Re: A harmless and amusing bug

• To: mathgroup at smc.vnet.net
• Subject: [mg76337] Re: [mg76215] A harmless and amusing bug
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 20 May 2007 02:22:08 -0400 (EDT)
• References: <200705181002.GAA12592@smc.vnet.net>

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

a=Rational[1,2]&

Now define b as follows. We use the same definition

b=Rational[1,2]&

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
False

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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