Is that a preprint? Some of the sections seem unfinished (for example, section 10).
Aaron Meurer On Sat, Mar 17, 2012 at 8:27 PM, Alan Bromborsky <[email protected]> wrote: > On 03/17/2012 04:59 PM, Aaron Meurer wrote: >> >> On Sat, Mar 17, 2012 at 2:45 PM, Aleksandar Makelov >> <[email protected]> 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 [email protected]. >>> To unsubscribe from this group, send email to >>> [email protected]. >>> For more options, visit this group at >>> http://groups.google.com/group/sympy?hl=en. >>> > See attached! > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > 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 [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
