+ The Schur cone induces the majorization ordering::
+
+ sage: set_random_seed()
+ sage: def majorized_by(x,y):
+ ....: return (all(sum(x[0:i]) <= sum(y[0:i])
+ ....: for i in range(x.degree()-1))
+ ....: and sum(x) == sum(y))
+ sage: n = ZZ.random_element(10)
+ sage: V = VectorSpace(QQ, n)
+ sage: S = schur_cone(n)
+ sage: majorized_by(V.zero(), S.random_element())
+ True
+ sage: x = V.random_element()
+ sage: y = V.random_element()
+ sage: majorized_by(x,y) == ( (y-x) in S )
+ True
+
+ If a ``lattice`` was given, it is actually used::
+
+ sage: L = ToricLattice(3, 'M')
+ sage: schur_cone(3, lattice=L)
+ 2-d cone in 3-d lattice M
+
+ Unless the rank of the lattice disagrees with ``n``::
+
+ sage: L = ToricLattice(1, 'M')
+ sage: schur_cone(3, lattice=L)
+ Traceback (most recent call last):
+ ...
+ ValueError: lattice rank=1 and dimension n=3 are incompatible
+