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Sage is a free open source symbolic and numerical mathematics software which is programmed in Python. Like Python which comes with batteries included, Sage comes with “matheries” included and is bundled with a host of math and visualization packages - jmol - java 3d molecule viewer, R and much more which can be invoked by importing.
The goal for Sage is to be a viable alternative to Mathematica , Maple and Matlab and it also has support for interaction and animation.
As you can see below you can mix latex and computation in many ways.
The co-creators also point to the need to enable transparency in mathematical research, that you can inspect the PDE solver or factorization into primes. This is completely opaque in Mathematica. There is also support for getting web data see example 2 and 3 which fetches data from NOAA and does an regression analysis on the time interval you choose. The second example fetches arctic ice data and plot for the month you choose. Sage also has a lot of very fast time series support and
The Azimuth project has some pages where Sage/Python/R code has been tested experimentally:
The easiest way is to create an account/pwd on the Sage Notebook cloud server and read the Quickstart and Sage tutorial in the references. Any worksheet you experiment with is private and not visible until you decide to publish it by pressing “publish” that particular notebook.
If you know R and wants to see how that works there is a recent tutorial which was presented on the lates UseR conference 2010.
This can be done on your own machine or by setting up a Sage server for several client notebooks. For the Azimuth project it is probably best to aim for the latter.
If you attempt to install Sage on a Windows machine, be sure to follow the instructions for VMware and not VirtualBox. Apparently, VirtualBox is not supported anymore. Once you know this, it is quite easy to get Sage up and running. Simply
Quickstart on how to interact shows how to get help on all type of mathematical objects and also how to see which operations they support. Which eases the learning procees of Sage
A few Sage quick references
Sage tutorial is the best way to get started with SAGE
Videos on both Python and Sage (http://www.sagemath.org/help-video.html)
Dive into Python Free to download
Automating Conversion of LateX to Sage by Robert Beezer
AskSage similar to Mathoverflow and Physicsoverflow. Based on Askbot and as addictive as them.
Follow the development at SAGE days
Cython a language that makes writing C extensions for the Python language as easy as Python itself. Cython is based on the well-known Pyrex, but supports more cutting edge functionality and optimizations.
Multiprocessing with Sage can be done with the optional MPI4Py package, see the following page and an example of running Laplace transforms in parallel. One other alternative is to use parallel Ipython.
Software Development for Sage
The latest Sage source code