On 29 Aug, 22:58, Alex Ghitza <aghi...@gmail.com> wrote: > 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). >
As Alex said, __cmp__ is a bit of a can of worms. It certainly isn't supposed to return any kind of mathematically meaningful result, but it's intended that *any* two Sage objects can be compared; so trying to make it test for inclusion etc wouldn't be a good idea. (Is Gamma0(7) greater than or less than RR[X, Y]? Don't lose too much sleep over this one.) > > 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) I would have thought that the right place to put this would be the ArithmeticSubgroup base class, with various specific implementations in derived classes as appropriate. > 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. I do -- it's disgusting :-) > > * commensurability? (.is_commensurable) > > Sounds good to me. Sounds pointless to me, because ArithmeticSubgroups are all commensurable with each other by definition! > > * 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. +1. David -- 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
