#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):
I think it is confusing to have `Cone.face_lattice()` and
`Cone_of_fan.face_lattice()` return lattices of `ConeFace` and
`Cone_of_fan` objects respectively, which have different attributes. This
will propagate to methods like `Cone.facets()` and `Cone_of_fan.facets()`.
But the more I think about it, the more I get convinced that
`Cone.face_lattice()` should construct a single-generating-cone fan and
return the cone lattice of this fan, without the fan on the top (in the
case of one cone this is still a lattice). It may require some thinking
about names of functions that return things of the "ambient object" (like
`Cone_of_fan.fan_ray_indices()`) but it will give uniform behaviour, no
duplicate code for similar functionality, and speed. Currenly, I think, if
you ask for a face lattice of an element of a face lattice, a new lattice
will be computed and constructed from scratch, but it can be just
extracted as a part of the big initial lattice. Being able to get these
sublattices quickly is essential, for example, for computing generating
functions for stringy Hodge numbers. I will see if there are any problems
with dependencies.
Sorry, it is taking longer than I expected, but the earlier such basic
things will be fixed, the better will code on top of them behave...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8987#comment:23>
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