On Friday, 5 April 2013 01:26:10 UTC+1, David Joyner wrote: > > A couple of questions: > How would you represent the Weyl gp? As a permutation group? >
Yes, as a permutation group. They are most easily expressed this way; for example the Weyl group of sln is just Sn, and for the other exceptional Lie algebras it easy enough to express them as permutation groups. Also in the WeylGroup class, I'd like to make the weight lattice accessible. How would you represent an element of a root system? As both > a dict or a vector (or just one or the other)? > At this point, I'm not 100% sure. The entire root system would either be a dict or a vector. If it was a vector, it would be easy to do calculations (i.e. like ARootSystem[0] + ARootSystem[1]), but a dict would be more valuable in displaying the roots for the user to see (ARootSystem = [1: (1,-1,0,0), 2: (0,1,-1,0), 3:(0,0,1,-1)], etc). Would you implement a group action on the root lattice? > Yes; this would help with functionality for the Weyl group. > Would you implement a Lie algebra as a vector space over QQ > with a bracket operation? If not, how? > Ideally, yes. I'd like to implement an abstract bracket operation which the user could specify, adn then sympy would check if it satisfies bilinearity, the Jacobi identity, etc and output if it is a Lie bracket as a boolean. > > > > On Thu, Apr 4, 2013 at 7:37 PM, Mary Clark <mary.sp...@gmail.com<javascript:> > > wrote: > >> Hello all, >> >> I've been working on and thinking about my proposal for a Lie Algebra >> module. Ideally I'd like to have the following classes: >> >> >> - Cartan Type (eg A4, B3, etc) >> - subclasses would implement Dynkin diagrams and the Cartan matrix >> - also include functions to return the rank of the given Lie >> algebra, and whether or not it is finite >> - Weyl group >> - This would return the Weyl group of a given classical Lie >> algebra, as well as be able to return the simple reflections >> - RootSystem >> - Output the root system of a given Cartan type >> - Keep the roots either in a dictionary or an array to allow the >> user to perform operations with the roots >> >> I'd also like to have files with the basic information about for the >> different classical Lie algebras (A,B,C,D,E,F,G). One source that is >> particularly useful is Lie Algebras: Theory and Algorithm by W.A. de >> Graaf. I also own several other books on Weyl groups and Lie algebras in >> general that I think would be quite useful for this project. >> >> I was hoping others could provide feedback on what I have so far for this >> project! >> >> -- >> 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+un...@googlegroups.com <javascript:>. >> To post to this group, send email to sy...@googlegroups.com <javascript:> >> . >> Visit this group at http://groups.google.com/group/sympy?hl=en-US. >> For more options, visit https://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-US. For more options, visit https://groups.google.com/groups/opt_out.
