaviour of GAP's implementation is based on a simple and
coherent extension of the Stirling numbers to negative integers n, k
which was outlined by Graham/Knuth/Patashnik in 'Concrete Mathematics'
Section 6.1 (see Table 253).
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Ticket URL: <http://trac.sagemath.org/ticket/17159>
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