Re: Pure recursive functions
- To: mathgroup at smc.vnet.net
- Subject: [mg38391] Re: Pure recursive functions
- From: atelesforos at hotmail.com (Orestis Vantzos)
- Date: Fri, 13 Dec 2002 04:10:24 -0500 (EST)
- References: <at9de0$q4r$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Use Block:
Block[{fact=If[#>0,# fact[#-1],1]&},fact[5]]
returns 5!
You can also use Module:
Module[{fact},
fact[n_]/;n>0 := n fact[n-1];
fact[0]=1;
fact[5]]
also returns 5!
Orestis Vantzos
Niall Palfreyman <niall.palfreyman at fh-weihenstephan.de> wrote in message news:<at9de0$q4r$1 at smc.vnet.net>...
> Hello,
>
> I'm new to Mathematica, and I have a question to which I've found no
> answers in the archives. Can you help?
>
> The issue is: how do I create a pure recursive function? Normally when
> creating a recursive function I use the name of the function to perform
> the recursive call:
>
> fact[n_] :=
> If[n == 1, 1, n fact[n - 1]]
>
> However this has the disadvantage that the symbol "fact" is now global.
> The logical step to make the name of the function local is something
> like:
>
> Function[factl, factl[5]] @@ {Function[n, If[n == 0, 1, n factl[n -
> 1]]]}
>
> or maybe:
>
> With[{fact = Function[n, If[n == 0, 1, n fact[n - 1]]]}, fact[5]]
>
> However both of these solutions steadfastly return the value "5
> fact[4]". I assume the problem is that the variables initialised in
> Function[] and With[] must be symbols, and cannot be patterns. But a
> recursion requires a pattern (n_ in the first, global, solution above).
> What do I do to get factorial to work _without_ making the symbol "fact"
> global?
>
> I'd be grateful for any help.
>
> Thanks,
> Niall.