I first thought about your second option, but as Sage has already a permutation class, plus a .to_matrix() method to obtain the matrix back, I'll go for 1, playing the coward as I won't dare create a Bistochastic class (I feel like I wouldn't know how to deal with the different possibilities ).... We'll be able to discuss it in the Trac ticket, by the way...
Thank you very much for your help ! :-) Nathann On Nov 19, 11:47 pm, Florent Hivert <florent.hiv...@univ-rouen.fr> wrote: > Hi ! > > > I just created the following ticket : > >http://trac.sagemath.org/sage_trac/ticket/7492 > > > which is about the decomposition of a doubly stochastic matrix as a > > convex sum of permutationsm also called the Birkhoff–von Neumann > > Theorem ( more information on the Trac ticket ). I could write this > > patch tomorrow, but I do not really know my way around the > > combinatorics functions, and I wondered where you think such a > > function should be added... :-) > > Great ! It's a nice theorem ! > > Before answering, I'd like to ask a question: what's your point of view on the > result ? More precisely what type will you choose for the result ? > > I see at least four possibilities: > > 1 - list of pairs coeff, Permutation; > 2 - list of pairs coeff, permutations matrix; > 3 - element of the vector space whose basis is the permutations; > 4 - element of the algebra of the symmetric group. > > You don't want to do anything with the product of permutations, do you ? So > you don't want to go for 4, which is a pity because you would have a very > natural place to put your functions (SymmetricGroupAlgebra). > > Do you want to do linear algebra on the results, then go for 3 ? In this case > I don't see any natural place. > > If 2 is your choice I would suggest creating a new file about bistochastic > matrices. > > If 1 is your choice then I would probably put it in permutations.py or in a > new file about bistochastic > > > By the way, could you think of a name for this function ? I'm at a > > loss for this one ! > > I would suggest that it should contains the words bistochastic and > permutations, either in the name of the function or in the name of the module > which contains it. Some random ideas: > > sage.combinat.permutations.bistochastic_convex_sum > sage.matrix.bistochastic.convex_sum_of_permutations > sage.combinat.bistochastic.convex_sum_of_permutations > ... > > Note that I'd like to have other people opinion because this is not very clear > to me. > > Cheers, > > Florent -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
