#10998: Categories for posets
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Reporter: nthiery
| Owner: sage-combinat
Type: enhancement
| Status: needs_work
Priority: major
| Milestone: sage-4.7.1
Component: combinatorics
| Keywords: days30, sd31
Work_issues:
| Upstream: N/A
Reviewer: Franco Saliola, Christian Stump, Nicolas M. Thiéry, Florent
Hivert | Author: Frédéric Chapoton, Christian Stump, Nicolas M. Thiéry
Merged:
| Dependencies: #11289, #10938, #9065
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Changes (by novoselt):
* cc: vbraun (added)
* keywords: days30 => days30, sd31
Comment:
Hi Nicolas!
With the patch:
{{{
sage: F1 = FaceFan(lattice_polytope.octahedron(3))
sage: F2 = FaceFan(lattice_polytope.octahedron(3))
sage: F1 == F2
True
sage: F1 is F2
False
sage: F1(2)[0]
2-d cone of Rational polyhedral fan in 3-d lattice N
sage: F1(2)[0].ambient() is F1
True
sage: F2(2)[0].ambient() is F2
False
}}}
The last command is heavily assumed to return True in the toric-related
code. The problem is that when the cone lattice of `F2` is constructed, it
is considered as the same poset as the cone lattice of `F1` and so all
cones of `F2` become linked to `F1`. Possible solutions are:
* Make cone lattices of fans which are "==" but not "is" distinct. This
should fix the issue without any complications as it will basically
restore the current state.
* Make "==" and "is" comparisons the same for fans. I think that this is
undesirable as there are arguments for making "==" be the mathematical
equivalence, which is even weaker than the current behaviour.
* Make fans unique based on the ordered list of rays and cone generators.
This should fix the issue but may have consequences. Also, while in
general unique fans may be good, it would be nice to still have a
possibility to make "==" the mathematical equivalence and IMHO it would be
absolutely terrible for performance and convenience of use if uniqueness
of fans was based on their mathematical equivalence.
Note: I'd rather not make cones unique based on the ordered list of rays
as I want to have a possibility to create different cones with the same
order of rays but different order of facet normals. This is not currently
implemented but would be extremely convenient for handling all kinds of
dualities and correspondences.
So, in short, I prefer to be able to create different posets of cones for
fans which are "==".
Thank you,
Andrey
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10998#comment:34>
Sage <http://www.sagemath.org>
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