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MathGroup Archive 2007

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Re: A harmless and amusing bug

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  • Subject: [mg76337] Re: [mg76215] A harmless and amusing bug
  • From: Andrzej Kozlowski <akoz at>
  • Date: Sun, 20 May 2007 02:22:08 -0400 (EDT)
  • References: <>

There is a simpler way to demonstrate essentially the same phenomonon  
wihtout any copying and pasting.
First define a by evaluating


Now define b as follows. We use the same definition


but before evaluating it we  convert it to StandardForm by selecting  
the cell bracket and using the Convert To menu. After converting the  
cell we evaluate it. Now

a === b

Just as in your example, a and b have different FullForm. I don't  
know whether to call this a bug or not as it seems to me a more or  
less inevitable consequence of the way atoms with head Rational are  
formated. But it's certainly strange and unintuitive.

Andrzej Kozlowski

On 18 May 2007, at 19:02, Fred Simons wrote:

> I found this example in a very old notebook of mine and I do not
> remember if this has already been discussed in this group.
> The following seems to be a harmless and amusing bug. It happens  
> both in
> Mathematica 5 and in Mathematica 6 under Windows.
> Execute the following command:
> y = x /. DSolve[x''[t]+ 2 x'[t]+ x[t]==Sin[t], x, t][[1]]
> Copy the result, paste it in the following command and execute.
> z =pasted result
> Obviously, y equals z. However,
> SameQ[y,z] --> False
> So here we have an example of two different Mathematica expressions  
> with
> the property that on level 1 all subexpressions are equal:
> And @@ Table[y[[i]] === z[[i]], {i, 0,2}] --> True
> It also is an example of two different expressions that convert to the
> same string:
> Equal[ToString /@ {y,z}] --> True
> The expression y has more leaves than can be found at level -1, and
> anyway less than the number of leaves of the expression z:
> {LeafCount[#], Length[Level[#, {-1}, Heads->True]]}& /@  {y,z} -->
> {{27,25},{29,29}}
> Fred Simons
> Eindhoven University of Technology

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