+ All rearrangement cones are proper::
+
+ sage: all([ rearrangement_cone(p,n).is_proper()
+ ....: for n in range(10)
+ ....: for p in range(n) ])
+ True
+
+ The Lyapunov rank of the rearrangement cone of order ``p`` in ``n``
+ dimensions is ``n`` for ``p == 1`` or ``p == n`` and one otherwise::
+
+ sage: all([ lyapunov_rank(rearrangement_cone(p,n)) == n
+ ....: for n in range(2, 10)
+ ....: for p in [1, n-1] ])
+ True
+ sage: all([ lyapunov_rank(rearrangement_cone(p,n)) == 1
+ ....: for n in range(3, 10)
+ ....: for p in range(2, n-1) ])
+ True
+