Abstract:

 Algorithms RegSer and SimSer are improved which are presented by Wang Dongming for computing a finite set of regular／simple systems from a given set／system ［P,Q］ of multivariate polynomials. A new strategy for triangular decomposition is given. A series of fine triangular systems are computed such that the union of the zero sets of the fine systems is equal to that of ［P, Q］. It is checked if each fine triangular system is regular. If some fine triangular system is not, a series of regular systems are computed for it. Simple systems are analogously obtained. The new algorithms are implemented in Maple, the efficiency of the routines is better than RegSer／SimSer which is shown by experimental results.

Key words: algorithm; triangular decomposition; regular system; simple system; Maple