#12448: The binomial implementation does a quotient of gamma values, which is
wrong
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Reporter: Snark | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: minor | Milestone:
Component: basic arithmetic | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by Snark):
There are several things to say about the matter:
1. for m an integer, indeed the formula you give is correct.
2. but it's possible to define the binomial with m non-integer using
gamma-functions, and I think that's what the one who coded the current
floating code had in mind.
3. my patch is about partially unwinding the gamma factors like you
mention (with step by step simplification which avoids overflows) before
finally calling the gamma function with small parameters.
4. but my patch should only start looping when the parameters are indeed
big (or it will be slow) and use symmetry so
binomial(float(1001),float(1)) works.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12448#comment:4>
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