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MathGroup Archive 2007

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Re: search for an operator in an expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78261] Re: search for an operator in an expression
  • From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 27 Jun 2007 05:24:36 -0400 (EDT)
  • References: <f5iuqu$a99$1@smc.vnet.net> <467D2013.6040903@gmail.com>

Daniel wrote:
> Is there a way to search for an operator in a symbolic expression? My wish is to show that there is only "+" in a very large expression. Rather than showing an expression on multiple pages I would like to perform a search that shows there is only "+" between the terms. Converting to a string does not seem to work since the expression is written on multiple lines(fractions, exponents etc..)
>
> Thanks

Hi Daniel,

If I have correctly understood what you want, the easiest way should be
to check the head of your expression. (Remember that in Mathematica
everything is an expression, that is something with a head and some
elements: head[e1, e2, ...] .) For instance, say we have the following
expression

In[1]:=
expr = Expand[(a + I*b)^5]

Out[1]=
a^5 + 5*I*a^4*b - 10*a^3*b^2 - 10*I*a^2*b^3 +
   5*a*b^4 + I*b^5

Its head is Plus.

In[2]:=
Head[expr]

Out[2]=
Plus

We can also look at the full form of the expression and see that it
contains many sub-expressions (with head Times or Complex for example);
however the head of the overall expression is Plus.

In[3]:=
FullForm[expr]

Out[3]//FullForm=
Plus[Power[a,5],Times[Complex[0,
   5],Power[a,4],b],Times[-1,10,Power[a,3],Power[b,2]],Times[Complex[
   0,-10],Power[a,2],Power[b,3]],Times[5,a,Power[
     b,4]],Times[Complex[0,1],Power[b,5]]]

In[4]:=
TreeForm[expr] (*TreeForm is mores appealing in version 6.0 *)

To summarize, the differences among the list {a, b, c}, the sum a + b +
c, and the product a * b * c are just in their respective heads.

In[5]:=
FullForm[{a, b, c}]

Out[5]//FullForm=
List[a,b,c]

In[6]:=
FullForm[a + b + c]

Out[6]//FullForm=
Plus[a,b,c]

In[7]:=
FullForm[a*b*c]

Out[7]//FullForm=
Times[a,b,c]

Finally, Apply is used to change the head of an expression. Below we
transform a product into a sum by changing its head.

In[8]:=
Plus @@ (a*b*c)

Out[8]=
a + b + c

HTH,
Jean-Marc


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