+
+ The Lyapunov rank of the positive operator cone is the product of
+ the Lyapunov ranks of the associated cones if they're all proper::
+
+ sage: K1 = random_cone(max_ambient_dim=4,
+ ....: strictly_convex=True,
+ ....: solid=True)
+ sage: K2 = random_cone(max_ambient_dim=4,
+ ....: strictly_convex=True,
+ ....: solid=True)
+ sage: pi_K1_K2 = positive_operator_gens(K1,K2)
+ sage: L = ToricLattice(K1.lattice_dim() * K2.lattice_dim())
+ sage: pi_cone = Cone([ g.list() for g in pi_K1_K2 ],
+ ....: lattice=L,
+ ....: check=False)
+ sage: beta1 = K1.lyapunov_rank()
+ sage: beta2 = K2.lyapunov_rank()
+ sage: pi_cone.lyapunov_rank() == beta1*beta2
+ True
+