#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 mmarco):
> 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.
>
But wouldn't that case already be covered by this section?
{{{
if zero_part_dim == face_dim:
# If the intersection of ``face`` with ``hyperplane``
# has the same dimension as ``face``, then this
# intersection *is* ``face``, so we can continue
# (without adding the other two intersections, since
# those are empty):
subdivided.append((signs + (0,), face))
continue
}}}
Also, I added the missing colons, but still the doc building complains.
--
Ticket URL: <http://trac.sagemath.org/ticket/19892#comment:8>
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