#13183: Implement index(cone) for fan morphisms
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.2
Component: geometry | Resolution:
Keywords: toric | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Andrey Novoseltsev | Merged in:
Dependencies: | Stopgaps:
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Comment (by novoselt):
Fibers are defined for any morphism, no matter whether it is a fibration
or not, so I'd like fiber methods to do something useful still. After some
more thinking I'd like to use None as described above, but return 0 for
non-finite index. Reason: I compute the index as the product of
invariants, then if it is 0 (indicating ZZ-factors) replace it with
infinity. Dropping this extra replacement simplifies life here and then we
can also just return this index for "incomplete covering", i.e. if there
is some fiber over the distinguished point, we return it with zero to
indicate that generically there are no such components at all. So possible
cases will be:
* (component, count) - surjective, count has to be positive;
* (component, 0) - non-surjective, but the distinguished point is
covered;
* (None, None) - even the distinguished point is not covered;
where the second element is always the index of a cone in the sense of
this ticket.
Those who want more details in the 0-case can use `restrict_to_image`
method, which makes only two other cases possible.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13183#comment:5>
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