#8987: Add support for rational polyhedral fans
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.4.4
Component: geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Comment(by novoselt):
Here is a condensed version of proposed/pending changes since it is easy
to get lost in the long posts above. I have modified some of the names,
let me know if there are any objections. Below `cone` is assumed to be
`Cone_of_fan`.
* `cone in fan` should check for equivalence of cones, i.e. the order of
rays does not matter
* `point in fan` should be possible
* `Fan()` should give a warning if some of the given cones are compatible
with others but are not generating
* Rename `cone.fan_rays` to `cone.fan_ray_indices`
* Rename `cone.fan_generating_cones` to `cone.star_generator_indices`
* Add `cone.adjacent`: adjacent cones (of the same dimension)
* Add `cone.faces`: all subcones of the cone (override the superclass
method to return `Cone_of_fan` objects and allow `dim/codim` options as in
other cases)
* Add `cone.facet_of`: supercones of one dimension higher
* Add `cone.facets`: subcones of one dimension lower
* Add `cone.star_generators`: return actual cone objects that generate
the star
* Do NOT add `cone.star` yet: I think such a function should return the
fan of the star (with or without the quotient)
* All these methods will ignore `fan` as the top element of the
`cone_lattice`. While I find it convenient to have `fan` in the complete
lattice for its construction, it does not really belong there.
* Remove `fan.cone_to_rays`
* Remove `fan.ray_to_cones`
* Do NOT add `fan.ray_to_cone(i)`, this is done as `fan.cones(1)[i]` or
`fan(1)[i]`
* Add `fan.cone_containing(rays/points)`: the smallest cone containing
all points or rays
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8987#comment:20>
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