The command
Variables[poly] gives me a list of all variables that appear in the expression poly, which involved sums, products, and rational powers. Sadly, it doesn't work for more complicated expressions, such as trigonometric functions. I was wondering if there is another command that can handle expressions such as $\sin(x)+\cos(y)$.
ClearAll[x, y, z, d, h, p, m, f, g, a, w]; expr = Sin[x] + Cos[y] + z^3 + Exp[d] + h + 3 h^2 + 4 h^3 + Integrate[Exp[p], p] + D[Sin[m]^Exp[f], m]*Series[Sin[g], {g, 0, 3}] + 2 (E^a BesselK[0, 2 Sqrt[E^a]]) C[2]/D[Gamma[w], {w, 2}]; Cases[Variables[Level[expr, -1]], x_ /; AtomQ[x] :> x] (* {a, d, f, g, h, m, p, w, x, y, z} *) 
Level[expr, {-1}], right? $\endgroup$ {-1} and once with AtomQ. You should either just subsume/supplant my answer or go back to the original form. (You're the one who encouraged me to post an answer; I'd have been glad to simply edit yours.) $\endgroup$ -1 and {-1} will work in your code; that's my point. With {-1} the AtomQ becomes redundant; that's why it's not in my answer. $\endgroup$ Using Nasser's expression code as an example:
expr = Sin[x] + Cos[y] + z^3 + Exp[d] + h + 3 h^2 + 4 h^3 + Integrate[Exp[p], p] + D[Sin[m]^Exp[f], m]*Series[Sin[g], {g, 0, 3}] + 2 (E^a BesselK[0, 2 Sqrt[E^a]]) C[2]/D[Gamma[w], {w, 2}]; You might use:
Variables @ Level[expr, {-1}] {a, d, f, g, h, m, p, w, x, y, z}
To extract indexed variables such as C[2] you could use:
Cases[expr, _[_Integer], {-2}] {C[2]}
-1 rather than {-1} because I wanted to allow for indexed variables like x[1]. Do you think I should try to extend my answer to handle both in Sin[z] + x[1], that is include z and x[1] in the output list? $\endgroup$ Variables for polynomials, and that limits what he means by variables. But indeed, that would also include things like x[1]! $\endgroup$ Integrate[Sqrt[1 + Exp[p^2]], {p, 0, 1}], which doesn't evaluate but is a constant? Just live with it? $\endgroup$ Clear[GetVariables] SetAttributes[GetVariables, HoldFirst]; GetVariables[expr_, f_:Identity, excludedContexts:{__String}:{"System`"}]:= Cases[Unevaluated[expr], a_Symbol/;!Or[ MemberQ[excludedContexts, Context[a]], MemberQ[Attributes[a], Locked | ReadProtected] ] :> f[a], {0, Infinity} ]//DeleteDuplicates It is used like
GetVariables @ {Exp[f[x]], Sin[x y^2]} (* {x, y} *) or, if you need to
GetVariables[{Exp[f[x]], Sin[x y^2]}, Hold] (* {Hold[x], Hold[y]} *) By default, it excludes the System` context, but other contexts can be specified, too.
sr = {Exp[v_] :> v, v1_^v2_ :> {v1, v2}}; variables[expr_] := FixedPoint[Replace[Variables[# /. sr], _[x_] :> x, {1}] &, expr] variables[Sin[Subscript[x, 1]] + Cos[Subscript[x, 2]]] (* {Subscript[x, 1], Subscript[x, 2]} *) variables[Sin[x] + Cos[y] + z^3 + Exp[d] + h + 3 h^2 + 4 h^3 + Integrate[Exp[p], p] + D[Sin[m]^Exp[f], m]] (* {d, f, h, m, p, x, y, z} *) Perhaps what you are looking for is as simple as
vars[expr_] := DeleteDuplicates@Cases[expr, _Symbol, \[Infinity]] vars[1 + y^2 + Sin[x] + Cos[x]] {y, x}
Probably there are expressions on which this will fail, but it might handle those you are interested in.
