On Sat, Mar 17, 2012 at 2:45 PM, Aleksandar Makelov <amake...@college.harvard.edu> wrote: > >> I think a main reference is "Permutation Group Algorithms" by Akos >> Seress - Cambridge Tracts in Mathemathics 152 published 2003. > > Thanks! The "Handbook of computational group theory" also looks like > serious business. Unfortunately, neither of these is a free resource; > I might end up buying one, I don't know. > >> I worked as a student last year and may apply as mentor this year. >> Please take a look at my branches in github. I was implementing the >> Schreier Sims algorithm but I ran out of time unfortunately. You could >> either help me merge my branches in or take off where I left. > > OK, I'll hopefully have the time to take a look this coming week. > >> Is this necessary? All groups are isomorphic to the permutation group >> anyway. Groups for specific structures can make use of functionality >> implemented for them (matrix group -> sympy matrices, galois -> polys) >> for basic operations and can implement the mapping to the perm group >> module for group theoretic operations. > > So I looked at the permutations module and it has a lot of nice group- > ish functions (like composing/inverting permutations, raising to > powers, conjugating permutations, getting the order (as an element of > the corresponding symmetric group) of a permutation, ...). These can > be incorporated in a representation of groups using permutation > groups; Galois groups would fit perfectly in this representation since > they naturally live inside the symmetric groups, and yes a lot of the > functions in the polys module will be helpful. > > Also, there are generators for common groups like S_n, C_n, D_n, A_n > in the context of permutation representations. All this provides a > nice foundation for defining a Group class or something like that, > with one of the ways of representing it being the permutation > representation. Other ways (e.g., matrices, character tables, list of > generators and relations) could probably be added later, and > functionality to go from one to representation to another? > > In other news, I found a bug inside the generators.py file in the > permutations module - the dihedral group D_2 of order 4 is given a > wrong permutation representation. I have a fix for this (well it's > quite straightforward, just manually considering the case n=2 and > outputting the right representation, because the general algorithm > fails there), what should I do about it?
Submit a pull request! This can be your patch for the patch requirement. Aaron Meurer > > Aleksandar Makelov > > -- > 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. > -- 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.
