On Thu, Mar 24, 2011 at 12:12 AM, Aaron S. Meurer <asmeu...@gmail.com> wrote: > On Mar 23, 2011, at 10:20 PM, Tim Lahey wrote: > >> Hi, >> >> I've been thinking about GSoC and looking at the various ideas people have >> been posting. By the way, I'd like to see perturbation theory included in >> general (i.e., not just for quantum mechanics) since it's used in stability >> analysis. > > Yes definitely. Another thing that should not be implemented only in physics.
My only hesitancy is that perturbation *theories* tend to be very specific to the equations you are solving. For example, even within quantum mechanics, there are probably a dozen different perturbation theories. The reason for this is that: * it is non-trivial to identify and fully solve the non-perturbed system. * Writing a perturbation series that converges at all or quickly is not an easy task. I don't disagree that it would be nice to have this, but I think it is not the place to *start* with perturbation theory for a GSoC project. I am biased, but the various quantum perturbation theories are well known and would be a good place for starting to identify the common aspects of all perturbation theories (similar to how the operators, commutators, etc. in physics.quantum will end up doing). >> >> I have a few linear algebra related ideas I'd like to see. One is "abstract" >> linear algebra. That is support for arbitrary matrix and vector >> calculations. So, one would just indicate that a symbol is a matrix/vector >> without stating the size. Then you could work with them. The non-commutative >> support is a start, but the transpose operation would need to be added along >> with derivatives. I have a Maple worksheet that has a crude version of this. >> This is used quite a bit in the Ritz approach to Finite Element Analysis. Yes, this could be quite useful. Cheers, Brian >> >> The other linear algebra thing to add is support for block matrices. So, one >> could specify a matrix like >> >> M = [[A,B],[C,D]] >> >> where A, B, C, and D are arbitrary matrices. Then, you could take the >> inverse and other standard linear algebra. This fits in with the "abstract" >> linear algebra support. This kind of thing pops up a lot in control theory. >> >> Cheers, >> >> Tim. >> >> --- >> Tim Lahey >> PhD Candidate, Systems Design Engineering >> University of Waterloo >> http://about.me/tjlahey > > These sound like good ideas. > > By the way, Sherjil Ozair is also applying to do some work on the matrices, > but I think he is planning on doing different stuff, like sparse matrices and > integration with the polys ground types (gmpy). Maybe you could collaborate > with him to apply to do different things. There are enough things to do in > the matrices to cover two projects, I think. That way (assuming you both had > high enough quality applications) you could both potentially be accepted at > the same time. > > Otherwise, if you apply to do the exact same thing, we will have to pick one > of you (again assuming both are good enough to be accepted). > > Aaron Meurer > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > > -- Brian E. Granger, Ph.D. Assistant Professor of Physics Cal Poly State University, San Luis Obispo bgran...@calpoly.edu elliso...@gmail.com -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
