Re: Changing Pure Function in Module

• To: mathgroup at smc.vnet.net
• Subject: [mg29832] Re: Changing Pure Function in Module
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 13 Jul 2001 04:19:14 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <9ijhui\$ri5\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

> I have the following function embedded in the findD code below.
>
> a[1] =5;
>
> a[n_]:= a[n] = (-1)^(n+1) (Abs[a[n-1]]+2)
>
> In[225]:=
> findD[n_]:=
> Module[{c=0},NestWhile[(c++;(-1)^c(Abs[#]+2))&,5,JacobiSymbol[#,n]!=-1&]]
>
> I would like to change the pure function to use the following (cleaner) function
> that requires no starting value (and starts for n = 1).
>
> In[255]:=
> a[n_]:= a[n]= (-1)^(n+1)*(2n + 3)

So just do it, but with

a[n_Integer]/; Positive[n]:= a[n]= (-1)^(n+1)*(2n + 3)

the code is *not* "cleaner" it is just with out the recursion.

Why not use

a[n_Integer] /; Positive[n] := a[n] = (-1)^(n + 1)*(2n + 3)

and

findD1[n_] /; Head[Sqrt[n]] =!= Integer :=
Module[{i = 1, ai},
While[True,
If[JacobiSymbol[ ai = a[i++] , n] == -1, Break[]];
];
ai
]

>
> Also, it would be important to test n prior to calling findD.  If n is a perfect
> square, findD will "never" converge.  Is there a simple way to test if n is
> square