# Asymptote: Macros and Packages

## Definitions

You can define your own functions in Asymptote. As an example, let's say you wanted to make a function called `newfunction` that takes a pair and a real value as input, and returns the pair . In addition, you want it to simply return the pair if no value of is specified, so you want to default to . 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 was set to by , and the actual function procedure goes in between `{}`. To define a function with no output simply put `void` before the function name. 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 `graph.asy` 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 `circle` command. To use this function and others in graph.asy, simply put the command

import graph;

at the top of your Asymptote document. Graph also has more advanced functions such as the ability to Graph a function

You can create your own package by simply creating a new .asy file (say `MyMacros.asy`) with your own definitions in it, and saving it in the directory in which Asymptote is installed (`C:\Program Files\Asymptote` by default). Then `import MyMacros;` 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 here or here (the latter link has a few usage examples).

This package includes the following definitions:

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

`*` These boolean functions test for equality within ps points in order to avoid approximation errors.