Another (new?) binomial bug

[kcrisman]

From sage-devel:

In [143]: [binomial(1,1),binomial(1,2),binomial(1,3),binomial(1,4)] 
Out[143]: [1, 0, 0, 0] 
In [144]: [binomial(1.0,1),binomial(1.0,2),binomial(1.0,3),binomial 
(1.0,4)] 
Out[144]: [1.00000000000000, 0.000000000000000, NaN, NaN] 

The problem is this:

sage: x = RealNumber('1.0')
sage: P = x.parent()
sage: P
Real Field with 53 bits of precision
sage: gamma(x+1)/gamma(P(Integer(4)+1))/gamma(x-Integer(4)+1)
NaN
sage: gamma(x-Integer(4)+1)
NaN

So we'll have to put in yet another check...

[hgranath]

Here is a patch that should fix this issue. Note that for x a negative floating point integer we hit gamma function poles both in the numerator and denominator. An alternative formula is used in the patch to avoid this.

By the way, is the cc field above supposed to notify me by mail? I did not get any.

[hgranath]

Sorry, my patch is off for negative x. I will send an updated patch later.

[kcrisman]

By the way, is the cc field above supposed to notify me by mail? I did not get any.

Yes, and it does usually work, but perhaps you don't have a correct email associated to your account. I don't know how to fix this, you may want to ask on sage-devel.

[hgranath]

Replying to kcrisman:

Yes, and it does usually work, but perhaps you don't have a correct email associated to your account. I don't know how to fix this, you may want to ask on sage-devel.

Thanks for the info, I found some place to enter my email so probably it will work now.

[kcrisman]

This seems to work fine, and agrees with integer calculations. Obviously passes tests.

But:

sage: binomial(0,0)
1
sage: binomial(0.,0)
NaN

I don't know which is the usual convention, but they should probably agree.

[hgranath]

New breakpoint

[hgranath]

Thanks for spotting this, new version is up.

[kcrisman]

Great, positive review!