#19368: Add LL() method for polyhedral closed convex cones.
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Reporter: mjo | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: geometry | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies: 19332
Stopgaps: |
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Now I finally have something useful to contribute.
The "Lyapunov-like" matrices/transformations provide a way to generalize
the complementarity slackness condition over other cones. Essentially you
expand `<x,s> = 0` into a system of equations `<L(x),s> = 0` and hope to
solve that. The space of all such transformations turns out to be the Lie
algebra of the automorphism group of the cone.
And now that we have `discrete_complementarity_set()`, we can find every
Lyapunov-like transformation using some basic linear algebra tricks:
`<L(x),s> = 0` if and only if `<L, sx^T> = 0` (trace inner product), so
all we have to do is compute an orthogonal complement.
The name `LL()` for the space of all Lyapunov-like transformations appears
in 5-10 papers, but isn't very descriptive. If you prefer, I like
`lyapunov_like_basis` just as much.
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Ticket URL: <http://trac.sagemath.org/ticket/19368>
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