odd behaviour in 2.2

*To*: mathgroup at yoda.physics.unc.edu*Subject*: odd behaviour in 2.2*From*: wmm at chem.wayne.edu (Martin McClain)*Date*: Thu, 2 Sep 93 18:55:05 EDT

Here is some new behaviour in 2.2 that seems like it needs professional attention: In[137]:= $Version Out[137]= Macintosh 2.2 (May 4, 1993) In[138]:= Remove[nameRule,aName,mat,matSq] (*everything*) Suppose there is a matrix you want to recognize by name: In[139]:= nameRule=Sin[1]^2 {{1,0},{0,1}}->aName Out[139]= 2 2 {{Sin[1] , 0}, {0, Sin[1] }} -> aName Now generate the same matrix in a slightly different way: In[140]:= mat = {{1,0}, {0,1}}//Sin; matSq = mat.mat Out[141]= 2 2 {{Sin[1] , 0}, {0, Sin[1] }} and test it to see if it is the named matrix: In[142]:= matSq/.nameRule Out[142]= 2 2 {{Sin[1] , 0}, {0, Sin[1] }} The nameRule did not work in 2.2, though this same script works well in 2.1, giving output "aName". However, the nameRule can be made to work in 2.2 if you Expand: In[143]:= Expand[matSq]/.nameRule Out[143]= aName Why did it work this time? What is the difference? In[146]:= matSq == Expand[matSq] Out[146]= True In[147]:= FullForm[matSq] Out[147]//FullForm= List[List[Power[Sin[1], 2], 0], List[0, Power[Sin[1], 2]]] In[148]:= FullForm[Expand[matSq]] Out[148]//FullForm= List[List[Power[Sin[1], 2], 0], List[0, Power[Sin[1], 2]]] They seem truly identical. However, the pattern matcher uses SameQ, or === (the Bible, 2nd ed., p. 289). So try it: In[145]:= matSq === Expand[matSq] Out[145]= False How come two things that look identical in FullForm come up False in SameQ, and therefore in the pattern matcher? They used to match in 2.1...