From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 13 Feb 2017 18:15:09 +0000 (-0500)
Subject: Add another test and an implementation comment for is_lyapunov_like_on.
X-Git-Url: http://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=cca6df801932a33628f734514b3cbc14dab70477;p=sage.d.git

Add another test and an implementation comment for is_lyapunov_like_on.
---

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index aeec0c9..0158757 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -422,12 +422,28 @@ def is_lyapunov_like_on(L,K):
         ...
         ValueError: The base ring of L is neither SR nor exact.
 
+    An operator is Lyapunov-like on a cone if and only if both the
+    operator and its negation are cross-positive on the cone::
+
+        sage: K = random_cone(max_ambient_dim=5)
+        sage: R = K.lattice().vector_space().base_ring()
+        sage: L = random_matrix(R, K.lattice_dim())
+        sage: actual = is_lyapunov_like_on(L,K)          # long time
+        sage: expected = (is_cross_positive_on(L,K) and  # long time
+        ....:             is_cross_positive_on(-L,K))    # long time
+        sage: actual == expected                         # long time
+        True
+
     """
     if not is_Cone(K):
         raise TypeError('K must be a Cone.')
     if not L.base_ring().is_exact() and not L.base_ring() is SR:
         raise ValueError('The base ring of L is neither SR nor exact.')
 
+    # Even though ``discrete_complementarity_set`` is a cached method
+    # of cones, this is faster than calling ``is_cross_positive_on``
+    # twice: doing so checks twice as many inequalities as the number
+    # of equalities that we're about to check.
     return all([ s*(L*x) == 0
                  for (x,s) in K.discrete_complementarity_set() ])