Extraneous factors in the Dixon resultant formulation
Deepak Kapur, Tushar Saxena · 1997
Elimination methods based on generalizations of the Dixon's resultant formulation have been demonstrated to be efficient for simultaneously eliminating many variables from polynomials. One of these methods, presented by the authors earlier, was even shown to exploit the sparse structure of a polynomial system as determined by its Newton polytope. This paper analyzes the extraneous factors in the projection operators computed by that method. It is shown that the projection operator of a polynomial system can be related to the projection operator of another system consisting of polynomials with smaller Newton polytopes and lower degrees, thus making resultant computation more efficient. If a larger polyomial system can be obtained from another smaller one by replacing variables by their powers, then the projection operator of the larger system is proved to be a power of the projection operator of the smaller one. This shows that the set of extraneous factors in the two projection operato...