Most importantly, Sage-3.0 finally has code for computing with modular abelian varieties. You almost certainly have no clue what those are, but suffice to say that I started the Sage project to compute with them, so having this code in Sage is a major milestone for me and the project.
We dramatically increased our automated testing and example suite so that 51.5 % of functions have autotested examples. There are now nearly 60,000 lines of input examples. In February our testing was in the 30% range. This was a huge amount of work by many many Sage developers, and it has the practical impact that when you type foo? it is nearly twice as likely that you'll see a helpful example.
There is now a new interface to R that uses a pseudotty; this is a completely different alternative to rpy, which makes it possible for the web-based Sage notebook to work as an R GUI, and also makes it so any R command can be used from Sage 100% exactly as in R. It is still clunky and has numerous issues, but it is fairly usable, documented, and has a test suite. Here it is drawing a plot in the notebook:
So what is the next step for Sage? We have finished rapidly expanding by incorporating major new components. Now we will work on making Sage more accessible and writing new code to make Sage highly competitive with all other options. I see The main goals for this coming year are as follows:
- Port Sage and as many of its components as possible to Microsoft Windows (32 and 64-bit, MSVC) and to Sun's Solaris. For the Windows port the main challenge is writing a native implementation of pexpect for 32 and 64-bit MSVC windows, and porting several math software projects (e.g., R) that until now haven't had the resources to move beyond 32-bit crippled mingw/cygwin. For Solaris, the main issues are simply fixing bugs and improving the quality of the Sage codebase. Michael Abshoff is leading the charge.
- Modular forms and L-functions -- greatly improve all linear algebra needed for modular forms computation; implement a much wider range of algorithms; run large computations and record results in a database. Mike Rubinstein and I will lead the charge.
- Symbolic calculus -- a native optimized and much more general implementation of symbolic Calculus in Sage. Gary Furnish is leading the charge.
- Combinatorics -- migrate the mupad-combinat group to Sage; implementation of a lot more native group theory in Sage. Mike Hansen is leading the charge.
- Statistics -- integrate R and scipy.stats much more fully into Sage with the goal of making Sage the best available environment for statistical computation and education. Harald Schilly is leading the charge.
- The Sage notebook -- separate the notebook from Sage (like I did with Cython); develop the notebook's interactive and visualization functionality much more, and make the notebook easier to use as a graphical frontend for all math software. I am leading the charge until I can find somebody else to do so.
- Magma -- greatly improve the ability of Sage and Magma to work together (many more automatic conversions between Sage and Magma datastructures, etc.); Magma is by far the best in the world and numerous calculations, and much important code been written in Magma, so it's critical that Sage be fully able leverage all that functionality. Also, this will make comparing the capabilities of the two systems much easier. I'm also leading the charge here.