I am writing this blag post from the <a href="http://www.math-conf.uni-hannover.de/spp1489/index.php" target="_blank">second annual meeting of the DFG priority programme SPP1489</a> (algorithmic and experimental methods in algebra, geometry and number theory). Apart from having a lot of fun, I am catching up on the recent developments in open-source computer algebra software. <span id="more-422"></span>
## The Players
The main problem seems to be that there are many different projects with fundamentally different history (and interface language). Let's get a small overview of the major players (up to my knowledge):
* <a href="http://www.math.uiuc.edu/Macaulay2/" target="_blank">Macaulay2</a> is particularly good at computing Betti numbers, Ext, cohomology of coherent sheaves on projective varieties, primary decomposition, integral closure, etc. The software has the prominent name of <a href="http://www.msri.org/~de/" target="_blank">David Eisenbud</a> on it, which also gives a good idea of what it was developed for. It has a very nice <a href="http://www.cygwin.com/" target="_blank">cygwin</a> port, which I find important.
* <a href="http://polymake.mathematik.tu-darmstadt.de" target="_blank">Polymake</a> is the one I did not get to work under <a href="http://www.cygwin.com/" target="_blank">cygwin</a>, so I could not give it a decent try. However, when it comes to anything that has to do with polytopes/polyhedra, it seems like a prominent choice.
* <a href="http://www.singular.uni-kl.de/" target="_blank">Singular</a> is the system developed by the very active group at <a href="http://www.mathematik.uni-kl.de/CDindex_e.html" target="_blank">Kaiserslautern</a>. As the name suggests, studying singularities of algebraic varieties is something it is good at. It can be installed in cygwin without a problem, just note that you will want to install the <b>rxvt</b> shell when you want to use <a href="http://www.singular.uni-kl.de/Manual/3-0-3/sing_1222.htm#SEC1281" target="_blank">singular's plotting capabilities</a> - it seems to be the default shell for the shortcuts that are created. You will probably still have to fix the shortcuts, though, since they link to <b>..\cygwin\bin\rxvt</b> rather than <b>..\cygwin\bin\rxvt.exe</b>. After that, <a href="http://surf.sourceforge.net/" target="_blank">surf</a> should be working and I personally just love it.
* <a href="http://www.gap-system.org/" target="_blank">GAP</a> seems to be the choice for doing computational group theory, but I did not have time to actually try it out. Its <a href="http://www.gap-system.org/Download/index.html" target="_blank">download section</a> has detailed descriptions on how to install it on mac, windows and *nix, though. Seems nice.
## Sage
Now, wouldn't you want <b>one</b> large software package that can do <b>everything</b> these systems do, all combined into one? Of course you would, and there has been one major effort to achieve this: The <a href="http://www.sagemath.org/" target="_blank">sage computer algebra system</a>. Now, while this is a good idea and has reasonable installation options for windows, mac and *nix, sage is not very easily extensible.
## If Life gives you Lemons ...
Presented during the conference was the software package <a href="http://www.lmona.de/" target="_blank">lmonade</a> (pronounced <b>lemonade</b>) which is still work in progress, but which offers a much more flexible way to reconcile various computer algebra systems. I am currently struggling to make it work under cygwin without success, but I did appreciate the basic idea. Moreover, I have great confidence in its author Burcin Erocal, who presented the software at the conference and who is outstandingly competent. So, I urge everyone to give lmonade a look and, possibly, some support.