#19368: Add LL() method for polyhedral closed convex cones.
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Reporter: mjo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: geometry | Resolution:
Keywords: | Merged in:
Authors: Michael Orlitzky | Reviewers: Andrey Novoseltsev
Report Upstream: N/A | Work issues: clarify trivial cone
Branch: | Commit:
u/mjo/ticket/19368 | 8bda4c2134f5e6460c6ce9bae5e0ba96679e54c3
Dependencies: #19332 | Stopgaps:
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Changes (by mjo):
* status: needs_work => needs_review
Comment:
Replying to [comment:5 novoselt]:
> Your use of the term "trivial cone" is confusing - after reading the
very first example I thought "Surely any transformation is Lyapunov-like
since there is no conditions to worry about!", yet their basis was empty.
To me "trivial cone" means "consisting of the origin"...
You are correct -- the important part of that doctest was that the space
is trivial. It's been updated, and I added an example of a trivial cone
(only the origin) in a non-trivial space.
[[BR]]
> Are these matrices expected to be non-integer? I.e. why base_field and
not base_ring?
The tensor products are integer matrices, but when we convert to long
vectors, I think a field is required. I assume the `complement()`
algorithm needs a field anyway, and the matrices that pop out can be
rational:
{{{
sage: K = Cone([(-5, -1, 0), (53, -2, 1), (-1, -1, 6)])
sage: K.lyapunov_like_basis()
[
[1 0 0] [ 0 1 0] [ 0 0 1]
[0 1 0] [ 44/4505 681/4505 -126/901] [ -15/901 75/901 911/901]
[0 0 1], [ -15/901 75/901 911/901], [ 87/901 -435/901 -5464/901]
]
}}}
I could normalize those after the fact?
--
Ticket URL: <http://trac.sagemath.org/ticket/19368#comment:9>
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