#14789: Implement hyperplane arrangements
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Reporter: kcrisman | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Comment (by dperkinson):
Sorry. I meant to write: "Two hyperplane arrangements are equal if their
sets of hyperplanes are equal. So "==" is perfectly clear and useful as
it is." I am traveling at the moment and a bit distracted.
Replying to [comment:19 dperkinson]:
> A hyperplane arrangement is a *set* of hyperplanes. Two hyperplane
arrangements are equal if their set of hyperplanes are equal. So "=="
perfectly clear and useful as it is.
>
> The issue of isomorphism is separable and it would be nice to implement
this. There can be an isomorphism that arises from an affine change of
coordinates of the ambient space, and there can be a combinatorial
isomorphism, meaning an isomorphism of intersection posets (e.g., an
arrangement and its essentialization).
>
> Could you be more precise about the other type of data that should
determine a hyperplane arrangement? The input would be a set of points.
From this set, how does one create a hyperplane arrangement?
>
> Thanks very much for you comments.
>
>
> Replying to [comment:18 dimpase]:
> > Replying to [comment:17 darij]:
> > [...]
> > > - Not sure if this is a good thing:
> > >
> > > {{{
> > > sage: a = HyperplaneArrangement([[2,4,6],[1,0,1]])
> > > sage: b = HyperplaneArrangement([[1,0,1],[2,4,6]])
> > > sage: a == b
> > > True
> > [...]
> >
> > to me, this is an indication of an issue that has to be carefully
sorted out: namely, a notion of equality vs isomorphism.
> > Especially as one might think about creating arrangements from other
data, e.g. often in my work I see arrangements obtained from a set of
points by taking all the possible hyperplanes on them.
> >
> > Until this is sorted out, I'd rather think of disabling `==` all
together.
--
Ticket URL: <http://trac.sagemath.org/ticket/14789#comment:20>
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