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 ---------------------------------------------------------------------