pure functions

• To: mathgroup at smc.vnet.net
• Subject: [mg23237] pure functions
• From: Helge Andersson <helgea at inoc.chalmers.se>
• Date: Sat, 29 Apr 2000 22:04:46 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

Of all the nice functions such as Map, Mapall, Thread, Apply .... I have
not been able to write a simple code to generate the following
procedure.

I have a two dimensional list like

li={{11,12,13,..},{21,22,23,...},{31,32,33,..},...}

Since i like to use the pure function command I would like to map my
pure function with arguments #1,#2,#3,.... on all the sublists in li.

Let me exemplify with a simple pure function that add to numbers.
(#1+#2)&

if exli={{1,2},{3,4},{5,6},{7,8}}

then I want to get the result
{3,7,11,15}

One solution, but not allways suitable for me, is the following

(#1+#2)&[Sequence @@ Transpose[exli]].

I want to get rid of the Transpose command and if possible also making
use of the /@ notation for Map. Since I have seen so many elegant
examples in the mailing lists I hope  I can get something out of this.

Finally, When using pure functions inside Mathematica defined functions
such as Select for instance,
Select[{1,2,3,4,5,6},#>3&]
why don't we need to specify the argument list after the &sign. I can
figure out that in this case the list sent to the Select command will be
used as argument list for the pure function but how does this work in
general. Which are the functions where this feature is possible?

/Helge

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