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A plane algebraic curve whose Newton polygone contains d lattice points canbe given by d points it passes through. Then the coefficients of its equationPoisson commute having been regarded as functions of coordinates of thosepoints. It is observed in the work by O.Babelon and M.Talon, 2002. We formulatea generalization of this fact in terms of separation of variables and proverelations implying the Poisson commutativity. The examples of the integrablesystems obtained this way include coefficients of the Lagrange and Hermitinterpolation polynomials, coefficients of the Weierstrass models of curves.

Some integrable systems of algebraic origin and separation of variables