#9972: Add toric lattice morphisms
-------------------------------------+--------------------------------------
Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6
Component: geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: switch to FanMorphism |
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Comment(by vbraun):
`ambient_ray_indices` is not natural! Natural operations on cones should
work without referring to a particular enumeration of the rays. Think
`cone1.intesection(cone2)` vs.
`set(cone1.ambient_ray_indices()).intersection(set(cone2.ambient_ray_indices()))`.
Of course sometimes you can't avoid it, definitely not in the internal
implementations, but higher-level code (like the toric varieties) could
easily move away from it. Case in point is that it is used only 9 times
(the other 4 are in doctests).
And this looks horrible
{{{
cone.ambient().ray_indices(cone)
}}}
precisely because it is bad! It will break things! Its like a big,
flashing sign: Do not write this code! You really want to use
`self.fan().ray_indices(cone)`!
I don't mind the availability of `cone.ambient_ray_indices()` so much if
you use it on the command line; In that case you know what your ambient()
is. But I think we should ban its use from the toric varieties code. Then
we algorithmically audit it for correctness by grepping
`sage/schemes/generic` for `ambient_ray_indices`. How does that sound?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:31>
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