On Thu, Sep 16, 2021 at 06:33:58PM -0000, Jonatan wrote: > Currently, math.factorial only supports integers and not floats, > whereas the "mathematical" version supports both integers and floats.
That's questionable. (Warning: maths geek post follows.) Mathematicians typically only use the notation n! (factorial) for non-negative integer arguments. If the argument could be any real number, they typically use Γ(x) (gamma). It is true that n! = Γ(n+1) so from a pragmatic point of view, we could have the factorial function accept any float. The HP-48 calculator does that. But the more modern TI-Nspire calculator doesn't. However, the gamma function is not the only way to extrapolate factorial to all real numbers. There are at least two well-known others: * Gauss' pi function Π(x) = Γ(x+1) so that Π(n) = n! * and Hadamard's gamma function H(x) But there are also others that are not as well known: http://www.luschny.de/math/factorial/hadamard/HadamardsGammaFunctionMJ.html As the above link suggests, Euler's gamma function may be the most famous extrapolation of factorial, but it is perhaps not the best. Although not everyone agrees with that: https://math.stackexchange.com/questions/1537/why-is-eulers-gamma-function-the-best-extension-of-the-factorial-function-to By the way, it is unclear why Legendre introduced the notation Γ with the shift of 1 compared to factorial. That shift simplifies some formulae, but complicates many others. The Hungarian-Irish mathematician Cornelius Lanczos called it "void of any rationality". (I love it when mathematicians say what they're really thinking.) So from a *mathematical* perspective: 1. Having factorial accept any real number may be strange and confusing if calculating combinations and permutations, or other applications where non-integer values make no sense for factorial. 2. If you want to extrapolate factorial to non-integer values, you might not want to extrapolate it using Euler's Γ (gamma) function. And from a *programming* perspective: 1. What advantage do we have in writing `factorial(2.5)` if you want to calculate `gamma(3.5)`? 2. We lose the type checking that protects us from some classes of error in applications where extrapolating to floats makes no sense. Looking at your implementation: > def better_factorial(n): > return n * math.gamma(n) that is not going to work: >>> factorial(23) == better_factorial(23) False The problem is that since floats only have about 17 significant figures or so, once you get to 23! the gamma function doesn't have enough precision to give an exact answer. Of course that's easily fixable. (Only call gamma if the input argument is a float.) In summary, I don't think that there is much real advantage in having the factorial function take float arguments and call gamma. And we certainly don't need a *second* factorial function that is exactly the same as gamma. Just use gamma directly. -- Steve _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/JMLHEMN3VW54PNOFMU3CQLGR4VYDYEBR/ Code of Conduct: http://python.org/psf/codeofconduct/
