An algorithm for an eigenvalues problem in the Earth rotation theory

In this paper we present a new algorithm to parameterize some kind of hypersurfaces. Our technique extends the Newton-Puiseux algorithm for plane curves to several variables. It is based on the introduction of an order in the monomials of several variables compatible with the total degree and in a recursive construction of a sequence of convex-hulls together with a tree search. We have developed this algorithm to determine the free frequencies (appearing as eigenvalues of a certain matrix) of realistic non-rigid Earth rotation models. We have implemented the algorithm in a Maple V package called PoliVar.