#9713: Add toric Chow group
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6.1
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Changes (by novoselt):
* status: needs_review => needs_work
Comment:
1. The discussed above fact that this patch implement the full Chow group
should be reflected in module level documentation.
1. Documentation from `ChowCycle.__init__` should be moved to the class
docstring, otherwise it is invisible.
1. Behaviour of `check=False` is strange for it: usually such an option
omits validity checks assuming that user will take care of it. Here it
seems to allow a different form of input. Is it inherited from the base
class? If so, maybe it should be fixed there...
1. Line 170 misses the second ":" in the end.
1. The first words of some docstrings have extra s'es, like "Returns" and
"Intersects".
1. It would be nice if the documentation and example for `count_points`
were expanded/clarified a little bit more. The phrase "integral over the
dual cohomology class" does not make it clear what is the integrand and to
what the cohomology class is dual. Is it the Chow cycle in both cases? The
example starts with a divisor and then integrates the square of this
divisor and counts points on the intersection of the Chow cycle of this
divisor with the original divisor. How about starting with some Chow cycle
with non-zero point count and then showing how to get a corresponding
cohomology class and integrate it?
1. For `intersect_with_divisor` it would be nice to give a reference to
the used algorithm (Fulton p.97?). I think also that
`intersection_with_divisor` would be a better name, since the function
returns the intersection rather than updates the original cycle. (I do
realize now that the same consideration should have been applied to some
methods that I have added...) By the way, this function has no
input/output description. And perhaps `i = I_gamma.pop()` does the same
thing as `i = iter(I_gamma).next()` in a little cleaner fashion. (It does
alter the set, but it is not used anyway.) What exactly is tested by the
long test with many zeros in this function? This function says that
divisor must be Cartier, but it is not checked, is it intended? Am I right
that it actually makes sense to use it with Q-Cartier divisors if the Chow
group is also rational?
1. `Chow_cycle` method of toric divisors does not have a doctest and
input/output description.
1. Line 394 misses closing quotes after True.
I didn't go over actual Chow group code yet, but will do it. Soon ;-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9713#comment:21>
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