#17123: Extending binomial(n,k) to negative integers n, k.
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Reporter: pluschny | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: binomial | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pluschny):
Darij: "If it is an extension, then call it `binomial_extension`
or whatever; do not usurp `binomial`."
Volker's proposal above is: "We could also have an optional
keyword argument binomial(n, k, extension='Knuth')". This
looks like a good idea to me, perhaps better with the name
'symmetrical' instead of 'Knuth'.
Darij: "Maple and Mathematica do not set standards in combinatorics."
But you can also not ignore them especially as Sage's
mission is to become a viable alternative to theses systems.
"We should be going for the definition which is the most
reliable and standard in *mathematical* literature. And
here it is the 0 one."
I agree. But this does not mean that we should block
interesting developments either. Volker's proposal shows
the way.
On a side note: Don Knuth is known to be happily hacking
with Mathematica for a long time
http://www-cs-faculty.stanford.edu/~uno/screen.jpeg
and reading his 'Convolution Polynomials' with it's many
implicit and explicit uses of the binomial function I
do not see him complain about the way Mathematica defines it.
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Ticket URL: <http://trac.sagemath.org/ticket/17123#comment:20>
Sage <http://www.sagemath.org>
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