  One-dimensional 3-body Wolfes model with 2- and 3-body interactions also
known as $G_2/I_6$-rational integrable model of the Hamiltonian reduction is
exactly-solvable and superintegrable. Its Hamiltonian $H$ and two integrals
${\cal I}_{1}, {\cal I}_{2}$, which can be written as algebraic differential
operators in two variables (with polynomial coefficients) of the 2nd and 6th
orders, respectively, are represented as non-linear combinations of $g^{(2)}$
or $g^{(3)}$ (hidden) algebra generators in a minimal manner. By using a
specially designed MAPLE-18 code to deal with algebraic operators it is found
that $(H, {\cal I}_1, {\cal I}_2, {\cal I}_{12} \equiv [{\cal I}_1, {\cal
I}_2])$ are the four generating elements of the {\it quartic} polynomial
algebra of integrals. This algebra is embedded into the universal enveloping
algebra $g^{(3)}$. In turn, 3-body/$A_2$-rational Calogero model is
characterized by cubic polynomial algebra of integrals, it is mentioned
briefly.
