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Generalization of Variables ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109221] Generalization of Variables ?
  • From: Jack L Goldberg 1 <jackgold at umich.edu>
  • Date: Sat, 17 Apr 2010 06:06:03 -0400 (EDT)

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[
                                    Map[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


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