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MathGroup Archive 2006

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Symbol and Pi and expressions evaluating to Pi

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70117] Symbol and Pi and expressions evaluating to Pi
  • From: "David Bakin" <davidbak at gmail.com>
  • Date: Wed, 4 Oct 2006 05:59:20 -0400 (EDT)

[I apologize if this question has been asked - as it surely must have
been already - my searches didn't get me to the answer in the
archives.  You can send me some better search terms and I'll be happy
with that as an answer, thanks!]

The Mathematica 5.1 help browser entry for Symbol under "Further Examples"
defines a function SymbolQ1 to determine if something is a Symbol as
follows:

Attributes[SymbolQ1] = {HoldAllComplete};
SymbolQ1[expr_] := AtomQ@Unevaluated[expr] && Head@Unevaluated[expr]===Symbol

Then it shows the following:

     In:= SymbolQ[Pi]
     Out= True
     In:= {a definite integral evaluating to Pi} == Pi
     Out= True
     In:= SymbolQ[that definite integral]
     Out= False

Yet FullForm[Pi] is the same as FullForm[that definite integral], and is Pi.

So I have two questions:
1) Why isn't SymbolQ[that definite integral] == True?  What is it if
it isn't a Symbol?
2) Why are FullForm[Pi] and FullForm[that definite integral] different?

Thanks!  -- Dave


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