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Topic: Exercise of Programming with Mathematica
Replies: 8   Last Post: Oct 23, 2013 11:33 PM

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Itai Seggev

Posts: 61
Registered: 7/29/13
Re: Exercise of Programming with Mathematica
Posted: Oct 20, 2013 11:19 PM
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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

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