#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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Comment(by novoselt):
Replying to [comment:35 nthiery]:
> I am still confused a bit: do you know where technically in the cone
code is there an ``==`` or ``is`` test done on some posets, which cause
the change of behaviour above?
When a fan computes its cone lattice, it constructs all of the required
cones (which are bound to the correct fan) and then converts them into a
poset. All further methods work with this poset. Since now posets are
unique and involve "==" checks for fans and cones, the poset of the second
fan is treated as the same one as the first one, so the second fan gets a
poset of cones bound to the first fan. The precise method of fans is
`_compute_cone_lattice`.
Now, I have actually realized, that it will have the same issue for cones,
it just does not break the existent doctests yet:
{{{
sage: C1 = Cone([(0,1)])
sage: C2 = Cone([(0,1)])
sage: C1 == C2
True
sage: C1 is C2
False
sage: C1.facets()[0]
0-d face of 1-d cone in 2-d lattice N
sage: C1.facets()[0].ambient() is C1
True
sage: C2.facets()[0].ambient() is C1
True
sage: C2.facets()[0].ambient() is C2
False
}}}
The code for cones is in `face_lattice` method. Again, I don't want to get
the same posets even for cones that have the same order of rays, and there
are arguments that "==" should treat rays as sets. So it would be nice to
force different posets for "==" objects.
Why exactly are posets unique? Isn't it expensive to check that two posets
are equivalent? I am interested in dealing with face lattices of about
10^5^ elements, how long would it take to check their equality? Maybe
elements of posets should be unique, but not posets themselves?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10998#comment:36>
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