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Re: Distinquishing #'s in nested pure functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126279] Re: Distinquishing #'s in nested pure functions
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Sat, 28 Apr 2012 05:28:15 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201204260933.FAA05752@smc.vnet.net>

f[x_, y_] := x - y

f[x, y] // FullForm

Plus[x,Times[-1,y]]

Plus is Listable, e.g.,

f[2, {-1, -2, -3}]

{3, 4, 5}

Consequently, the Map is not necessary

Select[{1, 2, 3}, f[#, {-1, -2, -3}] == {3, 4, 5} &]

{2}

However, often it is necessary to use a helper function to avoid
ambiguity, e.g.,

g[x_] := f[x, {-1, -2, -3}]

Select[{1, 2, 3}, g[#] == {3, 4, 5} &]

{2}


Bob Hanlon


On Fri, Apr 27, 2012 at 6:48 AM, Dave Snead <dsnead6 at charter.net> wrote:
> Hi,
>
> Is there a way to distinguish the #'s in nested pure functions?
>
> As a simple example:
>
> f[x_, y_] := x - y
>
> Select[{1, 2, 3}, (f[#, #] & /@ {-1, -2, -3}) == {3, 4, 5} &]
>
> I want the 1st # to correspond with the outer & (the equal)
> and the 2nd # with the inner & (the map)
> The answer in this example should by {2}
> (of course, the statement as written above does not do the job)
>
> Can Mathematica distinguish these #'s?
>
> Thanks in advance,
> Dave Snead
>



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