Decoupled Leading Terms Elimination Method And Its Software Design

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...