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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <l450e6$shr$1@smc.vnet.net>

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}]]