Sage: Ticket #17159: Stirling numbers at negative integers
https://trac.sagemath.org/ticket/17159
<p>
Inconsistent behaviour of the Stirling numbers at negative integers
and insufficient documentation of these cases.
</p>
<p>
(1) stirling_number2(-3, -5) gives <a class="missing wiki">OverflowError?</a>.
</p>
<p>
(2) stirling_number2(-3, -5,"maxima") gives <a class="missing wiki">TypeError?</a>.
</p>
<p>
(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).
</p>
<p>
(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).
</p>
<p>
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?)
</p>
<p>
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 <a class="missing wiki">Graham/Knuth/Patashnik?</a> in 'Concrete Mathematics'
Section 6.1 (see Table 253).
</p>
<p>
Also, use libGAP not GAP, as was done in <a class="closed ticket" href="https://trac.sagemath.org/ticket/16719" title="defect: replace gap.eval with libgap calls in combinat/combinat.py (closed: fixed)">#16719</a>.
</p>
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https://trac.sagemath.org/ticket/17159
Trac 1.1.6rwsWed, 15 Oct 2014 13:00:38 GMTdescription changed
https://trac.sagemath.org/ticket/17159#comment:1
https://trac.sagemath.org/ticket/17159#comment:1
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