Ordering in Solving Systems of Equations 1)

Abstract. To use a “good ” variable order is one of the effective ways to prevent the occurrence of large polynomials in an elimination method. In this paper, we present an algorithm of O(n3) to find such a “good ” order using algorithms from graph theory. Based on this algorithm, we present a new version of Wu-Ritt’s zero decomposition algorithm, which allows different orders for different triangular sets in the decomposition formula. 1