A harmless and amusing bug

*To*: mathgroup at smc.vnet.net*Subject*: [mg76215] A harmless and amusing bug*From*: Fred Simons <f.h.simons at tue.nl>*Date*: Fri, 18 May 2007 06:02:28 -0400 (EDT)

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

**Follow-Ups**:**Re: A harmless and amusing bug***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: A harmless and amusing bug***From:*"Chris Chiasson" <chris@chiasson.name>