#12965: X.Kaehler_cone().lattice() is not a lattice
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Reporter: novoselt | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-5.1
Component: algebraic geometry | Resolution:
Keywords: toric | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by novoselt):
Hi Volker,
Any thoughts on what would be the proper way to fix it? Modify `Cone`
constructor to take as the lattice of a cone in a vector space the
integral span of the basis and normalize/convert rays to live in this
span?
It seems to be correct, but it screws up printing where these rays live in
- this integral span shows as row span of the identity matrix without
mention of any class groups. It also means that rays cannot be lifted to
divisors, without first converting them to the rational class group
explicitly.
A half-way solution is to use span of the basis for normalization of rays,
but let rays be still elements of the rational divisor class group.
However, in this case, it seems that rays of a cone in the N-lattice must
have N_R as their parent and if we let rays live in the extension all the
customization work of toric lattices becomes irrelevant.
So I am inclining to the first solution - if `Cone` gets a rational vector
space V for the lattice, it actually works with `span(ZZ, V.gens())`.
Let me know what you think!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12965#comment:1>
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