Re: Problem with Position applied on 2D list?

*To*: mathgroup at smc.vnet.net*Subject*: [mg72605] Re: [mg72570] Problem with Position applied on 2D list?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 12 Jan 2007 05:05:34 -0500 (EST)*References*: <200701110656.BAA21663@smc.vnet.net>

On 11 Jan 2007, at 06:56, Heiko Damerau wrote: > Dear All, > > There is some strange behaviour of the Position[] function I am > struggling with: > > integerRandomTable = Table[Table[Random[Integer, 10], {10}], {10}]; > > Find the position of all lists containing the value 5 (just a simple > example): > > Position[integerRandomTable, _?(MemberQ[#, 5] &)] > > gives the expected result, e.g. {{1}, {3}, {4}, {5}, {6}, {7}, {8}}. > However, just asking for all lists not containing the value 5 > > Position[integerRandomTable, _?(Not[MemberQ[#, 5]] &)] > > Doesn't give the expected result but some strange thing, e.g. {{0}, > {1,0}, {1, 1}, {1, 2}, {1, 3}, {1, 4}, ..., {10, 3}, {10, 4}, {10, 5}, > {10, 6}, {10, 7}, {10, 8}, {10, 9}, {10, 10}, {10}, {}} > > What is the explanation for the different behaviour of MemberQ[] > and Not[MemberQ[]]? > > Thanks a lot in advance for any help. > > Best regards, > Heiko > The difference is actually as much a question of logic as of the way Position works. Note that Position, without explicit level specification, will look at all levels of your expression. Now, there is a difference between what happens when you want to find all positions of sub-expressions that contain 5 and those that do not contain 5. The only sub-expressions for which Member[#,5]& is True are sublists of your original list, so you get the expected result. But all kinds of other sub-expressions satisfy Not[Member[#,5]&. So to get what you want you should use level specification in Position like this: integerRandomTable = Table[Table[Random[Integer, 10], {10}], {10}]; Position[integerRandomTable, _?(MemberQ[#1, 5] & ),{1}] {{1}, {2}, {4}, {5}, {7}, {10}} Position[integerRandomTable, _?( !MemberQ[#1, 5] & ), {1}] {{0}, {3}, {6}, {8}, {9}} Of course, as you already know, the former case works without level specification but that is actually a kind of accident and in general it is safer to use level specification, unless you really want Mathematica to look at all sub-expressions of your expression. Andrzej Kozlowski Oxford, UK

**References**:**Problem with Position applied on 2D list?***From:*Heiko Damerau <heiko.damerau.news@cern.ch>