#11200: Add fibration check to FanMorphism
----------------------------+-----------------------------------------------
Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.7.1
Component: geometry | Keywords: toric
Work_issues: | Upstream: N/A
Reviewer: Volker Braun | Author: Andrey Novoseltsev
Merged: | Dependencies: #10140, #10882
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Changes (by novoselt):
* status: needs_work => needs_info
Comment:
Hi Volker,
I fixed the mistake you have found and wrote `is_surjective`.
While I am at it, I also started writing `is_injective`, but it is a bit
trickier: we want the lattice map to have index one in the saturation of
its image (in Sage, conveniently, `self.matrix().index_in_saturation() ==
1`) and for every (primitive) cone `tau` mapped to `sigma` the dimension
of `tau` must be the same as the dimension of the intersection of `sigma`
with the image lattice of the lattice map. To make this easier and
potentially simplify life in the future with computing fibers of generic
fan/toric morphisms, I am thinking of adding the following methods:
1. `image_lattice` to be the sublattice generated by the image of the
domain lattice.
1. `image_fan` to be the intersection of the codomain fan with the image
lattice.
1. `image_restriction` to be the fan morphism from the original domain
fan to the newly defined image fan.
Question: how should we name these methods? It seems to me that
`image_lattice` fits nicely with `kernel_lattice`, but two others may be
quite confusing/misleading, i.e. `image_fan` may refer to the image of the
domain fan in the image lattice. One possible solution is not to implement
such a method at all as it may be accessed via
{{{
phi.image_restriction().codomain_fan()
}}}
Any thoughts on this and the name for the `image_restriction` map?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11200#comment:6>
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