Expansion Of Nonlinear Algebraic Equations The We Relatively Simple Decomposition And Really Normal Decomposition Algorithm

In this Dissertation, we try first give a complete description for Exapanding WE's algorithm, which decompose a polynomials into components of normal ascending chain( or regular set) without factorization, and introduce Real regular decomposition.As an introduction, we give an overview of the history of solving nonlinear equation system, specially introduce the important sole of the method.This dissertation consist of four chapters.In chapter â…  ,we first outline the Wu 's elimination ,then introduce Zhang and Yang's WE approach ,which need not do decomposition of an algebraic set into the union of its irreducible varieties, to overcome the so-called "reducibility difficulty" in automated theorem proving. Employing division and Euclid^s algorithm.,we call it WE approach.In chapter â…¡,we introduce the concept of normal ascending ascending(or regular set), which was defined in 1992 by Zhang the and Yang, the powerful WR approach which decompose a polynomials set into components of normal ascending chain(or regular set) without factorization..Finally we introduce the faapanding WE's algorithm, which try to find speciall factor for decompostion.The method has been implemented in MAPLE system. It is an more efficient algorithm than WR.In chapter â…¢, we introduce WRSOLVE, Urn ixed decomposition and Dixon approach . By hint of the idea of WRSOLVE and WSOLVE, we get the Exapanding WESOLVE through the Exapanding WE's algorithm, which is more efficient algorithm than Umixed decomposition approach.In chapter â…£, we first prove a very important theroem in charpter II ,and get the approach of Real regular decomposition ,which improve the theory of the weakly Wu's non-degenerate condition to adapt one general zero decomposition method for efficient decomposition of affine algebraic varieties into normal ascending chains. The device based on neither GrY'obner base nor characteristic set.