Opened 4 years ago

Last modified 4 years ago

#17159 new defect

Stirling numbers at negative integers

Reported by: pluschny Owned by:
Priority: minor Milestone: sage-6.4
Component: combinatorics Keywords: Stirling numbers
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by rws)

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.

Change History (1)

comment:1 Changed 4 years ago by rws

  • Description modified (diff)
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