More examples and a better implementation for random_element().

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 0209433fffb9aa6324bad379b2d5e8ae502e3c16..a5f5f2f4fcf1ac603a9d8d48a75a0924003bd8cf 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -99,27 +99,46 @@ def random_element(K):
         sage: random_element(K)
         (0, 0, 0)
 
+    A random element of the nonnegative orthant should have all
+    components nonnegative::
+
+        sage: set_random_seed()
+        sage: K = Cone([(1,0,0),(0,1,0),(0,0,1)])
+        sage: all([ x >= 0 for x in random_element(K) ])
+        True
+
     TESTS:
 
-    Any cone should contain an element of itself::
+    Any cone should contain a random element of itself::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_rays = 8)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: K.contains(random_element(K))
         True
 
+    A strictly convex cone contains no lines, and thus no negative
+    multiples of any of its elements besides zero::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=8, strictly_convex=True)
+        sage: x = random_element(K)
+        sage: x.is_zero() or not K.contains(-x)
+        True
+
+    The sum of random elements of a cone lies in the cone::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=8)
+        sage: K.contains(sum([random_element(K) for i in range(10)]))
+        True
+
     """
     V = K.lattice().vector_space()
-    F = V.base_ring()
-    coefficients = [ F.random_element().abs() for i in range(K.nrays()) ]
-    vector_gens  = map(V, K.rays())
-    scaled_gens  = [ coefficients[i]*vector_gens[i]
-                         for i in range(len(vector_gens)) ]
+    scaled_gens = [ V.base_field().random_element().abs()*V(r) for r in K ]
 
     # Make sure we return a vector. Without the coercion, we might
     # return ``0`` when ``K`` has no rays.
-    v = V(sum(scaled_gens))
-    return v
+    return V(sum(scaled_gens))
 
 
 def positive_operator_gens(K):