#19867: Add Motzkin decomposition for convex cones
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Reporter: mjo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-
Component: geometry | duplicate/invalid/wontfix
Keywords: | Resolution:
Authors: Michael Orlitzky | Merged in:
Report Upstream: N/A | Reviewers: Andrey Novoseltsev
Branch: | Work issues:
u/mjo/ticket/19867 | Commit:
Dependencies: 19831 | 4e7391c09cbdde7dd9f6b027f08a0f68a14b1911
| Stopgaps:
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Changes (by mjo):
* milestone: sage-7.0 => sage-duplicate/invalid/wontfix
Comment:
Replying to [comment:10 novoselt]:
> If orthogonality is essential but we don't have a concept of it, then
perhaps we just should not have this method indeed.
No problem, I don't want to waste time on the things that aren't
important. I've inlined this function into the test suite for the paper.
> The current implementation returns a cone which lives in the ambient
lattice which spans L. I would argue that it should be a sublattice of the
ambient lattice, not a cone at all.
The choice to make it a cone was mostly for symmetry in the strictly
convex / solid cases, and so that things like `L.contains()`,
`L.is_trivial()`, and `K is L` would work. Nevertheless, I don't know WTF
I was thinking with this test:
{{{
sage: (C,L) = K.decomposition()
sage: x = K.random_element(ring=QQ)
sage: C.contains(x) or L.contains(x)
True
}}}
That's false in stupid cases like the sum of two generators, one from `C`
and one from `L`. Guess I had bad luck with the random number generator.
And the test after that should be,
{{{
x.is_zero() or not (C.contains(x) and L.contains(x))
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/19867#comment:11>
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