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Re: search for an operator in an expression

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  • Subject: [mg78392] Re: search for an operator in an expression
  • From: Albert <awnl at>
  • Date: Sat, 30 Jun 2007 06:05:10 -0400 (EDT)
  • References: <f5iuqu$a99$> <f5o8jr$5jo$> <f5qhdc$2jt$> <f5tcb1$2ir$> <f62k8u$bp5$>


>> you must distinguish between OutputFormat, what you see, and FullForm, 
>> what Mathematica sees. Try: FullForm[yourExpression] then you will see 
>> that you have 1 operator Plus with multiple arguments. If you want to 
>> see the number of arguments, you could e.g. use:
>> Cases[expression, Plus[x__] :> Length[x]]

while in principle this shows the principle of the in my opinion 
clearest way how to treat this, it does not work here and the nearely 
correct result is just an accident, as you can see when you check what 
the matches really are:

In[17]:= Cases[expr, Plus[x__] :> XXX[x]]

Out[17]= {XXX[2], XXX[d], XXX[a \[ExponentialE]^(-b x)],
  XXX[Sin[b + c]]}

you must be careful for these reasons:

- Plus has Attributes that influence pattern matching in a way that is
   not what we need here, among them Flat and Orderless.
- Cases looks for matches by Default only in level 1, to find all
   instances you need to explicitly tell it to.
- Plus[a,b] is a+b, so the number of plus signs in StandardForm is one
   less than the length of the arguments of the corresponding Plus
- x matches a Sequence in the above code, which Length does not really

Taking account of all these, the following should work for arbitrary 
expressions, although I did not really test it...

In[14]:= Total[
  Cases[expr /. Plus -> plus,plus[x__] :> (Length[{x}]-1),{0,Infinity}]

Out[14]= 4

By the way it is always a good idea to check whether pattern matching 
constructs really do what you want, in this case the following makes me 
believe I could be right :-)

In[19]:= Cases[expr /. Plus -> plus,plus[x__] :> XXX[x], {0,Infinity}]

Out[19]= {XXX[b, c], XXX[2, d, a Exp[-b x], Sin[plus[b, c]]]}

hope that works and helps,


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