Re: Exercise of Programming with Mathematica

*To*: mathgroup at smc.vnet.net*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)*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*: <20131018084528.A030C6A21@smc.vnet.net>

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

**References**:**Exercise of Programming with Mathematica***From:*Zhenyi Zhang <infozyzhang@gmail.com>