X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcone.py;h=1a3ee3b2fad16e3a05938cb7b9c6a0beae9518d1;hb=f9d0571d553891281fd31949871e27e1f973a281;hp=f3543a147ad8da3c5000015f3c53e837781180e5;hpb=fbaecc56ec029d6f813d76e26bd8891a41416bf0;p=sage.d.git

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index f3543a1..1a3ee3b 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -725,12 +725,85 @@ def is_lyapunov_like(L,K):
 
     EXAMPLES:
 
-    todo.
+    The identity is always Lyapunov-like in a nontrivial space::
 
-    TESTS:
+        sage: set_random_seed()
+        sage: K = random_cone(min_ambient_dim = 1, max_rays = 8)
+        sage: L = identity_matrix(K.lattice_dim())
+        sage: is_lyapunov_like(L,K)
+        True
+
+    As is the "zero" transformation::
 
-    todo.
+        sage: K = random_cone(min_ambient_dim = 1, max_rays = 5)
+        sage: R = K.lattice().vector_space().base_ring()
+        sage: L = zero_matrix(R, K.lattice_dim())
+        sage: is_lyapunov_like(L,K)
+        True
+
+    Everything in ``LL(K)`` should be Lyapunov-like on ``K``::
+
+        sage: K = random_cone(min_ambient_dim = 1, max_rays = 5)
+        sage: all([is_lyapunov_like(L,K) for L in LL(K)])
+        True
 
     """
     return all([(L*x).inner_product(s) == 0
                 for (x,s) in discrete_complementarity_set(K)])
+
+
+def random_element(K):
+    r"""
+    Return a random element of ``K`` from its ambient vector space.
+
+    ALGORITHM:
+
+    The cone ``K`` is specified in terms of its generators, so that
+    ``K`` is equal to the convex conic combination of those generators.
+    To choose a random element of ``K``, we assign random nonnegative
+    coefficients to each generator of ``K`` and construct a new vector
+    from the scaled rays.
+
+    A vector, rather than a ray, is returned so that the element may
+    have non-integer coordinates. Thus the element may have an
+    arbitrarily small norm.
+
+    EXAMPLES:
+
+    A random element of the trivial cone is zero::
+
+        sage: set_random_seed()
+        sage: K = Cone([], ToricLattice(0))
+        sage: random_element(K)
+        ()
+        sage: K = Cone([(0,)])
+        sage: random_element(K)
+        (0)
+        sage: K = Cone([(0,0)])
+        sage: random_element(K)
+        (0, 0)
+        sage: K = Cone([(0,0,0)])
+        sage: random_element(K)
+        (0, 0, 0)
+
+    TESTS:
+
+    Any cone should contain an element of itself::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_rays = 8)
+        sage: K.contains(random_element(K))
+        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)) ]
+
+    # 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