#11200: Add fibration check to FanMorphism
----------------------------+-----------------------------------------------
Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_review
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
----------------------------+-----------------------------------------------
Changes (by novoselt):
* status: needs_info => needs_review
* work_issues: sublattice duals and action =>
Old description:
> The main point of this ticket is to add `FanMorphism.is_fibration`
> method.
>
> I have also added several related methods and adjusted
> containment/embedding methods of fans to accommodate sublattices and make
> their behaviour more uniform: now cone containment check is an attempt to
> embed the given cone into the fan.
>
> I have also started using `@cached_method` decorator since it is
> convenient and its speed and documentation issues should be resolved in
> the near future. Note, however, that some methods of fans still should
> use manual cache since they need to preprocess arguments first.
New description:
The main point of this ticket was to add `FanMorphism.is_fibration`
method, but along the way injectivity, surjectivity, and splitting were
added as well.
I have also added several related methods and adjusted
containment/embedding methods of fans to accommodate sublattices and make
their behaviour more uniform: now cone containment check is an attempt to
embed the given cone into the fan.
I have also started using `@cached_method` decorator since it is
convenient and its speed and documentation issues should be resolved in
the near future. Note, however, that some methods of fans still should use
manual cache since they need to preprocess arguments first.
--
Comment:
OK, I propose this version for inclusion. I did not add `index(cone)`
functionality as it is not necessary for the current methods and it would
make sense only for those morphisms whose vector space map is surjective
(there should be perhaps another `is_xxx` method to test for this, but I
am not sure how to call it - `is_dense`?). Besides, someone else is likely
to work on further description of fan morphism fibers and it will be a
nice exercise to add cone indices ;-)
I made a small change to `free_module`, but didn't yet test consequences
on the whole library. I'll do it today and will fix any problems if there
are any.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11200#comment:12>
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