This post will explain the notation used to denote partial derivatives in the output from Sage.  It’s confusing at first, but a simple example will make it clear. Here is the input to Sage:

var('x y')
function('test', x, y)
show(test(x, y))
show(diff(test(x, y), x))
show(diff(test(x, y), x, 2))
show(diff(test(x, y), y))
show(diff(test(x, y), y, 2))

I defined a function of two variables called test.  When you run this in the notebook interface, you get:

I recently upgraded my desktop workstation from an old 32-bit version of Gentoo to 64-bit CentOS 5.  I downloaded and installed the latest version of Sage, and the process went smoothly. If you find this post helpful, please check out the Sage Beginner’s Guide at Packt Publishing.  Since I don’t use Sage every day, I actually refer to my own book on a regular basis!

Download

Since CentOS is designed to be binary compatible with Red Hat Enterprise Linux, the correct binary to download is sage-4.7.2-linux-64bit-red_hat_enterprise_linux_server_release_5.6_tikanga-x86_64-Linux.tar.gz

The easiest way to run Sage on Windows is with a virtual machine.  Sage is a collection of tools that were primarily developed for UNIX-based operating systems (such as Solaris or Mac OS X)  or UNIX-like operating systems (BSD, Linux, etc).  Since a standard Windows installation lacks many of the features provided by a UNIX-like environment, Sage is packaged as a Linux virtual machine.  You need free virtualization software–VMWare Player or VirtualBox--to run the virtual machine.  I find VMWare Player easier to work with, but it’s not an open-source solution.  VirtualBox is truly free software, but it’s also harder to configure.  When you download Sage, you can choose between a .ova file (for VirtualBox) or a zipped VMware virtual machine.  The easiest thing to do is choose the appropriate format for your VM.  However, it’s also possible to run the VMware image on Virtualbox, and I’ll show you how. If you want to learn more about Sage, check out the Sage Beginner’s Guide from Packt Publishing. Download, install, and run VirtualBox, and then click the “New” button to get started.  Also, unzip the .zip file that contains the VMware virtual machine.

I’ve recently gained a lot of experience with Sage, an open-source alternative to MATLAB, Mathematica, Maple, MuPAD, and Magma.  Here are a couple of links to check out:

Public notebook servers--try it online right now! Interactive examples with Sage

• Mathematical publications citing Sage

Sage vs. Mathematica

My experience with mathematical software started my freshman year at the University of Illinois when I signed up for a calculus class that was taught almost entirely with Mathematica.  I grew to love Mathematica’s symbolic computation and plotting capabilities, although I found its programming language to be cumbersome.  Once I was no longer a student, Mathematica was no longer an option due to the hefty licensing fees.  With the caveat that I haven’t used Mathematica in many years,  I will say that Sage compares very favorably to my experience with Mathematica.  Sage has a notebook interface that allows you to integrate code, results, text, typeset equations, and graphics in an interactive document that can be viewed with any standards-compliant web browser.  I don’t know how Sage stacks up against Mathematica in areas of advanced mathematics.  I have heard that Sage is far ahead of Mathematica in number theory, because the lead developer of Sage is a number theorist.