Opened 10 years ago
Closed 10 years ago
#10731 closed defect (fixed)
IndexError in toric sheaf cohomology
Reported by: | vbraun | Owned by: | AlexGhitza |
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Priority: | major | Milestone: | sage-4.6.2 |
Component: | algebraic geometry | Keywords: | |
Cc: | novoselt | Merged in: | sage-4.6.2.alpha4 |
Authors: | Volker Braun | Reviewers: | Andrey Novoseltsev |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
This computation dies unnecessarily:
sage: cell24 = Polyhedron(vertices=[ ... (1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1),(1,-1,-1,1),(0,0,-1,1), ... (0,-1,0,1),(-1,0,0,1),(1,0,0,-1),(0,1,0,-1),(0,0,1,-1),(-1,1,1,-1), ... (1,-1,-1,0),(0,0,-1,0),(0,-1,0,0),(-1,0,0,0),(1,-1,0,0),(1,0,-1,0), ... (0,1,1,-1),(-1,1,1,0),(-1,1,0,0),(-1,0,1,0),(0,-1,-1,1),(0,0,0,-1)]) sage: X = ToricVariety(FaceFan(cell24.lattice_polytope())) sage: D = -X.divisor(0) sage: D.cohomology() --------------------------------------------------------------------------- IndexError Traceback (most recent call last) /home/vbraun/Sage/24cell/<ipython console> in <module>() /home/vbraun/Sage/sage/local/lib/python2.6/site-packages/sage/schemes/generic/toric_divisor.pyc in _sheaf_cohomology(self, cplx) 1544 assert(h[1].dimension()==0) 1545 continue -> 1546 HH_list[ h[0]+1 ] = h[1].dimension() 1547 1548 return vector(ZZ, HH_list) IndexError: list assignment index out of range
Inside, the homology of an auxiliary simplicial complex is computed. For sufficiently complicated cases, vector spaces of dimension 0 are sometimes returned even if all higher-dimensional homology groups vanish. My sheaf cohomology code wrongly assumed that this would not be the case.
Attachments (1)
Change History (8)
comment:1 Changed 10 years ago by
- Cc novoselt added
- Status changed from new to needs_review
comment:2 Changed 10 years ago by
- Reviewers set to Andrey Novoseltsev
- Status changed from needs_review to needs_work
- Work issues set to add reference to the ticket in the doctest
comment:3 Changed 10 years ago by
I've added a reference to this trac ticket.
I don't think that the homology every returns negative degrees, but even if that were the case it would be mathematically correct as long as the homology group is zero-dimensional. As is, the auxiliary simplicial complex is higher-dimensional (but of course has no homology in degrees larger) than the dimension of the variety. So we can't blame the homology code...
comment:4 Changed 10 years ago by
- Status changed from needs_work to needs_review
comment:5 Changed 10 years ago by
- Status changed from needs_review to positive_review
comment:6 Changed 10 years ago by
- Work issues add reference to the ticket in the doctest deleted
comment:7 Changed 10 years ago by
- Merged in set to sage-4.6.2.alpha4
- Resolution set to fixed
- Status changed from positive_review to closed
Looks good, but misses the reference to this ticket.
Is it possible to get these 0-dimensional spaces even in negative degree? In general, is it how homology of this associated complex should behave? I.e. was it really a defect of toric code or there should be a follow-up ticket open for homology computation?