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Re: Extracting variables nested in functions
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: Re: Extracting variables nested in functions
*From*: PERKINS TYLER R <perkins at spot.colorado.edu>
*Date*: Tue, 15 Oct 91 17:46:35 -0600
> Does anyone know a method for extracting the variables from an expression
> which has some of its variables buried in functions, such as x in Cos[x/Pi],
> or b[1] and x[1] in Log[b[1], x[1]]? The built-in Variables seems to look for
> subexpressions in terms of which the expression is a _polynomial_, so it
> includes parts like Cos[x/Pi] in the list of "variables" it returns.
>
> Robby Villegas
> Knox College
Try the following:
In[1]:= Globs[ expr_ ] := Cases[
Level[ expr, {-1} ], (* "Leaves" of expr. Excludes heads. *)
_Symbol ? (Context[#] == "Global`" &) (* Match Global`s only *)
]
In[2]:= Globs[ 2 Cos[x/Pi] y^2 z ]
Out[2]= {y, z, x}
But note that this WILL list Global` variables which happen to have rules
associated with them, as long as they don't appear as the head of a subexpression
of expr. For instance,
In[3]:= Globs[ x y[Globs] ]
Out[3]= {x, Globs}
Notice that y is NOT listed, which might indeed be a variable of interest, and
Globs IS listed, which is probably not of interest, because it has rules
associated with it. I think the following would fix this, but only in 2.0:
(I don't have 2.0 yet, so I can't test it.)
Globs[ expr_ ] := Cases[
Level[ expr, {-1}, Heads->True ],
_Symbol ? ( (* Mma. 2.0 only! *)
DownValues[#] == {} && UpValues[#] == {} &
)
]
Tyler Perkins
perkins at spot.colorado.edu
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