To address the questions: - I would hope for this module to compute root systems, the weight lattice, the Weyl group, the Cartan matrix, and hopefully the Dynkin diagram (i.e. more or less what the linked Sage document covers). Ideally, the module would also be able to tell whether a given Lie algebra is nilpotent or solvable. These things are all symbolic, and can be extraordinarily difficult to compute by hand, especially once you move past n = 3. I've written programs in Mathematica to compute some of these, which has been dead useful.
-The solvability and nilpotency of a Lie algebra are analogous to the solvability and nilpotency of groups, so the code to that is used to compute these things in the groups module would be easily adapted to a Lie algebra module. Calculating things like ideals and subalgebras als have analogues with groups, so there is some tie in there. -In terms of applicability to research and research communities, I think this would be very useful. For example, quite recently, it has been shown that all finite dimensional cluster algebras are in a bijection with the classical semisimple Lie algebras. This was done through the Cartan matrices and root diagrams. Additionally, the actions of Lie groups are useful in expressing the concept of continuous symmetries of geometric objects. Lie algebras (because they are linear and much easier to work with than Lie groups) pop up all over in differential geometry. They're also useful to physicists as symmetry groups in particle physicists. For my own research (and that of my supervisor) Lie algebras are useful in describing boundary conditions for certain lattice systems and associated Young diagrams and other combinatoric objects. I'm not sure if all of this answered all the questions posed, and I hope that I have not been too rambly. On Feb 16, 2:29 am, Aaron Meurer <asmeu...@gmail.com> wrote: > To these, I would add the (perhaps obvious) question: what are some > specific things that the completed module might be expected to > compute? If these things are highly symbolic and difficult to compute > by hand, then this is exactly the sort of thing that belongs in SymPy, > I think. > > Aaron Meurer > > > > > > > > On Fri, Feb 15, 2013 at 7:07 PM, Matthew Rocklin <mrock...@gmail.com> wrote: > > (Given your previous e-mail I assume that you're asking because you're > > interested in doing a GSoC project) > > > This general type of topic is certainly appropriate for SymPy, however I'm > > not able to judge if this particular topic is useful or wanted. The utility > > might come from communities outside of SymPy. > > > In my experience SymPy GSoC projects are either inward-facing or > > outward-facing. This project sounds outward-facing because it targets an > > external community (mathematical physicists and the like). In these cases I > > think that the question of utility is up for debate. The impact and > > importance of this project to the broader community should be part of a > > project proposal. In this sense a GSoC proposal is good practice for other > > academic proposals. > > > Some questions: > > > 1. How does this fit into other modules that might already exist in SymPy? > > What does it leverage? What can it support in the future? > > 2. Are there other systems out there that already deal with Lie Algebras? > > (this is expected) > > 3. What communities would this work support? How would such a module be > > useful for researchers today? What important problems would be made easier > > by this work? > > > On Fri, Feb 15, 2013 at 5:52 PM, Mary Clark <mary.spritel...@gmail.com> > > wrote: > > >> Hi all, > > >> I've noticed that sympy doesn't have any classes which would deal with > >> Lie Algebras. I was wondering if this is a direction in which it > >> could be useful to extend sympy? Lie algebras (and by extension Lie > >> groups) have many applications in both physics and mathematics. It > >> could also be useful to have something about the semisimple Lie > >> algebras, their roots systems, Dynkin diagrams, etc. > > >> Is this something that would be useful/wanted? > > >> Mary > > >> -- > >> You received this message because you are subscribed to the Google Groups > >> "sympy" group. > >> To unsubscribe from this group and stop receiving emails from it, send an > >> email to sympy+unsubscr...@googlegroups.com. > >> To post to this group, send email to sympy@googlegroups.com. > >> Visit this group athttp://groups.google.com/group/sympy?hl=en. > >> For more options, visithttps://groups.google.com/groups/opt_out. > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to sympy+unsubscr...@googlegroups.com. > > To post to this group, send email to sympy@googlegroups.com. > > Visit this group athttp://groups.google.com/group/sympy?hl=en. > > For more options, visithttps://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
