#13183: Implement index(cone) for fan morphisms
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.7
Component: geometry | Resolution:
Keywords: toric | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Andrey Novoseltsev | Merged in:
Dependencies: #12544 | Stopgaps:
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Old description:
> For #12892 it would be useful to compute indices of cones as they define
> the number of components of each fiber. The index is defined in
> Yi Hu, Chien-Hao Liu, and Shing-Tung Yau. Toric morphisms and fibrations
> of toric Calabi-Yau hypersurfaces. Adv. Theor. Math. Phys., 6(3):457-506,
> 2002. arXiv:math/0010082v2 [math.AG].
> for the case of surjection of complete fans. The attached patch extends
> the definition to any morphism:
> * if the corresponded quotient of lattices is finite, return its order;
> * if it has free generators, return infinity;
> * if the codomain cone does not have covering domain cones at all,
> return None.
New description:
For #12892 it would be useful to compute indices of cones as they define
the number of components of each fiber. The index is defined in
Yi Hu, Chien-Hao Liu, and Shing-Tung Yau. Toric morphisms and fibrations
of toric Calabi-Yau hypersurfaces. Adv. Theor. Math. Phys., 6(3):457-506,
2002. arXiv:math/0010082v2 [math.AG].
for the case of surjection of complete fans. The attached patch extends
the definition to any morphism:
* if the corresponded quotient of lattices is finite, return its order;
* if it has free generators, return infinity;
* if the codomain cone does not have covering domain cones at all, return
None.
'''Apply:'''
1. [attachment:trac_13183_index_of_codomain_cone.patch]
1. [attachment:trac_13183_untwist_lattice_splitting.patch]
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Comment (by novoselt):
Apply trac_13183_index_of_codomain_cone.patch
trac_13183_untwist_lattice_splitting.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13183#comment:8>
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