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Re: Generalization of Variables ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109274] Re: Generalization of Variables ?
  • From: Rui <rui.rojo at gmail.com>
  • Date: Tue, 20 Apr 2010 05:50:22 -0400 (EDT)
  • References: <hqc14l$g2v$1@smc.vnet.net>

On Apr 17, 7:05 am, Jack L Goldberg 1 <jackg... at umich.edu> wrote:
> Hi Folks,
>
> The built-in command "Variables" does not give the (naively expected)  
> answer when it is called with functions such as x + Sin[x].  This  
> behavior is mentioned in the description of "Variables".
> I have constructed a generalization of "Variables" which works as  
> expected - I think?  I would appreciated a critique of this code which 
> addresses these issues:
>
> a) Is there a situation in which it fails?
>
> b) If the code works, can it be improved.
>
> Question b) is asked because I am not fully acquainted with all of  
> Mathematica's commands.
>
> Here is the code.
>
> variables[f_]:= Flatten[
>                         Union[
>                              Cases[
>                                     M=
ap[N,Level[f,{-1},z_Symbol]]/.True->{}
>                                     =
        ]
>
> I have tried "variables" on functions coded in the obvious manner, say,
> Sin[x]+Exp[x^2],  Sin[x+y]-z^2, etc. and a few esoteric examples.
>
> Jack

variables[expr_] :=
 DeleteDuplicates[
  Cases[
   expr, _Symbol?(! NumericQ[#] &), -1]]

Or maybe, if you have lots of more duplicates than Pi, E, and numeric
symbols,

variables[expr_] :=
 Cases[DeleteDuplicates[
   Cases[expr, _Symbol, -1]], _?(! NumericQ[#] &)]


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