#9337: Add toric divisors
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.6
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by vbraun):
Some people use "Mori vector" for the rays of the Mori cone, but
`Mori_cone` is probably better.
1. I'm fine with `Kahler_cone` actually returning the closure... right
now we don't have a way of specifying open cones and I don't think that it
is a priority. Plus there would be a lot of code complexity in
intersecting open/closed cones, which I'd be happy to avoid for toric
purposes.
2. Since all toric algorithms end up using the fan I found it useful to
have a local reference. I'm fine with either way, though.
3. You are usually the one who advocates the longer names ;-) The toric
Chow group prints itself like this:
{{{
sage: A = X.Chow_group()
sage: A.degree()
(Z, C7, Z^5 x C2 x C2, Z)
}}}
and it would be easy to lift the code from there. But in practice
you'll just want the dimension (no torsion here). So I think that, while
looking good, be actually in your way when working with it.
5. , 6. Fine with me!
7. In contrast to the toric lattices, the `ToricRationalDivisorClass` is
not that speed-sensitive. You probably got the class from a toric divisor
which is itself not that efficient either. If you derive from vectors
you'll save a few lines because you inherit addition/subtraction but
you'll have to write a cython file and override e.g. `__reduce__` now.
Judging from `toric_lattice_element.pyx` I think it'll be about the same
amount of code. But if you want to rewrite it I'm not going to stop you
:-)
8. how about `class_group(base_ring=QQ)`
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9337#comment:35>
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