On May 18, 2:45 pm, Volker Braun <vbraun.n...@gmail.com> wrote: > 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.
Barvinok's algorithm, as implemented in Latte (by J. de Loera and others) does such enumerations, so this seems to be a question of integrating things properly... Just in case, Dima > > 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 athttp://groups.google.com/group/sage-devel > URL:http://www.sagemath.org -- 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
