正则与简单系统算法的优化

Optimizations of regular and simple system algorithms

改进王东明提出的正则系统算法(简称RegSer算法)及简单系统算法(简称SimSer算法)的效率。提出新的分解策略:对于任意多项式系统或多项式组[P,Q],首先计算一组良好三角系统,得到[P,Q]的一种零点分解。其次判断每一良好系统是否是正则系统,若不是则将其正则化,即计算一组正则系统,给出该良好系统的零点分解。最后将每一正则系统简单化,即计算一组简单系统,给出该正则系统的零点分解,得到给定多项式系统或多项式组的简单分解。实验结果表明这种分解策略可以提高RegSer和SimSer算法的效率。

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 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 .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.