#9326: Add cohomology of toric varieties
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.5
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by novoselt):
If there is only one function for which it would be nice to have a
corresponding cone method, I'd wait before redoing toric varieties to make
copies of fans.
I don't like `HH` notation, which I associate with Hochschild
(co)homology... While it is used in Macaulay2, it does not quite seem to
be in the spirit of Sage. Macaulay2 is much more flexible in terms of
operators and it may be a good choice there, but here I would prefer
`cohomology_ring` etc. I don't see any problems with "What cohomology?"
question since it can be clearly indicated in the documentation of all
functions. (Do we plan to support multiple cohomology theories?)
I think `HH_class_of(cone)` ===> `cohomology_class(cone)` would be better.
Also `HH_exp(p)` ===> `cohomology_exp(p)` or better yet just `exp(p)`.
Even better would be `p.exp()` which will not require toric variety at
all, but that requires completely different handling so should be left
till after divisor patch is merged.
I propose to do the following with `c` and others:
{{{
def Chern_class(self, deg=None):
r"""
Return Chern class of the tangent bundle of the toric variety.
A synonym for this function is ``c``.
...
"""
... # actual code
c = Chern_class
}}}
This way we keep convenient access to all this functions, but at the same
time provide descriptive names, so that glancing on TAB-completion clearly
shows what is available. The same thing is done with `.numerical_approx()`
and `.n()` methods in Sage.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9326#comment:5>
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