#11384: Construct the complex of a fan
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7.1
Component: algebraic geometry | Keywords: sd31
Work_issues: | Upstream: N/A
Reviewer: Andrey Novoseltsev | Author: Volker Braun
Merged: | Dependencies:
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Comment(by vbraun):
1. The normal usage is `oriented_boundary(cone)`, so I would prefer
keeping the argument name as it is. Yes it also accepts a fan as a special
case, but trying to be general for generality's sake would make the help
less helpful, not more.
2. "ONF": One Never Forgets - Outward Normal First. Mnemonic for the
usual boundary orientation choice in algebraic geometry.
3. Sounds like a good idea. I'll look into it
4. No, all orientations are arbitrary. Only the relative orientations of
(cone,face) is not. The whole point of the method is a way to fix one
particular orientation such that one can write down the boundary complex
explicitly.
5. I'm sure there are optimizations but speed hasn't been a bottleneck
for me so far. Better to be correct than fast.
6. Ok will fix that.
7. It has the homology type of a point, so you can't compute anything
interesting by itself. It provides a way to fix one (arbitrary choice of)
orientations for all cones, mostly. I'll add a reference.
8. I don't really have something clever to say about the extended
complex. Its rather obvious that it works.
9. Ok will fix it.
10. in the `homology()` of a simplicial complex? It probably depends on
the algorithm that `SimplicialComplex` uses to compute the homology.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11384#comment:4>
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