Add some Proposition 3 tests for positive operators.

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 28a84231d1eb461a1e12d0df258f980e48f21f2d..d33a1c5bc317bf7a627f964ca11b78c45045b08a 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -217,12 +217,46 @@ def positive_operator_gens(K):
 
     TESTS:
 
-    A positive operator on a cone should send its generators into the cone::
+    Each positive operator generator should send the generators of the
+    cone into the cone::
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=5)
         sage: pi_of_K = positive_operator_gens(K)
-        sage: all([K.contains(p*x) for p in pi_of_K for x in K.rays()])
+        sage: all([ K.contains(P*x) for P in pi_of_K for x in K ])
+        True
+
+    Each positive operator generator should send a random element of the
+    cone into the cone::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=5)
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: all([ K.contains(P*K.random_element()) for P in pi_of_K ])
+        True
+
+    A random element of the positive operator cone should send the
+    generators of the cone into the cone::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=5)
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: L = ToricLattice(K.lattice_dim()**2)
+        sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L)
+        sage: P = matrix(K.lattice_dim(), pi_cone.random_element().list())
+        sage: all([ K.contains(P*x) for x in K ])
+        True
+
+    A random element of the positive operator cone should send a random
+    element of the cone into the cone::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=5)
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: L = ToricLattice(K.lattice_dim()**2)
+        sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L)
+        sage: P = matrix(K.lattice_dim(), pi_cone.random_element().list())
+        sage: K.contains(P*K.random_element())
         True
 
     The dimension of the cone of positive operators is given by the