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

*To*: mathgroup at smc.vnet.net*Subject*: [mg3911] Re: Not[OddQ] is not the same as EvenQ (sometimes)*From*: roth at sunny.mpimf-heidelberg.mpg.de (Arnd Roth)*Date*: Sun, 5 May 1996 23:13:04 -0400*Organization*: Max-Planck-Institut fuer Medizinische Forschung*Sender*: owner-wri-mathgroup at wolfram.com

In article <4m1hq2$pq4 at dragonfly.wolfram.com> "Arnold Seiken" <SEIKENA at gar.union.edu> writes: > 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 Count or Cases command where you get what you expect to get. > > Count[{1,3,5,7}, x_?(EvenQ[#]&)] > 0 > Count[{1,3,5,7}, x_?(!OddQ[#]&)] > 0 > Any explanations? The differences can be easily explained by noting that In[1]:= Options[Position] Out[1]= {Heads -> True} In[2]:= Options[Count] Out[2]= {Heads -> False} and In[3]:= Attributes[NumberQ] Out[3]= {Protected} In[4]:= Attributes[Positive] Out[4]= {Listable, Protected} and the the fact that EvenQ[] and NonNegativeQ[] also behave differently on the Head List: In[5]:= EvenQ[List] Out[5]= False In[6]:= NonNegative[List] Out[6]= NonNegative[List] (Negative and NonNegative are also Listable.) Try wrapping your inputs in Trace[] to see what happens depending on the Option for Position. I'm reluctant to put the Trace output here because it is a bit long. Sincerely, Arnd Roth Abteilung Zellphysiologie Max-Planck-Insitut fuer Medizinische Forschung Postfach 10 38 20, D-69028 Heidelberg, Germany http://sunny.mpimf-heidelberg.mpg.de/people/roth/ArndRoth.html ==== [MESSAGE SEPARATOR] ====