From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 19 May 2015 19:09:02 +0000 (-0400)
Subject: Factor out the is_full_space() function.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=08ff39a270e90e6263339da12144ddd2bfc6f3f5;p=sage.d.git

Factor out the is_full_space() function.
---

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 3b724a7..424a907 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -8,6 +8,47 @@ addsitedir(abspath('../../'))
 from sage.all import *
 
 
+def is_full_space(K):
+    r"""
+    Return whether or not this cone is equal to its ambient vector space.
+
+    OUTPUT:
+
+    ``True`` if this cone is the entire vector space and ``False``
+    otherwise.
+
+    EXAMPLES:
+
+    A ray in two dimensions is not equal to the entire space::
+
+        sage: K = Cone([(1,0)])
+        sage: is_full_space(K)
+        False
+
+    Neither is the nonnegative orthant::
+
+        sage: K = Cone([(1,0),(0,1)])
+        sage: is_full_space(K)
+        False
+
+    The right half-space contains a vector subspace, but it is still not
+    equal to the entire plane::
+
+        sage: K = Cone([(1,0),(-1,0),(0,1)])
+        sage: is_full_space(K)
+        False
+
+    But if we include nonnegative sums from both axes, then the resulting
+    cone is the entire two-dimensional space::
+
+        sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)])
+        sage: is_full_space(K)
+        True
+
+    """
+    return K.linear_subspace() == K.lattice().vector_space()
+
+
 def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None):
     r"""
     Generate a random rational convex polyhedral cone.
@@ -162,12 +203,6 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None):
             # ZZ.random_element() docs.
             return l + ZZ.random_element(u - l + 1)
 
-    def is_full_space(K):
-        r"""
-        Is this cone equivalent to the full ambient vector space?
-        """
-        return K.lines().dim() == K.lattice_dim()
-
     d = random_min_max(min_dim, max_dim)
     r = random_min_max(min_rays, max_rays)