X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcone.py;h=a327720132b3907562f269fc4872a2b829226a59;hb=48a7ad09084a859da72e39e60312bfffb6b806e9;hp=68fd1931e9d7a4a7fdf3a00a5636011c963e58dd;hpb=86442dc35e3dbbf69dc91caa1222d4dfce2fb106;p=sage.d.git

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 68fd193..a327720 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -513,6 +513,33 @@ def Z_transformation_gens(K):
         sage: Z_transformation_gens(K)
         []
 
+    Every operator is a Z-transformation on the ambient vector space::
+
+        sage: K = Cone([(1,),(-1,)])
+        sage: K.is_full_space()
+        True
+        sage: Z_transformation_gens(K)
+        [[-1], [1]]
+
+        sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)])
+        sage: K.is_full_space()
+        True
+        sage: Z_transformation_gens(K)
+        [
+        [-1  0]  [1 0]  [ 0 -1]  [0 1]  [ 0  0]  [0 0]  [ 0  0]  [0 0]
+        [ 0  0], [0 0], [ 0  0], [0 0], [-1  0], [1 0], [ 0 -1], [0 1]
+        ]
+
+    A non-obvious application is to find the Z-transformations on the
+    right half-plane::
+
+        sage: K = Cone([(1,0),(0,1),(0,-1)])
+        sage: Z_transformation_gens(K)
+        [
+        [-1  0]  [1 0]  [ 0  0]  [0 0]  [ 0  0]  [0 0]
+        [ 0  0], [0 0], [-1  0], [1 0], [ 0 -1], [0 1]
+        ]
+
     Z-transformations on a subspace are Lyapunov-like and vice-versa::
 
         sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)])