#19595: Implement a check that a hyperplane arrangement is free
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: geometry | Resolution:
Keywords: free, hyperplane | Merged in:
arrangement | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 05d7517656a9d911f6d97cc875bd82afb9f30f07
public/hyperplanes/check_free-19595| Stopgaps:
Dependencies: |
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Comment (by tscrim):
Replying to [comment:6 tscrim]:
> Replying to [comment:4 chapoton]:
> > * do you check for "freeness" or some stronger "inductive freeness" ?
>
> As I understand it, this is just freeness, but I will make a detailed
reading and double-check this.
This does not check inductive freeness because it does not check both the
exponent condition and the freeness of the restriction. However this would
make for a good followup.
> > * in `to_symmetric_space`
> > {{{
> > return S.sum(G[i]*c for i,c in enumerate(self.coefficients()[1:]))
> > }}}
> > why is there `[1:]` ?
>
> Because the first coefficient of a hyperplane is the constant part (as
the arrangements do not need to be central, i.e., they are allowed to be
affine hyperplanes).
In my recent push, I now forbid affine hyperplanes since I don't believe
they make sense in the symmetric space.
> > * maybe you should rather write
> > {{{chordality is equivalent to freeness}}}
> > and name the files "`check_freeness`"
>
> Will change.
Done.
--
Ticket URL: <http://trac.sagemath.org/ticket/19595#comment:8>
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