#16344: Comparing fans in non-saturated lattices
-------------------------+-------------------------------------------------
Reporter: jkeitel | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: algebraic | Keywords: toric
geometry | Authors: Jan Keitel
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | u/jkeitel/fan_comparison_sublattice
Commit: | Dependencies:
Stopgaps: |
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Fan comparison does not work if one fan lives in a non-saturated
sublattice (I hope that's the right term):
{{{
sage: N = ToricLattice(1)
sage: B = N.submodule([(2,)]).basis()
sage: f = Fan([Cone([B[0]])])
sage: B = N.submodule([(1,)]).basis()
sage: f2 = Fan([Cone([B[0]])])
sage: f == f2
Traceback (most recent call last):
...
ArithmeticError: cannot interpret [(1)] as a sublattice of Sublattice
<N(2)>!
}}}
The reason is simply that
{{{
sage: f.virtual_rays()
}}}
throws this exception. I don't know enough about fans to understand
whether they can be made to work in such lattices, too, but it is also
required in other places that the lattices for toric varieties be
saturated anyway. Therefore I'am attaching a branch that catches this
exception and does not compare the virtual rays of fans in such lattices,
which seems to fix the problem.
Lastly, why should one even worry about this? Since
{{{ToricDivisorGroup}}} inherits from {{{UniqueRepresentation}}}, it
compares fans of newly created toric varieties with all fans in the cache.
If one therefore has one malfunctioning fans, creating divisors in 'good'
toric varieties will fail, too:
{{{
sage: N = ToricLattice(2)
sage: B = N.submodule([(2,1), (1,2)]).basis()
sage: f = Fan([Cone([B[0], B[1]]), Cone([B[1], -B[0]-B[1]]),
Cone([-B[0]-B[1], B[0]])])
sage: X = ToricVariety(f)
sage: aK = -X.K()
sage: B = N.submodule([(1,0), (1,1)]).basis()
sage: B[0].parent() is B[0].parent().saturation()
True
sage: f2 = Fan([Cone([B[0], B[1]]), Cone([B[1], -B[0]-B[1]]),
Cone([-B[0]-B[1], B[0]])])
sage: X2 = ToricVariety(f2)
sage: from sage.schemes.toric.divisor import ToricDivisorGroup
sage: aK2 = -X2.K()
ArithmeticError: cannot interpret [(1, 2), (-1, -3)] as a sublattice of
Sublattice <N(1, 2), N(0, 3)>!
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16344>
Sage <http://www.sagemath.org>
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