HOMOGENEOUS BIVARIATE DECOMPOSITIONS

A homogeneous bivariate decomposition of a univariate polynomial f is of the form f = g(h, k) with polynomials g, h, Ic, where g is bivariat e and homogeneous. Such decompositions are of interest in robotics app lications. This paper gives a Structure Theorem relating these decompo sitions to certain block decompositions of the roots of f, decompositi on algorithms, and a classification of all constellations of degrees f or which ''almost all'' polynomials f have such a decomposition.