From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 7 Jan 2016 19:55:42 +0000 (-0500)
Subject: Add some lineality examples, remove one dimension one covered elsewhere.
X-Git-Url: http://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=f7c24573f7cb25b1af2ff589a945d74f3554758c;p=sage.d.git

Add some lineality examples, remove one dimension one covered elsewhere.
---

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 43ec8f7..d62ffa2 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -359,20 +359,8 @@ def positive_operator_gens(K):
         sage: actual == 3
         True
 
-    The cone of positive operators is solid when the original cone is proper::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=5,
-        ....:                 strictly_convex=True,
-        ....:                 solid=True)
-        sage: pi_of_K = positive_operator_gens(K)
-        sage: L = ToricLattice(K.lattice_dim()**2)
-        sage: pi_cone = Cone([p.list() for p in pi_of_K], lattice=L)
-        sage: pi_cone.is_solid()
-        True
-
-    The lineality of the cone of positive operators is given by the
-    corollary in my paper::
+    The lineality of the cone of positive operators follows from the
+    description of its generators::
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=5)
@@ -384,8 +372,33 @@ def positive_operator_gens(K):
         sage: actual == expected
         True
 
-    The cone ``K`` is proper if and only if the cone of positive
-    operators on ``K`` is proper::
+    The trivial cone, full space, and half-plane all give rise to the
+    expected linealities::
+
+        sage: n = ZZ.random_element().abs()
+        sage: K = Cone([[0] * n], ToricLattice(n))
+        sage: K.is_trivial()
+        True
+        sage: L = ToricLattice(n^2)
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: actual = Cone([p.list() for p in pi_of_K], lattice=L).lineality()
+        sage: actual == n^2
+        True
+        sage: K = K.dual()
+        sage: K.is_full_space()
+        True
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: actual = Cone([p.list() for p in pi_of_K], lattice=L).lineality()
+        sage: actual == n^2
+        True
+        sage: K = Cone([(1,0),(0,1),(0,-1)])
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: actual = Cone([p.list() for p in pi_of_K]).lineality()
+        sage: actual == 2
+        True
+
+    A cone is proper if and only if its cone of positive operators
+    is proper::
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=5)