From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 11 Jan 2016 14:34:10 +0000 (-0500)
Subject: Add tests for the dimension of the Z-transformation cone.
X-Git-Url: http://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=57824cb514182bb70be721827edd38843a339ed1;p=sage.d.git

Add tests for the dimension of the Z-transformation cone.
---

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index a327720..28ad0a4 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -562,7 +562,8 @@ def Z_transformation_gens(K):
         ....:                                  for (x,s) in dcs])
         True
 
-    The lineality space of Z is LL::
+    The lineality space of the cone of Z-transformations is the space of
+    Lyapunov-like transformations::
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=4)
@@ -575,7 +576,8 @@ def Z_transformation_gens(K):
         sage: z_cone.linear_subspace() == lls
         True
 
-    And thus, the lineality of Z is the Lyapunov rank::
+    The lineality of the Z-transformations on a cone is the Lyapunov
+    rank of that cone::
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=4)
@@ -587,7 +589,10 @@ def Z_transformation_gens(K):
         sage: z_cone.lineality() == K.lyapunov_rank()
         True
 
-    The lineality spaces of pi-star and Z-star are equal:
+    The lineality spaces of the duals of the positive operator and
+    Z-transformation cones are equal. From this it follows that the
+    dimensions of the Z-transformation cone and positive operator cone
+    are equal::
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=4)
@@ -597,13 +602,46 @@ def Z_transformation_gens(K):
         sage: pi_cone = Cone([p.list() for p in pi_of_K],
         ....:                lattice=L,
         ....:                check=False)
-        sage: pi_star = pi_cone.dual()
         sage: z_cone = Cone([ z.list() for z in Z_of_K],
         ....:               lattice=L,
         ....:               check=False)
+        sage: pi_cone.dim() == z_cone.dim()
+        True
+        sage: pi_star = pi_cone.dual()
         sage: z_star = z_cone.dual()
         sage: pi_star.linear_subspace() == z_star.linear_subspace()
         True
+
+    The trivial cone, full space, and half-plane all give rise to the
+    expected dimensions::
+
+        sage: n = ZZ.random_element().abs()
+        sage: K = Cone([[0] * n], ToricLattice(n))
+        sage: K.is_trivial()
+        True
+        sage: L = ToricLattice(n^2)
+        sage: Z_of_K = Z_transformation_gens(K)
+        sage: z_cone = Cone([z.list() for z in Z_of_K],
+        ....:               lattice=L,
+        ....:               check=False)
+        sage: actual = z_cone.dim()
+        sage: actual == n^2
+        True
+        sage: K = K.dual()
+        sage: K.is_full_space()
+        True
+        sage: z_of_K = Z_transformation_gens(K)
+        sage: z_cone = Cone([z.list() for z in Z_of_K],
+        ....:                lattice=L,
+        ....:                check=False)
+        sage: actual = z_cone.dim()
+        sage: actual == n^2
+        True
+        sage: K = Cone([(1,0),(0,1),(0,-1)])
+        sage: Z_of_K = Z_transformation_gens(K)
+        sage: actual = Cone([z.list() for z in Z_of_K], check=False).dim()
+        sage: actual == 3
+        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