Re: newbie list question

*To*: mathgroup at smc.vnet.net*Subject*: [mg115012] Re: newbie list question*From*: dr DanW <dmaxwarren at gmail.com>*Date*: Tue, 28 Dec 2010 06:50:43 -0500 (EST)*References*: <if70bt$330$1@smc.vnet.net>

Your first lesson in functional programming. First, if you are serious about learning Mathematica, you should pick up a book that covers the fundamentals, like The Mathematica Cookbook from O'Reilly. I've been using Mathematica for over 20 years, and I still read one of these books every so often because there is always something I have missed. I would suggest reading the Doc Center, but alas it has become so fragmented over the last few versions that it does not read as a book (a linear introduction of concepts) which would really help the new user. Here are your lists: In[1]:= listA = {4, 5, 8, 2, 6, 4}; In[2]:= listB = {8, 4, 2}; When facing a problem like this you want to build up your expression. Only the very gifted can write an elegant Mathematica expression in one pass. First, consider the question "how do I find the position of one specific element in listA?" After reading tutorial/ TestingAndSearchingListElements, you realize that Position[] is the function you need: In[3]:= Position[listA, 4] Out[3]= {{1}, {6}} well, that gave you every position of 4 in listA, presented as a list (which makes more sense if you are looking for elements in a matrix, but is done this was for a list for consistency). So, use Part[] (also done as double brackets [[ ... ]] ) to extract the value you need: In[4]:= Position[listA, 4][[1,1]] Out[4]= 1 Great, so you can do it for one value, but you have a list. This is the functional programming part. In functional languages, once you have a function to do something once, there are functions that you can use to work that function over elements of a list (or matrix, or more deeply nested structures.) In this case, you need Map[]. In[5]:= (Position[listA, #1][[1,1]] & ) /@ listB Out[5]= {3, 1, 4} Where is Map? This is the part that throws a lot on new users, the use of operators instead of function names looks like the cat walked across the keyboard. Once again, break it down. First you need to make a Function[]. Completely spelled out, this would be Function[{x}, Part[ Position[listA, x], 1, 1 ] ] in operator shorthand, it becomes (Position[listA, #1][[1,1]] & ) where the #1 indicates the first slot of the function (a generic tag for the first argument in the function call) and the & is the operator for Function[]. In Mathematica, operators can be placed before (prefix) in the middle (infix) or after (postfix) the arguments. This sounds confusing at first, but it makes sense as you use it. Finally, the operator /@ is an infix operator for Map[]. Map[ list, fun ] (or fun /@ list ) throws the function fun at every element of list and returns a list of the results. Practice with this. Experiment with it in Mathematica, see what happens when you change things in the expression, or have a more deeply nested structure you are looking in. Enjoy, Daniel

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