#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: | b3db54c53f3a571f7408e14b7274ed9c9f00feaf
public/hyperplanes/check_free-19595| Stopgaps:
Dependencies: |
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Comment (by 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.
> * 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).
> * maybe you should rather write
> {{{chordality is equivalent to freeness}}}
> and name the files "`check_freeness`"
Will change.
--
Ticket URL: <http://trac.sagemath.org/ticket/19595#comment:6>
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