  A plane algebraic curve whose Newton polygone contains d lattice points can
be given by d points it passes through. Then the coefficients of its equation
Poisson commute having been regarded as functions of coordinates of those
points. It is observed in the work by O.Babelon and M.Talon, 2002. We formulate
a generalization of this fact in terms of separation of variables and prove
relations implying the Poisson commutativity. The examples of the integrable
systems obtained this way include coefficients of the Lagrange and Hermit
interpolation polynomials, coefficients of the Weierstrass models of curves.
