Re: Or in a Select question

*To*: mathgroup at smc.vnet.net*Subject*: [mg67092] Re: Or in a Select question*From*: dh <dh at metrohm.ch>*Date*: Fri, 9 Jun 2006 01:07:37 -0400 (EDT)*References*: <e68q6i$d0p$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Janos, your logic is o.k. apart from the Or (||) where you need an And (&&). Daniel János wrote: > Hi, > > I have a list > > lst={a,b,c} > > I make another list from it the following way: > > In[2]:= > pp = Partition[Tuples[lst, > 2], 2, 1] > Out[2]= > {{{a, a}, {a, b}}, > {{a, b}, {a, c}}, > {{a, c}, {b, a}}, > {{b, a}, {b, b}}, > {{b, b}, {b, c}}, > {{b, c}, {c, a}}, > {{c, a}, {c, b}}, > {{c, b}, {c, c}}} > > From here I would like to select all the elements whose sublists > contain only different elements. So my "logical" selection was: > > In[54]:= > Select[pp, > #1[[1,1]] =!= #1[[1,2]] || > #1[[2,1]] =!= #1[[2, > 2]] & ] > Out[54]= > {{{a, a}, {a, b}}, > {{a, b}, {a, c}}, > {{a, c}, {b, a}}, > {{b, a}, {b, b}}, > {{b, b}, {b, c}}, > {{b, c}, {c, a}}, > {{c, a}, {c, b}}, > {{c, b}, {c, c}}} > > Well, that did not do any damage to the list. After some time I came > up with this one: > > In[49]:= > Complement[pp, Select[pp, > Xor[#1[[1,1]] =!= > #1[[1,2]], > #1[[2,1]] =!= #1[[2, > 2]]] & ]] > Out[49]= > {{{a, b}, {a, c}}, > {{a, c}, {b, a}}, > {{b, c}, {c, a}}, > {{c, a}, {c, b}}} > > That looks OK, but also looks too complicated. Why my "logical" one > does not work here? > > Interestingly if I just use either the left or right side of the Or, > that partial select is working. For example: > > In[65]:= > Select[pp, #1[[1,1]] =!= > #1[[1,2]] & ] > Out[65]= > {{{a, b}, {a, c}}, > {{a, c}, {b, a}}, > {{b, a}, {b, b}}, > {{b, c}, {c, a}}, > {{c, a}, {c, b}}, > {{c, b}, {c, c}}} > > Now if I try with Cases and conditional pattern matching then the > selection for sublists with identical elements works: > > In[98]:= > Cases[pp, {u_, v_} /; > u[[1]] === u[[2]] || > v[[1]] === v[[2]]] > Out[98]= > {{{a, a}, {a, b}}, > {{b, a}, {b, b}}, > {{b, b}, {b, c}}, > {{c, b}, {c, c}}} > > If I change here the === to =!=, then I do not get again that I expect: > > In[103]:= > Cases[pp, > (({u_, v_} /; u[[1]]) =!= > u[[2]] || v[[1]]) =!= > v[[2]]] > From In[103]:= > \!\(\* > RowBox[{\(Part::"partd"\), > ":", "\<\"Part specification \\!\\(u \[LeftDoubleBracket] 2 \ > \[RightDoubleBracket]\\) is longer than depth of object. \ > \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\ > \"RefGuideLinkText\ > \\\", ButtonFrame->None, ButtonData:>\\\"General::partd\\\"]\\)\"\>"}]\) > From In[103]:= > \!\(\* > RowBox[{\(Part::"partd"\), > ":", "\<\"Part specification \\!\\(v \[LeftDoubleBracket] 2 \ > \[RightDoubleBracket]\\) is longer than depth of object. \ > \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\ > \"RefGuideLinkText\ > \\\", ButtonFrame->None, ButtonData:>\\\"General::partd\\\"]\\)\"\>"}]\) > Out[103]= > {} > From In[104]:= > Part::"partd":"Part specification \!\(u \[LeftDoubleBracket] 2 \ > \[RightDoubleBracket]\) is longer than depth of object. \ > \!\(\*ButtonBox[\"More\[Ellipsis]\", ButtonStyle->\"RefGuideLinkText > \", \ > ButtonFrame->None, ButtonData:>\"General::partd\"]\)" > From In[104]:= > Part::"partd":"Part specification \!\(v \[LeftDoubleBracket] 2 \ > \[RightDoubleBracket]\) is longer than depth of object. \ > \!\(\*ButtonBox[\"More\[Ellipsis]\", ButtonStyle->\"RefGuideLinkText > \", \ > ButtonFrame->None, ButtonData:>\"General::partd\"]\)" > > if I change =!= to only != then I still do not get that I expect: > > In[108]:= > Cases[pp, {u_, v_} /; > u[[1]] != u[[2]] || > v[[1]] != v[[2]]] > Out[108]= > {} > > Obviously I am not GETting something here :) > > Thanks ahead, > > János > P.S. It is 5.1 on OSX 10.4.6. I know that Or evaluates in a non- > traditional way and looked the Appendix - that is how I ended up with > Xor. > > > > > > > ---------------------------------------------- > Trying to argue with a politician is like lifting up the head of a > corpse. > (S. Lem: His Master Voice) >