X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcone.py;h=d33a1c5bc317bf7a627f964ca11b78c45045b08a;hb=9d6b29ab0aa0c8c6395834d316d48aa90b3b6c45;hp=eb5316330f6afefdc3b452482bfbd6d59deabbd2;hpb=263ce239a456e5e073a9a8835cdf6cf7e0dfaa98;p=sage.d.git

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index eb53163..d33a1c5 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -152,13 +152,15 @@ def motzkin_decomposition(K):
         sage: S.is_equivalent(expected_S)
         True
     """
-    # The lines() method only gives us one generator for each line,
-    # so we negate the result and combine everything for the full set.
-    S = Cone([p*l for p in [1,-1] for l in K.lines()], K.lattice())
+    # The lines() method only returns one generator per line. For a true
+    # line, we also need a generator pointing in the opposite direction.
+    S_gens = [ direction*gen for direction in [1,-1] for gen in K.lines() ]
+    S = Cone(S_gens, K.lattice())
 
     # Since ``S`` is a subspace, the rays of its dual generate its
     # orthogonal complement.
-    P = K.intersection( Cone(S.dual(), K.lattice()) )
+    S_perp = Cone(S.dual(), K.lattice())
+    P = K.intersection(S_perp)
 
     return (P,S)
 
@@ -215,12 +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