Homogeneous Bivariate Decompositions

A homogeneous bivariate decomposition of a univariate polynomial f is of the form f = g(h, k) with polynomials g, h, k, where g is bivariate and homogeneous. Such decompositions are of interest in robotics applications. This paper gives a Structure Theorem relating these decompositions to certain block decompositions of the roots of f , decomposition algorithms, and a classification of all constellations of degrees for which "almost all" polynomials f have such a decomposition.