> Are there improvements that can be made to SymPy's
> factorial or not?

It depends how you explain the difference between the behaviour
in Sage and SymPy.

If my speculation is right the basic product prod_i=0^n a[i]
is implemented suboptimal in SymPy. Otherwise this product
would (for large n) be faster than the iterated product
"for p in range(a,b): L *= p" used in SysPy's 'factorial'.
This is a typical example for an unbalanced multiplication
and well known to be suboptimal.

> Are there improvements that can be made to SymPy's
> factorial or not?

Probably, if layered on some implementation of the product
mul(list) which is asymptotically fast. And SysPy certainly
should have such an implementation. If it indeed has such
an implementation (which I do not know) than I am clueless
at the moment.

Peter

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