An extended fast algorithm for constructing the Dixon resultant matrix

In recent years, the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms. The recursive algorithm is a very efficient algorithm, but which deals with the case of three polynomial equations with two variables at most. In this paper, we extend the algorithm to the general case of n+1 polynomial equations in n variables. The algorithm has been implemented in Maple 9. By testing the random polynomial equations, the results demonstrate that the efficiency of our program is much better than the previous methods, and it is exciting that the necessary condition for the existence of common intersection points on four general surfaces in which the degree with respect to every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by our program.