Re: Getting stuck with finding an elegant solution without global variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg124821] Re: Getting stuck with finding an elegant solution without global variables*From*: "Oleksandr Rasputinov" <oleksandr_rasputinov at ymail.com>*Date*: Wed, 8 Feb 2012 05:31:10 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On Tue, 07 Feb 2012 09:08:28 -0000, Fredob <fredrik.doberl at gmail.com> wrote: > Hi, > > I am trying to find an elegant solution, i.e. without a global > variable to the following problem: > > Given a list, e.g. {1,2,3,4}, create a new list where each element is > a function of the "i th" element and the rest of the list, e.g. > > Branch[Elem_, List_] := Elem + Cases[List, Except[Elem]] > > The the result would be {{3, 4, 5}, {3, 5, 6}, {4, 5, 7}, {5, 6, 7}} > > I have used Map[f, List] but then I have to use a global variable in f > to access the list itself, e.g. BranchG[Elem_] := Elem + Cases[List, > Except[Elem]] > It seems to me that you are asking not for elegant solutions per se, but rather for solutions in a pure functional style. As such I assume that it is not so much global variables that you wish to avoid using as any user-defined named symbols (variables) at all. Actually, the clearest way to accomplish this (in my opinion) is indeed to use Map: Function[{f, lst}, Through[f[Part, Delete][lst, #]] & /@ Range@Length[lst] ][Plus, {1, 2, 3, 4}] {{3, 4, 5}, {3, 5, 6}, {4, 5, 7}, {5, 6, 7}} Obviously other functions can be used as well, such as Times: Function[{f, lst}, Through[f[Part, Delete][lst, #]] & /@ Range@Length[lst] ][Times, {1, 2, 3, 4}] {{2, 3, 4}, {2, 6, 8}, {3, 6, 12}, {4, 8, 12}} Or we can return a closure over the list, leaving f unspecified until later: In := Function[lst, Function[f, Through[f[Part, Delete][lst, #]] & /@ Range@Length[lst] // Evaluate ] ][{1, 2, 3, 4}] Out = Function[f$, {f$[1, {2, 3, 4}], f$[2, {1, 3, 4}], f$[3, {1, 2, 4}], f$[4, {1, 2, 3}]} ] In := %[Plus] Out = {{3, 4, 5}, {3, 5, 6}, {4, 5, 7}, {5, 6, 7}} And just for fun here is one without Map: Function[{f, lst}, Range@Length[lst] // Function[idx, Through[f[Part, Delete][lst, idx]], Listable ] ][Plus, {1, 2, 3, 4}] {{3, 4, 5}, {3, 5, 6}, {4, 5, 7}, {5, 6, 7}} Although it is not so important here as we have not employed any user-defined symbols in the above, I would caution you against using symbol names starting with capital letters. Especially names like List, which are already in use for fundamental Mathematica language constructs.