Hello, I am going to improve the functionality of nef partitions and fix some issues in the current implementation (sage.geometry.lattice_polytope.NEFPartition), which was written before I understood what are nef partitions and included into Sage before mandatory refereeing. Worst issues: - it is allowed to create a nef partition as a sequence of numbers without specifying the associated polytope, but without the polytope these numbers are meaningless; - during pickling the reference to the polytope is dropped even if it was given, because polytopes are supposed to restore this reference, but it will not work for a standalone nef partition.
So I want to do the following: 1) deprecate NEFPartition class; 2) replace it with NefPartition derived from SageObject rather than Sequence; 3) require the polytope (Delta_polar) during construction and perform a check that the input is indeed a nef partition (unless check=False was given), do not interfere with pickling; 4) remove "polytope" method, since there are many polytopes related to a nef partition and such a name is confusing; 5) add methods "Delta", "nabla", "Delta_polar" and "nabla_polar": while the last two can be obtained as "Delta().polar()", it would be nice to include a docstring for them explaining their meaning in nef partitions; 6) "Delta" and "nabla" will take an optional argument so that they can return "Delta_i" and "nabla_i" polytopes as well; 7) deprecate "LatticePolytopeClass.mif" since this functionality belongs to a nef partition and in any case it should have a more meaningful name. Regarding names of different polytopes, I want to follow p.63 of "Mirror Symmetry and Algebraic Geometry" by Cox & Katz, i.e. the starting point is assigning a part to each vertex of Delta_polar, these parts together with the origin span nabla_i's, whose Minkowski sum is nabla. On the polar side, Delta is the Minkowski sum of Delta_i's and their convex hull is nabla_polar. Any objections or other comments? Andrey -- 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
