+ Each positive operator generator should send the generators of the
+ cone into the cone::
+
+ sage: set_random_seed()
+ sage: K = random_cone(max_ambient_dim=5)
+ sage: pi_of_K = positive_operator_gens(K)
+ sage: all([ K.contains(P*x) for P in pi_of_K for x in K ])
+ True
+
+ Each positive operator generator should send a random element of the
+ cone into the cone::
+
+ sage: set_random_seed()
+ sage: K = random_cone(max_ambient_dim=5)
+ sage: pi_of_K = positive_operator_gens(K)
+ sage: all([ K.contains(P*K.random_element(QQ)) for P in pi_of_K ])
+ True
+
+ A random element of the positive operator cone should send the
+ generators of the cone into the cone::
+
+ sage: set_random_seed()
+ sage: K = random_cone(max_ambient_dim=5)
+ sage: pi_of_K = positive_operator_gens(K)
+ sage: L = ToricLattice(K.lattice_dim()**2)
+ sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L)
+ sage: P = matrix(K.lattice_dim(), pi_cone.random_element(QQ).list())
+ sage: all([ K.contains(P*x) for x in K ])
+ True
+
+ A random element of the positive operator cone should send a random
+ element of the cone into the cone::
+
+ sage: set_random_seed()
+ sage: K = random_cone(max_ambient_dim=5)
+ sage: pi_of_K = positive_operator_gens(K)
+ sage: L = ToricLattice(K.lattice_dim()**2)
+ sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L)
+ sage: P = matrix(K.lattice_dim(), pi_cone.random_element(QQ).list())
+ sage: K.contains(P*K.random_element(ring=QQ))
+ True
+
+ The lineality space of the dual of the cone of positive operators
+ can be computed from the lineality spaces of the cone and its dual::