Hi, On Sun, 29 Aug 2010 10:02:05 -0700 (PDT), Vincent D <20100.delecr...@gmail.com> wrote: > I'm working on arithmetic subgroup in sage.modular.arithgroup > especially on arithgroup_perm, and I do not know what does the method > __cmp__ must do (it is not specified in sage.groups.group.Group where > I guess it is the right place): > * equality and inclusions? In this case, the given implementations > of Gamma, Gamma0 and Gamma1 fail because of the class > ArithmeticSubgroup_perm which can potentially represent any subgroup > of SL(2,Z). But, this latter class has the advantage that any > implementation of an arithmetic group can be converted into it (from a > coset graph) and then be compared.
This is a thorny issue which I would let others address (what should happen if G and H are not mathematically comparable? raise error? return -1? and there are changes in the comparison philosophy between python 2 and python 3). > Other way, I would like to have advices on the best names for the > following methods: > * adding minus identity to a subgroup to get an even subgroup? > (.to_even_subgroup) An option to this would be to make it into a method of the ambient group (which is SL(2,Z) in your case but could be more general). By this I mean something like S = SL2Z() H = <your favorite subgroup> E = S.even_subgroup(H) where the last thing would return the smallest even subgroup containing H. Of course, if you got H without having explicitly defined S, this means that you would have to do something like E = H.ambient_group().even_subgroup(H) I don't have strong opinions about this, just wanted to suggest the alternative. > * commensurability? (.is_commensurable) Sounds good to me. > * conjugacy of subgroups in SL(2,Z)? (.is_conjugate) there could be > a conflict between conjugacy of elements and conjugation of > subgroups... I don't think there would be a conflict, because these would be methods of different classes: H.is_conjugate(N) would give conjugacy of subgroups as H would be a subgroup; g.is_conjugate(x) would be conjugacy of elements since g is a group element. Best, Alex -- Alex Ghitza -- http://aghitza.org/ Lecturer in Mathematics -- The University of Melbourne -- Australia -- 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
