#14789: Implement hyperplane arrangements
-------------------------------------+-------------------------------------
Reporter: kcrisman | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: combinatorics | Resolution:
Keywords: days54 | Merged in:
Authors: David Perkinson, | Reviewers: Travis Scrimshaw
Volker Braun | Work issues:
Report Upstream: N/A | Commit:
Branch: | 7a7c6aca580a7fc1481d60f8deb37129aa2b90f8
public/geometry/14789-hyperplane_arrangements| Stopgaps:
Dependencies: |
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Comment (by vbraun):
What is
{{{
sage: H.<x,y,z> = HyperplaneArrangements(QQ)
sage: H(0)
}}}
supposed to return? You could either argue the empty arrangement (neutral
element in the additive semigroup) or the entire space defined by the
degenerate "hyperplane" 0=0. I really don't want to allow that kind of
degenerate hyperplanes. So that leaves us with the former, but I still
find `H(0)` confusing and, by extension, `H(x) == 0`.
There is no easy way to find out which ambient hyperplane went where in
`restriction()`, in particular it involves choices:
{{{
sage: H.<x,y> = HyperplaneArrangements(QQ)
sage: H(x-y, x+y, x).restriction(x)
Arrangement <y>
}}}
So its alwasy going to be convoluted. If you need to know the sign vector
of a point in terms of the ambient space arrangement then just compute the
sign vector there.
I can fix up the 0-dimensional and empty arrangement case...
--
Ticket URL: <http://trac.sagemath.org/ticket/14789#comment:55>
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