#19892: Face semigroup of hyperplane arrangement
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Reporter: darij | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: geometry | Resolution:
Keywords: hyperplane | Merged in:
arrangements, semigroups, | Reviewers:
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):
Replying to [comment:4 mmarco]:
> I am going through the code, but there are some explanations I don't
fully understand. For instance, can you give an example of the phnomenon
explained in
>
> {{{
> # Do not append ``zero_part`` yet! It might be
> # redundant (in the sense that some of its defining
> # inequalities are always equalities on it). Check
for
> # this:
> }}}
>
> please?
>
When your hyperplanes have the equations x == 0, y == 0 and x + y == 0,
then the face (x == 0 & y == 0) of the hyperplane arrangement formed by
the first two will intersect the halfspace x + y >= 0 in itself, and we
want to record this as a 0 sign, not as a +1 sign. Remember that all the
faces here are closed faces.
Sorry for the doc bug! If you could fix this (in the hopefully obvious
way; I tend to get the "::"s wrong in docstrings), I'd be really grateful.
--
Ticket URL: <http://trac.sagemath.org/ticket/19892#comment:5>
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