#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):
Well, it seems to me that it is done except for `_repr_` changes which I
plan to do tomorrow. Changes will be trivial, but involve a lot of doctest
adjustment.
I have renamed `ambient_dim` to `lattice_dim`. That seemed to be very
natural, in fact, I didn't even have to change the docstring "Return the
dimension of the ambient lattice." The original proposal actually was not
working because lattices don't have `dim`, they have `dimension`, and
`cone.lattice().dimension()` is a bit long, plus it does not show in
<TAB>-completion. I prefer `dim` to `dimension` since it is clear enough,
however it seems that many things in Sage stick with the long version. In
particular, this is the case for ambient spaces (in the sense of schemes
classes), so `ToricVariety` inherits it. I think that actually both
versions should exist, but the correct way to do it is to change ambient
space class and that better be done in a separate ticket from adding a new
module.
I have not switched equality of cones checked by `==` to ignore the order,
although containment of cones in fans does not care about it. I agree that
"mathematical equality" (which is currently available via `is_equivalent`)
may be better, although it would be inconsistent with fans, but I am
afraid of performance penalty. I do not have currently any benchmarks to
support my case and I may very well be wrong. So I propose to leave it as
is for the moment and once it is actually possible to do things with toric
varieties and we can check it on several "real projects" with big fans we
can decide on the final behaviour. As I understand, switching from
"computer" to "mathematical" equivalence should not break any well-written
code, it may only allow to rewrite it in a more convenient way. On the
contrary, if we switch now and later decide to go back it may lead to bugs
in unexpected places.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8987#comment:43>
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