Re: Get list of function variables?

• To: mathgroup at smc.vnet.net
• Subject: [mg83295] Re: Get list of function variables?
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Sat, 17 Nov 2007 05:14:50 -0500 (EST)
• References: <fhjs5v\$4t3\$1@smc.vnet.net>

```Jason Quinn wrote:
> This seems simple but how do I get the arguments to an arbitrary
> function? Ideally something like getVariables[f] that just accepts the
> function name as its argument.
>
> If I have f[x_,y_]:=a*x^2+b*y^2,  getVariables[f] should return {x,y}
> If I have g[n_,m_]:=a*n^2+b*m^2, getVariables[g] should return {n,m}
> If I have h[w_,x_,y_,z_]:=A*w*x*y*z+B, getVariables[h] should return
> {w,x,y,z}
>

"Functions" in Mathematica are completely different animals than
functions in C-like languages (or functions in the mathematical sense),
so your request doesn't really make sense.  But take a look at DownValues[].

For example, consider the following (nonsensical) definition:

f[x_, y_] := x + y
f[{x_, y_}] := x y
f[x__] /; Length[{x}] > 4 := "something"
f[_] := 0

What should getVariables[f] return?

Also, x and y are localized to f[x_,y_]:=a*x^2+b*y^2, so these symbol
names are useless outside the function definition.  It could have been
written as f[p_,q_]:=a*p^2+b*q^2.

Szabolcs

```

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