Checking what a function depends on

Question

I'd like to define specific partial derivative operators that change based on if the passed expression is a function of, for example, x vs. xi. I'm not finding anything in the documentation on how to code a check for the expressions dependence. My question is, if given some function f[x,y], how can I check the variables that it depends on?

Possible duplicate of How to define custom differential operator using the arguments of the expression? — Carl Woll, Sep 05 '18 at 21:43
I think it should be possible to also use DownValues[f] to find what the function depends on, since the DownValues has the function signature right there. It just needs to be parsed out and to extract all the symbols from inside f[x_,y_,....] and this part might be tricky to do. ?DownValues — Nasser, Sep 06 '18 at 01:50

score 12 · Accepted Answer · answered Sep 05 '18 at 21:30

12

Perhaps Internal`DependsOnQ:

h = f[x, g[y]];
Internal`DependsOnQ[h, #] & /@ {x, y, g[y], w}

{True, True, True, False}

answered Sep 05 '18 at 21:30

kglr

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Checking what a function depends on

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