Re: beginner question about syntax

*To*: mathgroup at smc.vnet.net*Subject*: [mg109105] Re: beginner question about syntax*From*: telefunkenvf14 <rgorka at gmail.com>*Date*: Mon, 12 Apr 2010 23:02:51 -0400 (EDT)*References*: <hputp3$lh7$1@smc.vnet.net>

On Apr 12, 5:48 am, AK <aaa... at googlemail.com> wrote: > Hi, > > I'm a fairly seasoned user of another system who's just started using > Mathematica. Although at the moment I'm just playing around with > Mathematica (without any specific task at hand), trying to figure out > the Mathematica way of doing things from the documentation > (particularly the examples) there are some things I can't seem to wrap > my head around. For example, can anyone explain the outputs for the > inputs below: > In[1]:= Map[Function[x, x^2], a] > Out[1]:= a > In[2]:=Map[Function[x, x^2], a + b + c] > Out[2]:= a^2 + b^2 + c^2 > > If I enclose the second argument of Map[] inside a list, I get the > expected output, but I don't understand what the operations given in > the example above represent and why the outputs are what they are. > Would appreciate an explanation for what's going here... thank you in > advance. Pure functions are easier to understand using the following notation, where the #1 stands for the first variable in your function. Evaluating it just returns the same thing. In[1]:= #1^2& Out[1]= #1^2& If you want to apply the pure function to 'a', one way to do this is: In[2]:= #1^2&[a] Out[2]= a^2 Note that if I add another variable, I get the same thing: In[3]:= #1^2&[a,b] Out[3]= a^2 Map[] can also be used to apply the pure function. (Note: (1) Mathematica applies Map at level 1, by default. (2) Most people use the /@ notation rather than wrapping with Map[] all the time.) In[4]:= #1^2&/@{a} Out[4]= {a^2} Also note that the following: In[5]:= #1^2&/@(a) Out[5]= a And for your second example, I'm not sure if you wanted: In[6]:= #^2&/@(a+b+c) Out[6]= a^2+b^2+c^2 Or, In[7]:= #^2&/@{a+b+c} Out[7]= {(a+b+c)^2} I'm sure someone else will chime in with a better/clearer answer and a lecture on levels of expressions in Mathematica... -RG