#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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Comment(by novoselt):
10. It is probably worth mentioning what is the point of `A(Cone(cone))`
after `A(cone)`. I actually didn't even know that `Cone(cone)` works!
Fortunately, it works as expected ;-)
11. In `_rational_equivalence_relations` I find it very difficult to
understand the LaTeX expression, which does not get typeset in the
documentation (since it is a private method), especially since it does not
explain what is "! over =", what is `n_{\rho, \sigma}`, and how d, k, n,
and p are related (I guess pairs of them are equal). I think that this
description should be moved to some visible place (module documentation or
`relation_gens`?) and there should be a reference to where it was taken
from.
12. What is the purpose of the super call in `__eq__` for Chow groups? Do
we want anything but a Chow group equal to a Chow group?
13. I think that `_cone_to_V` would be more efficient if it was
implemented via a dictionary. I don't know how significant such a speed up
will be in real computations, but I think it is worthwhile to do this
change.
14. There is a note in `degree` method about smooth varieties: "Using the
cohomology ring instead of the Chow group will be much faster." I think
that this is a very important point and it should be also mentioned in the
module level documentation and in the Chow group method of toric
varieties. (Perhaps with explanations of why this is the case.) Examples
of this method are very nice! I'd remove the sentence "The resulting fan
is not the fan over a convex cube."
15. I think it would be more natural if `gens` without parameters
returned the union of all `gens` of specified degree. Is it possible to
implement? (I.e. is it possible to force the quotient module to use these
generators? I definitely don't suggest "just" returning union of degree
generators.)
16. For `relation_gens` wouldn't it be more natural to return elements of
the covering module, i.e. lifts of the current output?
17. Line 979: you meant `== QQ`.
18. Would it make sense to derive `ChowGroup_degree_class` from some kind
of a group rather than `SageObject`?
That's it for the current patch!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9713#comment:22>
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