What is the most elegant way to see if an expression is affected by a certain symbol?

Question

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Determine whether some expression contains a given symbol

Let's say I have some expression:

sample = {1, 1/q, f[m]}

And I want to check it if it has the symbol m in it.

My question: Is there a clean or fast way of checking if m is in the equation?

What I came up with so far:

Do[StringFreeQ[ToString[sample], "m"], {i, 300}] // AbsoluteTiming
(* {0.0120007, Null} *)

and

Do[(sample /. m -> Unique[]) === (sample /. m -> Unique[]), {i, 300}] // AbsoluteTiming
(* {0.0100005, Null} *)

These solutions work, but I feel like there might be a faster, functional way of doing this.

@Rojo Don't MemberQ and FreeQ only check on the first level? I checked this for MemberQ before. — VF1, Sep 27 '12 at 03:52
No, FreeQ checks all levels by default. Both can take a level specification anyway — Rojo, Sep 27 '12 at 03:53
That's because D[m, t] evaluates to 0. If you want to check in held expressions, hold the evaluation with Hold or Unevaluated — Rojo, Sep 27 '12 at 03:55

score 0 · Accepted Answer · answered Sep 27 '12 at 03:54

0

How about:

sample = {1, 1/q, ff[f[m]]};
FreeQ[sample, m]
(* False *)

answered Sep 27 '12 at 03:54

1 Answers1