X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcone.py;h=1ab6b97c128cde3d1e176032cf0d90f601057166;hb=46b32aa189efc76f3403fe410a622ee21329812b;hp=f78c27e7e8ba748274b968601fff61c4701a98c1;hpb=5b7044f0fad38851282ffdc07b55b98c11b7f78e;p=sage.d.git

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index f78c27e..1ab6b97 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -176,7 +176,8 @@ def positive_operator_gens(K):
 
     A positive operator on a cone should send its generators into the cone::
 
-        sage: K = random_cone(max_ambient_dim = 6)
+        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()])
         True
@@ -184,16 +185,30 @@ def positive_operator_gens(K):
     The dimension of the cone of positive operators is given by the
     corollary in my paper::
 
-        sage: K = random_cone(max_ambient_dim = 6)
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim = 5)
         sage: n = K.lattice_dim()
         sage: m = K.dim()
         sage: l = K.lineality()
         sage: pi_of_K = positive_operator_gens(K)
-        sage: actual = Cone([p.list() for p in pi_of_K]).dim()
-        sage: expected = n**2 - l*(n - l) - (n - m)*m
+        sage: L = ToricLattice(n**2)
+        sage: actual = Cone([p.list() for p in pi_of_K], lattice=L).dim()
+        sage: expected = n**2 - l*(m - l) - (n - m)*m
         sage: actual == expected
         True
 
+    The lineality of the cone of positive operators is given by the
+    corollary in my paper::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim = 5)
+        sage: n = K.lattice_dim()
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: L = ToricLattice(n**2)
+        sage: actual = Cone([p.list() for p in pi_of_K], lattice=L).lineality()
+        sage: expected = n**2 - K.dim()*K.dual().dim()
+        sage: actual == expected
+        True
     """
     # Matrices are not vectors in Sage, so we have to convert them
     # to vectors explicitly before we can find a basis. We need these
@@ -286,6 +301,13 @@ def Z_transformation_gens(K):
         sage: z_cone.linear_subspace() == lls
         True
 
+    And thus, the lineality of Z is the Lyapunov rank::
+
+        sage: set_random_seed()
+        sage: K = random_cone(min_ambient_dim = 1, max_ambient_dim = 6)
+        sage: z_cone  = Cone([ z.list() for z in Z_transformation_gens(K) ])
+        sage: z_cone.lineality() == K.lyapunov_rank()
+        True
     """
     # Matrices are not vectors in Sage, so we have to convert them
     # to vectors explicitly before we can find a basis. We need these