#11384: Construct the complex of a fan
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7.1
Component: algebraic geometry | Keywords: sd31
Work_issues: | Upstream: N/A
Reviewer: Andrey Novoseltsev | Author: Volker Braun
Merged: | Dependencies:
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Changes (by novoselt):
* keywords: => sd31
* reviewer: => Andrey Novoseltsev
* status: needs_review => needs_work
Comment:
1. In `oriented_boundary` can we replace throughout `cone` with something
more neutral, like `cell` or `part`, since it is allowed to be the whole
fan?
1. What exactly is "outward normal first" orientation?
1. How about representing the output of `oriented_boundary` as a formal
sum with plus/minus 1 coefficients? Wouldn't it be more convenient?
1. It would be nice to be more clear what is arbitrary and what is not.
As I understand, the only randomness is in the choice of orientation of
non-full-dimensional *generating* cones, the rest is then determined.
1. To reduce randomness of the last case, perhaps one can compute the
determinant of the pivot matrix of the (cone rays | identity) matrix)? It
may perhaps be also a little faster than working with quotients.
1. The code crashes on
{{{
sage: fan = toric_varieties.P(3).fan()
sage: cone = fan(0)[0]
sage: fan.oriented_boundary(cone)
}}}
1. Are there any references that would be suitable to put into
documentation of `complex` method? What is it used for and what is
computed by its homology groups? Is it possible to have torsion? I guess
yes, since QQ would be faster otherwise, but it would be nice to have an
example!
1. Would be nice also to say something about the differential maps and
why it is possible to define the extended complex for complete fans.
1. "The orientation of each cone is chose as..." must be "chosen".
1. Is there a reason why "-1" term is printed in the end? It looks like a
bug (not in this patch, of course).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11384#comment:3>
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