Sage: Ticket #14897: binomial(x, m) gives incorrect answer when m is float
https://trac.sagemath.org/ticket/14897
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Essentially, this stuff
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<pre class="wiki">sage: binomial(10, 0.1)
1
</pre><p>
What I would have expected it to give as output is
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<pre class="wiki">sage: gamma(10+1)/gamma(10-0.1+1)/gamma(0.1+1)
1.32919082253922
</pre><p>
This enhancement has to be done on the sage side since both mpir and pari don't give the correct answer. Using the gamma function in these special cases will also take care of complex numbers.
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<p>
But, we must avoid changing the whole implementation to the gamma function - that was also giving incorrect results and was fixed in <a class="closed ticket" href="https://trac.sagemath.org/ticket/12448" title="defect: The binomial implementation does a quotient of gamma values, which is wrong (closed: fixed)">#12448</a>. The <code>sage.rings.arith.binomial</code> function itself is a bit of a mess and it is hard to figure out what will eventually get executed in that code.
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en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/14897
Trac 1.1.6vbraun_spamThu, 30 Jan 2014 21:20:52 GMTmilestone changed
https://trac.sagemath.org/ticket/14897#comment:1
https://trac.sagemath.org/ticket/14897#comment:1
<ul>
<li><strong>milestone</strong>
changed from <em>sage-6.1</em> to <em>sage-6.2</em>
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</ul>
Ticketvbraun_spamTue, 06 May 2014 15:20:58 GMTmilestone changed
https://trac.sagemath.org/ticket/14897#comment:2
https://trac.sagemath.org/ticket/14897#comment:2
<ul>
<li><strong>milestone</strong>
changed from <em>sage-6.2</em> to <em>sage-6.3</em>
</li>
</ul>
Ticketvbraun_spamSun, 10 Aug 2014 16:51:03 GMTmilestone changed
https://trac.sagemath.org/ticket/14897#comment:3
https://trac.sagemath.org/ticket/14897#comment:3
<ul>
<li><strong>milestone</strong>
changed from <em>sage-6.3</em> to <em>sage-6.4</em>
</li>
</ul>
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