Re: Not[OddQ] is not the same as EvenQ (sometimes)

*To*: mathgroup at smc.vnet.net*Subject*: [mg3898] Re: Not[OddQ] is not the same as EvenQ (sometimes)*From*: Robert Knapp <rknapp>*Date*: Sat, 4 May 1996 23:24:03 -0400*Organization*: Wolfram Research, Inc.*Sender*: owner-wri-mathgroup at wolfram.com

Arnold Seiken wrote: > > Dear Mathematica experts, > > Position[{2,3,4,5,6,7}, x_?(EvenQ[#]&)] > {{1}, {3}, {5}} > Position[{2,3,4,5,6,7}, x_?(!OddQ[#]&)] > {{0}, {1}, {3}, {5}} > Therefore, for this example, the pattern x_?(EvenQ[#]&) is not equivalent to > the pattern x_?(!OddQ[#]&). The latter matches with the head List of {2,3,4,5,6,7}, the former does not. But > Position[{-2,3,4,-5,6,7}, x_?(NonNegative[#]&)] > {{2}, {3}, {5}, {6}} > Position[{-2,3,4,-5,6,7}, x_?(!Negative[#]&)] > {{2}, {3}, {5}, {6}} > shows that the Head List is sometimes ignored by Position. Finally > Position[{1,3,5}, x_?(!OddQ[#]&)] > {{0}} > Position[{2,3,4,5,6,7}, x_?(!NumberQ[#]&)] > {{0}, {}} > Position[{2,3,4,5,6,7}, x_?(!Positive[#]&)] > {} > seems to show that there are really three possible outcomes when using Not in a pattern involving the Position command. This does not occur for either the Cou > > Count[{1,3,5,7}, x_?(EvenQ[#]&)] > 0 > Count[{1,3,5,7}, x_?(!OddQ[#]&)] > 0 > Any explanations? > The explanation is that Position looks at all levels of it argument, including the head. Look at the FullForm to the list in question: In[1]:= expr = {2,3,4,5,6,7}; In[2]:= FullForm[expr] Out[2]//FullForm= List[2, 3, 4, 5, 6, 7] it head is the symbol List. Furthermore, by convention, the "0th" element of an expression is its head. Thus: In[3]:= expr[[0]] Out[3]= List now the symobol List is neither Odd nor Even, so it does not satisfy EvenQ, but it does satisfy Not[OddQ[#]]& . This is why Position is giving {{0},...} in that case. On the other hand, Count does not by default go into the heads. This can be changed by an option: In[4]:= Count[{1,3,5,7},x_?(!OddQ[#]&),Heads->True] Out[4]= 1 In[5]:= Count[{1, 3, 5, 7},x_?EvenQ,Heads->True] Out[5]= 0 Rob Knapp Wolfram Research, Inc. http://www.wri.com/~rknapp ==== [MESSAGE SEPARATOR] ====