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Re: Exercise of Programming with Mathematica

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  • Subject: [mg131873] Re: Exercise of Programming with Mathematica
  • From: Itai Seggev <itais at wolfram.com>
  • Date: Sun, 20 Oct 2013 23:40:47 -0400 (EDT)
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On Fri, Oct 18, 2013 at 04:45:28AM -0400, Zhenyi Zhang wrote:
> Here is a rule designed to switch the order of each pair of expressions in a list. It works fine on the
> first example, but fails on the second.
> In[1]:= {{a, b}, {c, d}, {e, f}}/.{x_, y_} :> {y, x}
> Out[1]= {{b, a}, {d, c}, {f, e}}
> In[2]:= {{a, b}, {c, d}}/.{x_, y_} :> {y, x}
> Out[2]= {{c, d}, {a, b}}
> Explain what has gone wrong and rewrite this rule to correct the situation, that is, so that the second
> example returns {{b, a}, {d, c}}

Nothing has gone wrong.  :)  Seriouly, You're entirely input is an ordered pair
with x -> {a,b} and y -> {c, d}.  The reason the first example works is that it
has 3 pairs, so the binding isn't possible.  Remember, ReplaceAll (/.)  always
looks for the larges subexpression it can match first. 

> My solution is the most stupid one.
> 
> {{a, b}, {c, d}}/.{{x_, y_}, {w_, t_}} :> {{y, x}, {t, w}}
> 
> May I ask any elegant solutions?

With this pattern, x and y cannot themselves be lists:

In[115]:= {{a, b}, {c, d}} /. {x : Except[_List],  y : Except[_List]} -> {y, x}

Out[115]= {{b, a}, {d, c}}

--
Itai Seggev
Mathematica Algorithms R&D
217-398-0700 



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