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Getting started with Julia

Julia is a freely available open-source programming language aimed at technical computing.

As it is open source, indeed with a liberal MIT license, it can be installed for free on many types of computers (though not phones or tablets). There are some web sites that provide access to Julia:

JuliaBox provides a web-based interface to Julia built around IJulia. An account is needed and can be requested.

Sagemath provides another web-based solution and an Jupyter front end, as well. This is free for most use.

Installing Julia locally

Binaries of Julia are provided at julialang.org. Julia has an official released version and a developmental version. Unless there is a compelling reason, the latest released version should be downloaded and installed for use.

The base Julia provides a command-line interface, or REPL (read-evaluate-parse).

Basic interactive usage

Once installed, Julia can be started by clicking on an icon or typing julia at the command line. Either will open a command line interface for a user to interact with a Julia process. The basic workflow is easy: commands are typed then sent to a Julia process when the "return" key is pressed for a complete expression. Then the output is displayed.

A command is typed following the prompt. An example might be 2 + 2. To send the command to the Julia interpreter the "return" key is pressed. A complete expression or expressions will then be parsed and evaluated (executed). If the expression is not complete, julia's prompt will still accept input to complete the expression. Type 2 + to see. (The expression 2 + is not complete, as the infix operator + expects two arguments, one on its left and one on its right.)

               _
   _       _ _(_)_     |  A fresh approach to technical computing
  (_)     | (_) (_)    |  Documentation: http://docs.julialang.org
   _ _   _| |_  __ _   |  Type "?help" for help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 0.4.1 (2015-11-08 10:33 UTC)
 _/ |\__'_|_|_|\__'_|  |  Official http://julialang.org/ release
|__/                   |  x86_64-apple-darwin13.4.0

julia> 2 + 2
4

Above, julia> is the prompt. These notes will not include the prompt, so that copying-and-pasting can be more easily used. Input and output cells display similarly, though with differences in coloring. For example:

2 + 2

IJulia, a better learning enviroment for Julia

A more forgiving interface for learning is provided through the IJulia interface. This is the interface for JuliaBox. The IJulia interface can be installed relatively easily by following these steps:

  • Run these commands to install two packages:
Pkg.update()
Pkg.add("PyCall")
Pkg.add("IJulia")
  • Once this is done, you can start the notebook with these commands:
using IJulia
notebook()

Add-on packages

Julia has 100s of external, add-on packages that enhance the offerings of base Julia. The above showed how to add two packages to a system. In these notes, we will rely on a few packages. These will need to be installed. The following commands will download and install the needed packages:

Pkg.update()
Pkg.add("Plots")
Pkg.add("Gadfly")
Pkg.add("PyCall")
Pkg.add("SymPy")
Pkg.add("Roots")
Pkg.add("ImplicitEquations")
Pkg.add("PyPlot")
""")

The SymPy package and the PyPlot package require some add-ons for the Python environment. These should be installed as well, a Python environment, if not already existing, should be installed withe PyCall package.

The basics of working with IJulia

The very basics of IJulia are covered here.

An IJulia notebook is made up of cells. Within a cell a collection of commands may be typed (one or more).

When a cell is executed (by the triangle icon or under the Cell menu) the contents of the cell are evaluated by the Julia kernel and any output is displayed below the cell. Typically this is just the output of the last command.

2 + 2
3 + 3

If the last commands are separated by commas, then a "tuple" will be formed and each output will be displayed, separated by commas.

2 + 2, 3 + 3

Comments can be made in a cell. Anything after a # will be ignored.

2 + 2  # this is a comment, you can ignore me...

Graphics are provided by external packages. There is no built-in graphing. We primarily use the Gadfly package for graphics, but through the Plots package.

The plots package is loaded and the Gadfly backend is chosen via

using Plots
gadfly()

The choice of Gadfly as a backend is optional, the Plots package does its best to be backend agnostic.

With that in hand, to make a graph of a function over a range, we follow this pattern:

plot(sin, 0, 2pi)

A few things:

  • Cells are numbered in the order they were evaluated.

  • This order need not be from top to bottom of the notebook.

  • The evaluation of a cell happens within the state of the workspace, which depends on what was evaluated earlier.

  • The workspace can be cleared by the "Restart" menu item under "Kernel". After restarting the "Run All" menu item under "Cell" can be used to re-run all the commands in the notebook. This will also reload any packages.