#19892: Face semigroup of hyperplane arrangement
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Reporter: darij | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.1
Component: geometry | Resolution:
Keywords: hyperplane | Merged in:
arrangements, semigroups, | Reviewers: Miguel Marco
polyhedra | Work issues:
Authors: Darij Grinberg | Commit:
Report Upstream: N/A | 2ba781d9bec2db5d4e088a528729d3dbfaa11952
Branch: | Stopgaps:
public/ticket/19892 |
Dependencies: |
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Comment (by darij):
Thanks for looking through this, Miguel!
Replying to [comment:9 mmarco]:
> The code looks correct to me. But I have a couple
suggestions/comments/questions:
>
> - The way to construct the closed faces seems a bit overcomplicated. My
impression is that a recursive approach (take the delition of the last
hyperplane, compute the closed faces, and then intersect them with the
three sides of the deleted hyperplane) would probably be simpler (but
maybe slower). Did you consider it?
Isn't this what I am doing? Or do you want me to make the method fully
recursive, i.e., build a hyperplane arrangement out of the first n-1
hyperplanes, then call the `closed_faces` method on that, and then just
cut with the last hyperplane? I think that wouldn't be any faster than
what I have done, plus I am not sure that it would work, because when you
call `HyperplaneArrangement` the hyperplanes are getting sorted in some
way, and I'm not sure whether removing a hyperplane wouldn't mess up the
order of the remaining ones.
> - I think that the semigroup algebra should provide an option to
provide the names of the generators.
Good point, done.
I'll take care of the doc shortly, once it's done building.
--
Ticket URL: <http://trac.sagemath.org/ticket/19892#comment:10>
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