#9713: Add toric Chow group
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by vbraun):
I'll try to add the missing docstrings.
I was intentionally using `A_k` and not `A^{d-k}` because this patch
implements the Chow homology and not the cohomology. I'm not sure to which
extend they are the same over singular/noncompact varieties over ZZ.
I'm not entirely happy with the output either. But printing all the cones
(even if we abbreviate them) will very quickly produce multi-line output.
Right now, the output is essentially in a random basis corresponding to
`cycle.parent().degree()`.
{{{
sage: cycle = X.Chow_group().gen(1)
sage: cycle
The Chow cycle (0, 1, 0, 0, 0, 0)
sage: cycle.parent().degree()
(Z, Z x Z, Z x Z, Z)
sage: cycle.lift()
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
}}}
For all practical purposes, the user should use `lift()` to get the
coefficients of the cones in the given order
`flatten(toric_variety.fan().cones())`. Would printing
{{{
Chow cycle ((0,), (1, 0), (0, 0), (0,))
}}}
make you more happy? Note that some methods (in particular, intersection
with a divisor) need to change the cycle within its Chow class, so even
"simple" cycles will produce output where all coefficients are turned on.
This is part of why I don't want to print the cone information explicitly.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9713#comment:4>
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