From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 5 Aug 2015 01:18:41 +0000 (-0400)
Subject: Update some comments for lyapunov_rank().
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=a51031e565e6910f71f9052da7e2e1b355035fcb;p=sage.d.git

Update some comments for lyapunov_rank().
---

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,