Except[] with levelspec

Question

I am trying to determine all the variables used in list. For This I use:

DeleteDuplicates[Cases[l1,_Symbol,-1]]

This is great except that \Pi etc. are symbols too. I want to add Except to this Cases command to discard numeric symbols but I'm not sure where to add it.

I tried different combinations, but I either get errors, or it will interpret it differently to what I intended.

Alternatively, is there a better way of achieving this?

Answer 1

As an example, let us consider the following expression:

expr= Log[ 3 Sin[x] + 2 Exp[Pi+ 4 a b + 1/7]];

This is not a polynomial, so the function Variables cannot be used. On level -1 we have the atoms:

Cases[expr,_, {-1}]

(* {2,E,1/7,4,a,b,\[Pi],3,x} *)

Observe that 1/7 is an atom! We restrict ourselves to symbols:

Cases[expr,_Symbol, {-1}]

(* {E,a,b,\[Pi],x} *)

This is not restrictive enough; we only want the symbols that do not have a value. Using Kuba's advice to use function composition:

Cases[ expr, _Symbol?(Not @*  NumericQ), {-1}]

(* {a,b,x} *)

Answer 2

You can use WolframLanguageData with Alternatives to built the Except.

numConstFunc = Except[Alternatives @@ Symbol /@
    WolframLanguageData[
      EntityClass[
       "WolframLanguageSymbol", {"FunctionalityArea", "NumericConstantFunctions"}], 
     "Name"], _Symbol];

Then

expr= Log[ 3 Sin[x] + 2 Exp[Pi+ 4 a b + 1/7]];

Cases[expr, numConstFunc, {-1}]
(* {a, b, x} *)

Hope this helps.