> My vote is to have factorial(n) = n(n-1)...2.1 whenever n is integer.
>
> Cheers,
>
> Florent
We certainly need to allow for symbolic input too, so that Sage can
simplify expressions involving factorials and binomial coefficients
such as:
sage: var('k,n')
(k, n)
sage: f = factorial(k)*factorial(n-k)*binomial(n,k); f
factorial(-k + n)*factorial(k)*binomial(n, k)
sage: f.full_simplify()
factorial(n)
My vote would be to allow symbolic input and to set factorial(n) =
n(n-1)...2.1 whenever n is a non-negative integer, but for
factorial(x) to raise an error whenever the expression x is numerical
but not equal to a non-negative integer.
In this case full_simplify() should not turn expressions involving
factorial() into expressions involving gamma(), or vice versa.
This might be contrary to the philosophy behind the symbolics module,
though. Let me know what you think.
Best,
Tom
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