From a51031e565e6910f71f9052da7e2e1b355035fcb Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Tue, 4 Aug 2015 21:18:41 -0400 Subject: [PATCH] Update some comments for lyapunov_rank(). --- mjo/cone/cone.py | 16 ++++------------ 1 file changed, 4 insertions(+), 12 deletions(-) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 48b4061..02d5258 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -442,7 +442,7 @@ def LL(K): def lyapunov_rank(K): r""" - Compute the Lyapunov (or bilinearity) rank of this cone. + Compute the Lyapunov rank (or bilinearity rank) of this cone. The Lyapunov rank of a cone can be thought of in (mainly) two ways: @@ -461,16 +461,7 @@ def lyapunov_rank(K): An integer representing the Lyapunov rank of the cone. If the dimension of the ambient vector space is `n`, then the Lyapunov rank will be between `1` and `n` inclusive; however a rank of `n-1` is - not possible (see the first reference). - - .. note:: - - In the references, the cones are always assumed to be proper. We - do not impose this restriction. - - .. seealso:: - - :meth:`is_proper` + not possible (see [Orlitzky/Gowda]_). ALGORITHM: @@ -659,7 +650,8 @@ def lyapunov_rank(K): sage: lyapunov_rank(K) == len(LL(K)) True - Test Theorem 3 in [Orlitzky/Gowda]_:: + We can make an imperfect cone perfect by adding a slack variable + (a Theorem in [Orlitzky/Gowda]_):: sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, -- 2.44.2