#8989: Add support for Fano toric varieties
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Reporter: novoselt | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.5
Component: algebraic geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Comment(by vbraun):
That was precisely my point: Since you have a `CPRFanoToricVariety_field`
object in front of you when calling any method, you cannot freely exchange
polyhedron and dual polyhedron any more. There is no confusion in
`my_toric_variety.nabla()`.
I agree that comparisons with other variables might be confusing, but the
problem is that the other variable is confusingly-named. I can always
write `not_X = X; X == not_X` and will get `True`. But that is not `X`'s
fault, nor can `X` do anything to prevent it. As soon as the user refrains
from creating local variables named `nabla` or `delta` everything is fine.
Mirror symmetry becomes
{{{
X.nabla() == Y.delta()
}}}
Furthermore:
* `fan_polytope` still does not distinguish face/normal fan
* `spanned_polytope` is spanned by what, the rays or the monomials?
* `face_polytope` don't like it either ;-)
Its hard to say "the polytope whose face-fan is the fan of the toric
variety" in a python identifier without agreeing on some sort of code.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8989#comment:14>
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