       RE: Finding variables in a very long expression (corrected)

• To: mathgroup at smc.vnet.net
• Subject: [mg31409] RE: Finding variables in a very long expression (corrected)
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Sat, 3 Nov 2001 05:29:15 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```> 	Yesterday I replied to Jose Flanigan's question about
> 	how to find all variables in an expression.
> 	In that reply I wrote ....
> 	-------------
> 	> Consider expr below.
> 	>
> 	> In:=
> 	>   expr=Sqrt[x*y]+x*z+w Sqrt[x]z^(1/n)+Pi/3;
> 	>   w=v;
> 	>
> 	> The simple line below almost works, but the list includes
> 	> Pi which isn't a variable.  The third argument of Cases
> 	> here is a level specification.  You can read about Cases
> 	> and level specification at my web site (URL below).
> 	>
> 	> In:=
> 	>   Union[Cases[expr, _Symbol, {0, -1}]]
> 	>
> 	> Out=
> 	>   {n, Pi, v, x, y, z}
> 	>
> 	>
> 	> The next line eliminates symbols such as Pi.
> 	>
> 	> In:=
> 	>   Union[Cases[expr, _Symbol?( !NumericQ[#]& ), {0, -1} ]]
> 	>
> 	> Out=
> 	>   {n, v, x, y, z}
> 	>
> 	> --- The Plot Thickens ---
> 	> At the 1999 Developer Conference Robby Villegas explained
> 	> that this sort of thing gets tricky when you are working
> 	> with symbols that were previously removed.  Consider the
> 	> lines below where the symbol (v) is removed.  If I had my
> 	> way removing a symbol would make the kernel work as if the
> 	> symbol never had any values, but that's not the way it works.
> 	>
> 	> In:=
> 	>   Remove[v]
> 	>
> 	> In:=
> 	>   Union[Cases[expr, _Symbol?( !NumericQ[#]& ), {0, -1} ]]
> 	>
> 	> Out=
> 	>   {n, Removed[v], x, y, z}
> 	>
> 	>
> 	> If you want to make sure your list of variables is free of
> 	> Removed Symbols use the next line (based on Robby Villegas talk).
> 	>
> 	> In:=
> 	>   Union[Cases[expr, _Symbol?
> 	>              ( !NumericQ[#] && NameQ[ToString[#]]& ), {0, -1}
> 	>         ]]
> 	>
> 	> Out=
> 	>   {b, x, y, z}
> 	>
> 	>
> 	-----------------------
> 	However in the the next example the approach used
> 	above doesn't find the symbols (f) and (g).
>
> 	In:=  expr=D[ x^3+f[x]+g'[x]+Abs[x], x];
>
>
> 	In:=  Union[Cases[expr, _Symbol?(!NumericQ[#]&), {0,-1} ] ]
>
> 	Out=  {x}
>
>
> 	The next line returns a list of symbols we are differentiating.
> 	This line really demontrates how versitle Cases[..] can be. You
> 	could use Union on the result to elliminate duplicates if there
> 	are any.
>
>   In:= Cases[expr, Derivative[_][func_]:>func, {0,-1}, Heads->True]
>
>   Out=  {Abs, f, g}
>
>
>   -----------
>   The next few lines give another approach.  In the first line below
>   I don't bother to ensure I only get non-numeric symbols because
>   symbols such as Pi will be discarded with my last step.
>
>   In:= lst=Union[ Cases[expr, _Symbol, {0,-1}, Heads->True] ]
>
>   Out=  {Abs, Derivative, f, g, Plus, Power, Times, x}
>
>
>   You probably only want the user symbols {f, g, x}.
>   The code below will take care of that.
>
>   In:= MyVariables=Names["Global`*"];
>           Select[lst, MemberQ[MyVariables, ToString[#] ]& ]
>
> 	Out:= {f, g, x}
>
>
> 	You could if you want use this last step on the list
> 	{Abs, f, g} above if you prefer that approach and want
> 	to get rid of (Abs). In todays post I don't bother to
> 	ensure Removed symbols are discarded, but you can do
> 	that if you wish.
> 	-------
>
> 	Regards,
> 	   Ted Ersek
> 	  Check Mathematica Tips, Tricks at
> 	  http://www.verbeia.com/mathematica/tips/Tricks.html
>

```

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