Independence analysis of equations extended by XL algorithm

Abstract

Aiming at problems of solving multiple quadratic equation systems, the redundancy of extending equations by eXtended Linearization (XL) algorithm is analyzed. It is proved that there is redundancy in equations extended by XL algorithm. The upper bound, [mn(n+3) m(m 3)]/2, of the number of linearly independent equations in the new system of equations, which extends from n-variable quadratic equations consisting of m equations, is given.