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Re: Exercise of Programming with Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131886] Re: Exercise of Programming with Mathematica
  • From: mike.honeychurch at gmail.com
  • Date: Wed, 23 Oct 2013 23:46:14 -0400 (EDT)
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On Tuesday, October 22, 2013 3:54:30 PM UTC+11, Alexei Boulbitch 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}}
> 
> 
> 
> 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?
> 
> 
> 
> Thanks.
> 
> 
> 
> 
> 
> You are right, this is a nice exercise in Mathematica. Considering it as such, I would like to offer few solutions that were not yet mentioned. Some of them are not shorter. What's the matter, is it not the exercise?
> 
> 
> 
> Here are two list to try with:
> 
> 
> 
> lst1 = {{a, b}, {c, d}, {e, f}};
> 
> lst2 = {{a, b}, {c, d}};
> 
> 
> 
> 1. Mapping Permute onto a list:
> 
> 
> 
> Map[Permute[#, Cycles[{{2, 1}}]] &, lst1]
> 
> Map[Permute[#, Cycles[{{2, 1}}]] &, lst2]
> 
> 
> 
> {{b, a}, {d, c}, {f, e}}
> 
> 
> 
> {{b, a}, {d, c}}
> 
> 
> 
> 2. Using Transpose + Rule:
> 
> 
> 
> Transpose[lst] /. {x_, y_} -> {y, x} // Transpose
> 
> 
> 
> {{b, a}, {d, c}}
> 
> 
> 
> 3. Transpose and hands:
> 
> 
> 
> {Transpose[lst1][[2]], Transpose[lst1][[1]]} // Thread
> 
> 
> 
> {{b, a}, {d, c}}
> 
> 
> 
> Or {Transpose[lst1][[2]], Transpose[lst1][[1]]} // Transpose
> 
> 
> 
> 4. Mapping a rule onto a list:
> 
> 
> 
> Map[ReplaceAll[#, {x_, y_} -> {y, x}] &, lst1]
> 
> Map[ReplaceAll[#, {x_, y_} -> {y, x}] &, lst2]
> 
> 
> 
> {{b, a}, {d, c}, {f, e}}
> 
> 
> 
> {{b, a}, {d, c}}
> 
> 
> 
> 5. Using Thread+Rule+Thread or Transpose
> 
> 
> 
> Transpose[Thread[lst1] /. {x_, y_} -> {y, x}]
> 
> 
> 
> {{b, a}, {d, c}, {f, e}}
> 
> 
> 
> Thread[Thread[lst1] /. {x_, y_} -> {y, x}]
> 
> 
> 
> {{b, a}, {d, c}, {f, e}}
> 
> 
> 
> Have fun, Alexei
> 
> 
> 
> Alexei BOULBITCH, Dr., habil.
> 
> IEE S.A.
> 
> ZAE Weiergewan,
> 
> 11, rue Edmond Reuter,
> 
> L-5326 Contern, LUXEMBOURG
> 
> 
> 
> Office phone :  +352-2454-2566
> 
> Office fax:       +352-2454-3566
> 
> mobile phone:  +49 151 52 40 66 44
> 
> 
> 
> e-mail: alexei.boulbitch at iee.lu


While there are many ways to do this I usually use Part

lst1 = {{a, b}, {c, d}, {e, f}};

lst1[[All, {2, 1}]]



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