I am confused with the google-group - I posted the second message last night, but I don't see it. And it shows 5 message on the top, but I can only see 4. I don't know if others can see it, but (it seems no, so I'll copy it from a saved file: --------------------------------------- To add to the previous post, my future plans are:
- Make sure that faces enumeration is the same everywhere, especially for vertices and facets. This is relevant for lattice polytopes, polyhedra, cones, and fans. We have had recently to fix some doctests in Polyhedra because of random sorting and I have had to fix some of the new doctests when I switched from 4.4 to 4.4.2.rc0. - Write good plotting functions. For Fano toric varieties they must be well-coordinated with lattice polytopes and I want to make the latter ones more convenient and flexible. - Improve morphisms and their doctests in schemes in general. My first attack on documenting/improving schemes.generic.homset&morphism was not very succesful, but I am going to continue. TestSuite(s).run() should eventually work for schemes and ambient spaces! While it may seem reasonable to first fix these issues and then add new classes, I think that it is also good to have more "generic" ambient spaces for testing purposes. Besides, with toric varieties merged I will definitely understand at least some modules in schemes ;-) - Implement classes to be used for lattices of cones/fans/lattice polytopes. Ironically, lattice polytopes don't support lattices! For cones and fans providing "lattice=" argument should "just work". - While some of my "old" code got incorporated into the posted patches, I still have quite a bit of written code which I hope to convert into this framework. - Quoting Volker: "implement everything that is known!" --------------------------------------- Alex, thank you for such a quick response! Now we have 5 out of 6 prerequisites reviewed! Volker, thank you for looking over the code and commenting it! I will move the Kaehler cone to toric varieties. Plot functions actually belong to fans, while toric varieties should provide meaningful labels, although for Fano varieties it can make sense to have something more special involving the polytope and its unused points. In any case for now I would like to ask to keep the existing function as is with the comment that it will be replaced soon - it does provide a somewhat useful plot and it is probably not the highest priority to get pretty pictures. For "Fano"... I thought a lot about it as I also don't quite like that it is necessary to keep in mind several more words. Proposition 3.5.5 in Cox&Katz book says "Delta is reflexive if and only if P_Delta is Fano". That differs from the definitions in Nill's paper, who also points out that sometimes people imply "smooth" when they say Fano. How about this: - leave the module name fano_toric_variety - rename class to FanoToricVarietyCrepantResolution_field - rename constructor to FanoToricVarietyCR - say in the introduction that for us Fano means Gorenstein Fano (omitting "Gorenstein" seems to be quite common, we can also consider later allowing "non-canoninal Fano polytopes") - change printing to "Crepant resolution of (Gorenstein?) Fano toric variety of dimension n" This way we also don't have to worry about coherency of subdivisions, which is less trivial than crepancy. Once this is settled, my first priority will be to add classes for lattices. I don't think we should have separate classes for M and N, because they are "the same" on the one hand and there may be need for more than two (even in the same dimension) on the other one. I envision "Lattice" as derived in Sage from ZZ^n with custom names, dual(), and morphisms between them (which will automatically induce toric morphisms between objects living in the same lattice - that way we get automatic embeddings for all affine subvarieties including the canonical embedding of the torus!). I will also go over you lattice classes to see what else is needed. I should be able to finish this and post a patch by the end of May (probably not for lattice polytopes yet, as this will be quite involved and in fact I feel a need to change a lot in lattice polytopes in general). Dima, thank you for the reference! 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
