#10882: Add kernel fan to fan morphism
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: geometry | Keywords: toric geometry
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by novoselt):
* work_issues: degenerate cases =>
Comment:
After some thinking, I have decided to make `kernel_fan` live in the
kernel sublattice. The drawback is that currently sublattices don't work
extremely well as ambient ones for cones and fans, but that should
eventually change. I have made some changes improving the situation, but
dual objects still don't work and so one cannot ask for cones of this
kernel fan (the doctest is marked as not tested). I propose to include it
nevertheless, since the constructed fan is still correct and will be
completely functional once other part are improved. (And the "old" version
is still available as explicit `preimage_fan` of the origin.)
I have also tweaked the fan constructor a little to ensure adding at least
the origin cone and allowing one to specify the fan lattice which is
different then cone lattices, as long as it is possible to do the
conversion:
{{{
sage: P2 = toric_varieties.P2()
sage: f = P2.fan()
sage: f
Rational polyhedral fan in 2-d lattice N
sage: Fan(f.generating_cones())
Rational polyhedral fan in 2-d lattice N
sage: Fan(f.generating_cones(), lattice=f.lattice().dual())
Rational polyhedral fan in 2-d lattice M
}}}
If the lattice is not given explicitly, no conversion will be made and all
cones must belong to the same lattice. But giving the lattice explicitly
may be quite handy for switching between lattices/sublattices/quotients
and the above example with "switching to dual" is sometimes used when one
wants to compare fans of polar polytopes and think of them as fans in the
same lattice.
Ready for review!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10882#comment:2>
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