#15224: Iterate over the points of a toric variety
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Reporter: vbraun | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.12
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: sd53 | Reviewers:
Authors: Volker Braun | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0dc5e0b9a5c9fb1ff3ee3a18e48acd487bfdaae5
u/vbraun/toric_variety_points | Stopgaps:
Dependencies: |
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Comment (by ursula):
There are some subtleties involving singular varieties that this code does
not take into account. For example, if you take the normal fan to the
standard 2-dimensional simplex (ReflexivePolytope(2,0)), you get a
quotient of the projective plane by a diagonal action of a group of order
3. When the base ring is GF(7), 2 is a 3rd root of unity and [1:2:4]
generates the diagonal action, so [1:1:1] and [1:2:4] should be
identified. But they are listed as different points by this iterator!
The obvious fix is to restrict to the case of nonsingular varieties; this
behavior would match the existing function for counting points on a toric
variety.
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Ticket URL: <http://trac.sagemath.org/ticket/15224#comment:12>
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