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
