Hi all, I talked to David Cox and they are planning an appendix in their upcoming book where they survey the different toric variety packages in computer algebra systems. David was interested in covering Sage as well; Their deadline is end of August.
Andrey's package is a nicer framework, but realistically can't compute much. My package can compute mostly everything for which there is a known toric algorithm, but doesn't have the nice framework. To get anywhere before August, I would suggest the following: - Add classes for N/M lattice to the framework. - I'll merge my Cone/ToricVariety with Andrey's Cone_of_fan/ ToricVariety_field classes. - Add the ChowCycle and Divisor classes from my package to compute Chow homology and sheaf cohomology etc. Think about the best framework later. I'm mostly OK with the first three parts of Andrey's patches, but not the FanoToricVariety (#8989) part: - Can we rename it to PolytopalToricVariety or ReflexiveToricVariety something like that? Most aren't Fano in the strict sense, so the name grates a bit with me. - Kahler cone and plotting should be implemented in the ToricVariety_field base class, not here. Finally a future project: To really deal with singular toric varieties and/or Weyl/Q-Cartier divisors we need some way to find the integral points in a non-integral polytope. LatticePolytope() can only deal with integral polytopes (that is, spanned by integral vertices). There is some mixed integer programming code out there that could be assimilated. Best wishes, Volker -- 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
