【作者】 沈可微；

【导师】 罗玉峰；

【作者基本信息】 南昌大学 ， 机械电子工程， 2006， 硕士

【摘要】 多项式方程组的构造性理论及有关算法，在计算机自动推理、数学机械化、工程技术等领域日趋重要。吴文俊消元法和Groebner基法是两种非常完整的多项式方程组的符号解法。主项解耦消元法综合了这两种算法的优点，是一种新的多项式方程组的符号解法。本文主要研究主项解耦消元法算法理论、应用及软件的存储结构和程序结构。 本文在分析现有的算法基础上，借鉴Groebner基法和吴文俊消元法，系统地阐述了多项式方程组主项解耦消元法的基本概念和算法原理；给出了主项解耦中间余式和主项解耦中间余式集的明确定义，消除了中间余式的歧义性，使得中间余式的求解具有规范性：对其求余算法也给出了详细的定义和过程描述，加速求余的过程使得整个算法的效率提高；并对其终止判据也做了补充和完善，使得此方法更加完备且适用范围更加广阔，成为一种通用性较强的一种算法。 本文在分析主项解耦消元法算法的基础上，为其软件实现提出了软件系统的存储方案的设计和程序方案的设计。 本文将主项解耦消元法运用于机构学和几何定理机器证明的应用实例中，不但使该方法的可行性得到验证，而且也取得了良好的效果。更多还原

【Abstract】 The constructive theories and algorithms involved in polynomial sets play a more and more important role in computer automated reasoning, mathematics mechanization and engineering technology. Both Wu-WenJun elimination method and Groebner Basis method are complete symbolic methods of solving polynomial sets. The decoupled leading terms elimination method is a new symbolic method of solving polynomial sets which synthesizes the merits of Wu’s elimination method and Groebner Basis method. In this paper, we mainly research into the theories and algorithm of the decoupled leading terms elimination method, its applications, its access structure and program strcture of software system.According to the anlysis of the existing methods, we systemically formed the basic concepts and the principles of the decoupled leading terms elimination method by means of drawing lessons form the basic concepts and principles of Wu’s method and Groebner Basis method, In this paper, we make a definition of mid- remainder and mid-remainder sets, which has avoided the different meanings of the mid-remainder and make it more normative. We also make a definition of the algorithm of pseudo divisions of the decoupled leading terms elimination method in更多还原