#19867: Add Motzkin decomposition for convex cones
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Reporter: mjo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: geometry | Resolution:
Keywords: | Merged in:
Authors: Michael Orlitzky | Reviewers: Andrey Novoseltsev
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/mjo/ticket/19867 | 303093b3f737d9f0a578d59eaa0cc98414d1e003
Dependencies: 19831 | Stopgaps:
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Comment (by mjo):
Replying to [comment:2 novoselt]:
> I don't think "cone's" is correct English, at least it sounds weird.
>
> The way you set it up, it is NOT the direct sum, but Minkowski sum.
I clarified it to be the Minkowski sum of orthogonal things.
> If Motzkin decomposition is not standard, why is it called like this
here? I mean it would be nice to elaborate that it is not just your
invention ;-)
There is a ".. NOTE" stating that the name is nonstandard. The "cone
decomposition theorem" is variously attributed to Motzkin, and his
decomposition of polyhedra is closely related, but I'm prevented by the
language barrier from seeing just how appropriate the name might be.
Supposedly the pointed/subspace decomposition was used in the original
paper on the double description method but I can't find that online
either.
I don't mind changing the name -- got any ideas? The name "lineal
decomposition" doesn't seem to be taken.
>
> I would put extra check to handle corner cases so that the strict
component of a strictly convex cone `is` this cone in Python sense, same
with subspaces.
Done!
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Ticket URL: <http://trac.sagemath.org/ticket/19867#comment:4>
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