Hi Andrey, > Volker and I have some disagreement on names used in > http://trac.sagemath.org/sage_trac/ticket/9296 and it would be VERY > nice to get other people opinions. I'll try to be short.
First of all, a general comment: +1 to have those question more frequently discussed on sage-devel. It's the only way to have a chance to get different part of sage to be consistent. > In toric geometry it is important/convenient to distinguish a lattice > and its dual. Standard names for them are N and M with fans living in > N and monomials corresponding to points in M. However these lattices > are dual and therefore interchangable, which is used in Batyrev- > Borisov mirror constructions. It is also possible to have more than > one lattice of the same dimension with different names and no > relations at all or some non-trivial identification between elements > (e.g. some parts of Gross-Siebert mirror constructions, or even > "traditional" quotient and sub- lattices associated to cones). I'm not an expert of it, but there seem to be a very similar question in root systems and Coxeter groups. The convention is to call RS.co***_space or RS.co***_lattice the dual of RS.***_(space|lattice): sage: A2 = RootSystem(["A", 2]) sage: A2.root_lattice() Root lattice of the Root system of type ['A', 2] sage: A2.coroot_lattice() Coroot lattice of the Root system of type ['A', 2] sage: A2.weight_lattice() Weight lattice of the Root system of type ['A', 2] sage: A2.coweight_lattice() Coweight lattice of the Root system of type ['A', 2] sage: A2.coweight_space() Coweight space over the Rational Field of the Root system of type ['A', 2] > Now, if we have a cone C living in lattice N with dual M, then it has > associated lattices traditionaly denoted by N(C), N_C, M(C). The > question is - how to name the corresponding methods of C? Volker > prefers names like C.N, C.N_quotient, C.M. I prefer names like > C.spanned_lattice, C.quotient_lattice, C.spanned_lattice_dual. > > Volker's arguments: > * names like C.N are short > * they correlate better with notation that beginners are likely to see > in textbooks > * advanced users will not have troubles tracking down appropriate > lattices > > My arguments: > * names like C1.N and C2.N are very confusing if C1 lives in lattice N > and C2 in its dual lattice M, especially when both cones are used for > some task > * they are also not clear for cones living in lattice L > * it is not very clear whether C.N corresponds to mathematical obejct > N(C) or N_C, which is bad since both are important and both are used > * thinking of myself as an advanced user of toric geometry, I would > have some troubles tracking down lattices. > > For more details you may refer to the ticket. Please help us to choose > good names! +1: C.spanned_lattice, C.quotient_lattice, C.spanned_lattice_dual. My general two cents: explicit (=long) is better than implicit (=short). However it should be easy for the user to define its own short names. 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
