> It looks like the top level binomial() function is a mess already.
>
>  - binomial does not accept variable when only in the lower argument
>        http://trac.sagemath.org/sage_trac/ticket/9634
>
>  - binomial does not accept float
>        http://trac.sagemath.org/sage_trac/ticket/9633

Oh, yes - several of us have tried to make it work better with various
input, but likely it could be completely rewritten at this point.

> Looking at the code in sage/rings/arith.py, I see that the if statement
> starting at line 2999 is a duplicate of that in at line 2961.
>
> Replacing the top level binomial function with the symbolic one defined
> in sage.functions.other should provide an easy fix for all these
> problems. I wonder if it effects the speed too much.

I couldn't figure out how to do this at the time, but certainly this
was a goal in some earlier revisions.  No matter how I imported it,
the arith.py one is the one that would show up, but this would be a
great goal.

- kcrisman

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