The maximality of the dixon matrix on corner-cut monomial supports

Abstract

It has been established that the bivariate Dixon matrix persists to be the exact resultant when there are at most two exposed points at each corner of a corner-cut support; but it becomes singular when there are four or more exposed points at any of the corners. For the remaining case of three or fewer exposed points at each of the corners, it is observed that the Dixon matrix is maximal but its determinant is a multiple of the resultant with a priori known bracket powers as the extraneous factors. The maximality of the Dixon matrix for the three-or-fewer exposed points case has been established mechanically for the special situation in which the excess degree is unity when there are three exposed points at a corner. This paper presents a greatly simplified mechanical proof so that its validity can be easily verified. © 2008 Springer-Verlag Berlin Heidelberg.