Re: pure functions

• To: mathgroup at smc.vnet.net
• Subject: [mg23292] Re: [mg23237] pure functions
• From: Bojan Bistrovic <bojanb at python.physics.odu.edu>
• Date: Sun, 30 Apr 2000 21:13:42 -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
>

This does the trick:
In[1]:= exli={{1,2},{3,4},{5,6},{7,8}};
In[2]:= ((Plus@@ #1) &) /@ exli
Out[2]= {3,7,11,15}

Parenthesis aren't necessary; they are for the reader's benefit. There's no
need for any argument list in your example since  (#>3)& is applied to every
element of the list, not to the whole list.

Bye, Bojan

--
---------------------------------------------------------------------
Bojan Bistrovic,                                      bojanb at jlab.org
Old Dominion University, Norfolk VA & Jefferson Lab, Newport News, VA
---------------------------------------------------------------------

```

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