On Jan 17, 2009, at 5:45 AM, mhampton wrote: > Currently Phcpack is an optional package for sage. Its main purpose > is to numerically compute isolated solutions of polynomial systems, > although it has some other functionality as well (e.g. computing mixed > volumes, witness sets for higher-dimensional solution components). > > I have wanted Phcpack to be standard in Sage for a while, but have > been blocked by concerns about portability. Phcpack is written in > Ada. Recently Jan Verschelde (the author of Phcpack) and his students > have added some C and Python interfaces, which help integration > efforts but don't solve the portability issue. > > I discussed this situation recently with Jan (who I am cc'ing on this > email in case he has clarifications or corrections) and he seems > willing to work with me on porting Phcpack into Sage as a native > program. Although Phcpack is pretty fast, there are closed source > programs that seem quite a bit faster at the moment (although its not > a simple comparison, they different strengths and weaknesses). A Sage > implementation could be quite a bit faster by taking advantage of > Sage's linear algebra and other components. > > My plan for doing this is to move in the functionality piece by piece > starting in late Febuary (earlier if I can magically find extra > time). The first piece will be a parameter-homotopy path tracker, > since I understand that part the best at the moment and its relatively > straightforward. This would take as input a polynomial start system > and a list of solutions to the start system, and a target system. The > algorithm would deform the start system and its solutions into the > target system and its corresponding solutions. There is quite a bit > of literature on how to do this, and if Jan helps me understand how > Phcpack does this I think it won't be hard to get something running. > Optimizing it will probably take longer but I know there are some Sage > developers out there who might find it fun to help. > > After the parameter homotopy, we would need: > > 1) A way to compute mixed volumes and the cells of a mixed > subdivision. Jan ported a C implementation in Ada to do this, so he > thinks it might be fairly easy for him to do this. > > 2) Create ways to generate start systems and their solutions. The > main way is to use the mixed subdivision from (1), but there are some > alternatives. > > 3) Routines for "endgames" - issues that arise at the end of > homotopies, where solutions might be degenerate in various senses. > > 4) Techniques for higher-dimensional solution components. > > I imagine that Jan and I and our students will do most of this, but we > will need some help and I am soliciting it in advance. One thing I > need is a deeper knowledge of Cython, which will be crucial in getting > our implementation competitive with closed source alternatives.
This sounds great. The math is (as far as I know) outside my field of expertise, but I'm always up for learning something new (subject to time constraints) and I do know quite a bit about Cython. At some point, this sounds like it would make a good coding sprint project at a Sage Days too. The site http://wiki.sagemath.org/SageDays has a listing but seems out of date. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
