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{{Asymptote}}

==Definitions==
You can define your own functions in Asymptote.  As an example, let's say you wanted to make a function called <tt>newfunction</tt> that takes a pair <math>(a,b)</math> and a real value <math>r</math> as input, and returns the pair <math>(a+r,b+r)</math>.  In addition, you want it to simply return the pair <math>(a,b)</math> if no value of <math>r</math> is specified, so you want <math>r</math> to default to <math>0</math>.  The code would be as follows:
  pair newfunction(pair z, real r=0)
  {
   real a,b;
   a=z.x;
   b=z.y;
   return (a+r,b+r);
  }

Put this definition in an asymptote document and then test it using some command like  
 draw(newfunction((20,30))--newfunction((20,30),30)--(0,0)--cycle);  
See if it works!

Notice that the function must be declared a pair since it returns a pair, and each of the variables must be declared some data type too.  The default value of <math>r</math> was set to <math>0</math> by <math>r=0</math>, and the actual function procedure goes in between <tt>{}</tt>.  This is the general format for a function definition.

==Packages==
Asymptote comes with several packages that contain useful functions for various purposes.  For example, the package <tt>graph.asy</tt> contains the function 
  Circle(pair p, real r, int n=400);
which is a more accurate circle (having 400 nodes by default) than the built-in <tt>circle</tt> command.  To use this function and others in graph.asy, simply put the command
 import graph;
at the top of your Asymptote document.

You can create your own package by simply creating a new .asy file (say <tt>MyMacros.asy</tt>) with your own definitions in it, and saving it in the directory in which Asymptote is installed (<tt>C:\Program Files\Asymptote</tt> by default).  Then <tt>import MyMacros;</tt> in your document, and you'll be set!
  
===The Olympiad Package===
We have created an Olympiad package for Asymptote which includes macros for all the constructions that come up most often in Olympiad geometry problems!  You can obtain the package olympiad.asy by clicking [[http://web.mit.edu/monks/www/olympiad.asy here]].  

This package includes the following definitions:

[[Image:Olympiad1.gif]]

[[Image:Olympiad2.gif]]

[[Image:Olympiad3.gif]]

[[Image:Olympiad4.gif]]

[[Image:Olympiad5.gif]]

'''Note:''' A sequence of variables without type declarations indicates that they are the same type as the variable preceding it.  For example, the notation <tt>concurrent(pair A, B, C, D, E, F)</tt> indicates that all of the variables should have type pair.

<tt>*</tt> These boolean functions test for equality within <math>10^{-5}</math> ps points in order to avoid approximation errors.

[[Asymptote: Advanced|Next: Advanced]]