Opened 10 years ago
Closed 9 years ago
#11384 closed enhancement (fixed)
Construct the complex of a fan
Reported by: | vbraun | Owned by: | AlexGhitza |
---|---|---|---|
Priority: | major | Milestone: | sage-5.0 |
Component: | algebraic geometry | Keywords: | sd31 |
Cc: | novoselt | Merged in: | sage-5.0.beta5 |
Authors: | Volker Braun | Reviewers: | Andrey Novoseltsev |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #11558 | Stopgaps: |
Description (last modified by )
For some toric algorithms one needs to choose orientations for cones, essentially to construct the homology complex of the cone complex. This patch implements new methods fan.oriented_boundary(cone)
and fan.complex()
to return chosen boundary orientations of cones and the resulting homology complex.
Attachments (2)
Change History (18)
comment:1 Changed 10 years ago by
- Cc novoselt added
- Status changed from new to needs_review
comment:2 Changed 10 years ago by
comment:3 Changed 10 years ago by
- Keywords sd31 added
- Reviewers set to Andrey Novoseltsev
- Status changed from needs_review to needs_work
comment:4 Changed 10 years ago by
- 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. - "ONF": One Never Forgets - Outward Normal First. Mnemonic for the usual boundary orientation choice in algebraic geometry.
- Sounds like a good idea. I'll look into it
- 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.
- I'm sure there are optimizations but speed hasn't been a bottleneck for me so far. Better to be correct than fast.
- Ok will fix that.
- 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.
- I don't really have something clever to say about the extended complex. Its rather obvious that it works.
- Ok will fix it.
- in the
homology()
of a simplicial complex? It probably depends on the algorithm thatSimplicialComplex
uses to compute the homology.
comment:5 Changed 10 years ago by
- Status changed from needs_work to needs_review
comment:6 Changed 10 years ago by
- Dependencies set to #11558, #11559
Updated doctests because #11559 changes the ordering.
comment:7 Changed 10 years ago by
- Description modified (diff)
comment:8 Changed 9 years ago by
Apply trac_11384_fan_complex.patch
comment:9 Changed 9 years ago by
Line 2656 still has "chose" instead of "chosen" ;-)
comment:10 Changed 9 years ago by
Fixed!
Also fixed some doctests that relied on the order of boundary cones, I think something changed in the poses stuff. Now applies cleanly against sage-5.0.beta4
comment:11 Changed 9 years ago by
Is #11599 still supposed to be in front? That one has to be rebased as well.
comment:12 Changed 9 years ago by
I didn't have to rebase #11599, my patch queue is:
trac_12280_padic_hnf_without_zero_rows.patch trac_11384_fan_complex.patch trac_11599_no_circular_imports.patch trac_11599_homset_new_coercion_model.patch trac_11599_rename_morphisms.patch trac_11599_toric_morphisms.patch trac_11599_reviewer.patch
I'm working on implementing your requests there, though.
comment:13 Changed 9 years ago by
Oops, sorry - I meant #11559, which is the second dependency here.
comment:14 Changed 9 years ago by
- Dependencies changed from #11558, #11559 to #11558
Oh yes I removed the dependency on #15599, forgot to remove it from the ticket description.
comment:15 Changed 9 years ago by
- Status changed from needs_review to positive_review
That ticket has a really challenging number ;-)
comment:16 Changed 9 years ago by
- Merged in set to sage-5.0.beta5
- Resolution set to fixed
- Status changed from positive_review to closed
oriented_boundary
can we replace throughoutcone
with something more neutral, likecell
orpart
, since it is allowed to be the whole fan?oriented_boundary
as a formal sum with plus/minus 1 coefficients? Wouldn't it be more convenient?complex
method? What is it used for and what is computed by its homology groups? Is it possible to have torsion? I guess yes, since QQ would be faster otherwise, but it would be nice to have an example!