#9972: Add toric lattice morphisms
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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 novoselt):
In what sense `ambient_ray_indices` is dangerous? If ambient structures of
two cones are different, there is no point to look at these attributes at
all. Otherwise they are the same if and only if cones are the same.
I am definitely against moving `ambient_ray_indices` to `Cone_of_fan`
because the point in having it is uniform treatment of faces of cones and
cones of fans, which are pretty much the same things. In fact, even
`star_generators` make sense for faces of a cone in the sense of
containing facets, it just should not be called that name. So currently
the main reason for a `Cone_of_fan` to exist is that terminology for faces
of cones and cones of fans is a bit different. I think that it should stay
this way as much as possible, so that all cones behave the same.
I am also against new containment check - cones are equal if they have the
same rays in the same order and equivalent if they define the same set of
points. If the same cone happened to belong to different fans and so has
two objects representing it, it does not change anything. We can check if
cones belong to the same ambient structure for code optimization, but the
output should be the same. Note that in this case this check actually can
be done in generic cones and there is no need to override the method for
`Cone_of_fan`.
I still don't understand exactly what are you trying to achieve in general
and in particular why do we need `get_cone` method. I agree that
`fan.contains` should return `True` only for (some) cones and not for
anything else, because a fan is a collection of cones. I agree that it may
be good to have uniqueness of `Cone_of_fan` but I don't see any reasons
for doing this except for some performance gain and it is not clear how
significant it can be. It also seems to me that it makes more sense to
make all cones unique based on the ordered rays and the ambient structure,
because essentially this is how cones of fans can be made unique.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:18>
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