#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 novoselt):
Well, I guess I mostly agree, I probably went over the top in my struggle
for the best and cleanest names ever ;-) So while I think that it is quite
likely to have `nabla` and `delta` as local variables, it does make sense
to use them for methods.
However, I am still against assigning different names to polar polytopes.
In the notation for nef-partitions that you have cited, `delta` and
`nabla` are not polar, in fact, they are not dual in any sense by
themselves, but their decompositions are dual and their polars are
expressed as convex hulls of Minkowski summands. I envision for complete
intersections methods like
{{{
sage: CI.Delta()
sage: CI.Delta(i)
sage: CI.nabla()
sage: CI.nabla(j)
}}}
and while these are different objects from toric varieties, I would like
same-named methods to return the same things.
So if you really don't want `Delta` to denote the polytope whose face fan
is used for the toric variety, I propose `X.Delta()` to return the
polytope whose normal fan is used. Indices of points used for coordinates
will refer to `X.Delta().polar()`. If you would like to have a "direct"
access to this polytope from `X`, then I think the method should be called
`X.Delta_polar()`. While its implementation will be trivial, it is
probably good to have it, since it will allow us to put appropriate
documentation there related to toric varieties, rather than just taking
polar polytopes. That gives us also `Delta_polar_point_to_coordinate`
which is a bit lengthy, but I don't mind it and you think that it will not
be used very often, so it should not be a problem.
Does it sound like a good compromise?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8989#comment:15>
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