  We try to write (generic) elements of classical simple Lie algebras as sums
of as few elements of the orbit C of long root vectors as possible. If the Lie
algebra in question is sl_n or sp_n, then C consists of all rank 1 matrices in
the Lie algebra, and an element of rank k is the sum of k elements of C. If, on
the other hand, the Lie algebra is o_n, then C consists of all rank 2 matrices
with square zero, and the situation is much more complicated. We explicitly
describe, in this case as well, the closure of the set of all sums of k
elements of C, also known as the (k-1)st secant variety of C.
