We give a self-contained presentation and comparison of two different
algorithms to explicitly solve quantum many body models of indistinguishable
particles moving on a circle and interacting with two-body potentials of
$1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the
second one is a limiting case of a novel algorithm to solve the elliptic
generalization of the Sutherland model. These two algorithms are different in
several details. We show that they are equivalent, i.e., they yield the same
solution and are equally simple.