#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 | Resolution:
Keywords: Stirling numbers | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by rws:
Old description:
> 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).
New description:
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).
Also, use libGAP not GAP, as was done in #16719.
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Ticket URL: <http://trac.sagemath.org/ticket/17159#comment:1>
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