[RFC] changing output of binomial

[Chris Smith]

Currently, binomial presents results in terms of gamma. And if they evaluate you see a number or with Number real and/or imaginary parts. In #18960 we are experimenting with changing this so the class remains unevaluated unless it evaluates into an expression free of the writing function, `gamma`. So `binomial(nt, Rational(15, 6))` would remain unevaluated instead of becoming `8*gamma(nt + 1)/(15*sqrt(pi)*gamma(nt - Rational(3, 2)))`. This expression can be obtained by using `.rewrite(gamma)` and will evaluate to a numerical value with `evalf`.

/c

[Aaron Meurer]

I agree that such rewrites shouldn't happen by default. In this case,
the gamma expression isn't even simpler than the binomial. I would
expect combsimp(), for instance, to go from the gamma form to the
binomial (or beta()), not the other way around.

By the way, there's a related issue
https://github.com/sympy/sympy/issues/14577. We still need to properly
document why the binomial is defined the way it is for negative
arguments.

Aaron Meurer

On Tue, Mar 31, 2020 at 9:37 AM Chris Smith <smi...@gmail.com> wrote:
>
> Currently, binomial presents results in terms of gamma. And if they evaluate you see a number or with Number real and/or imaginary parts. In #18960 we are experimenting with changing this so the class remains unevaluated unless it evaluates into an expression free of the writing function, `gamma`. So `binomial(nt, Rational(15, 6))` would remain unevaluated instead of becoming `8*gamma(nt + 1)/(15*sqrt(pi)*gamma(nt - Rational(3, 2)))`. This expression can be obtained by using `.rewrite(gamma)` and will evaluate to a numerical value with `evalf`.
>
> /c
>

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