Or in a Select question

• To: mathgroup at smc.vnet.net
• Subject: [mg67066] Or in a Select question
• From: János <janos.lobb at yale.edu>
• Date: Thu, 8 Jun 2006 04:54:07 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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->\\
\\\", 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->\\
\\\", ButtonFrame->None, ButtonData:>\\\"General::partd\\\"]\\)\"\>"}]\)
Out[103]=
{}
From In[104]:=
Part::"partd":"Part specification \!\(u \[LeftDoubleBracket] 2 \
\[RightDoubleBracket]\) is longer than depth of object. \
\", \
ButtonFrame->None, ButtonData:>\"General::partd\"]\)"
From In[104]:=
Part::"partd":"Part specification \!\(v \[LeftDoubleBracket] 2 \
\[RightDoubleBracket]\) is longer than depth of object. \
\", \
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 :)

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)

```

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