Question

I would like to get a List (ideally a set — discarding repetition — but assuming there’s no direct way to do this I’ll just use Union) of the leaves from a given expression.

For example, the expression

ArcTan[(-1 + 2*x)/Sqrt[3]]/Sqrt[3]

has a LeafCount of 18:

• -1 (3)
• 2 (3)
• 3 (2)
• x
• ArcTan
• Plus
• Power (2)
• Rational (2)
• Times (3)

so I would like something like

{-1, 2, 3, x, ArcTan, Plus, Power, Rational, Times}

Actually, I really just want the functions so

{ArcTan, Plus, Power, Rational, Times}

would be ideal — but presumably there’s some not-too-difficult way to filter these when I have them.

I’ve had some luck with

H[s_] := If[LeafCount[s] == 1, s, Head[s]]
H /@ Level[expr, 1, Heads -> True]
H /@ Level[expr, 2, Heads -> True]
(* ... *)

but I feel like there must be a better way.

Answer 1

Your own solution does not seem bad:

expr = ArcTan[(-1 + 2*x)/Sqrt[3]]/Sqrt[3];

H[s_] := If[LeafCount[s] == 1, s, Head[s]]

H /@ Level[exp, -1, Heads -> True] // Union

{-1, 2, 3, ArcTan, Plus, Power, Rational, Times, x}

---

Brett Champion’s method is more streamlined, but I would change it a little:

Union@Cases[expr, h_[___] :> h, {0, -1}]

This way you pick up a top level head, such as ArcTan in:

expr = ArcTan[(-1 + 2*x)/Sqrt[3]];