The Nature Of The Triangular Columns Excellent Set Theory And Its Applications

Characteristic set method is a commonly used method for solving systems of polynomial equations introduced by the Chinese mathematician Wu Wenjun. This method does not only basically focus on the zero set of polynomials but also give its structural descriptions. In general, the zero sets are complex with numerous redundant branches. Consequently it is very important that how to simplify the zero set and reduce the redundant branches effectively.In the theory of elimination, it can be determined in advance applying the extension theorem which partial solutions obtained by the elimination technology could extend to complete solution. Unfortunately, there may be some partial solutions which can not be determined applying the extension theorem. Accordingly the extension theorem should be further improved in order to determine this issue effectively.This paper based on the above questions considers polynomial system as the main study object and discusses the following terms:1. A detailed study of the properties of the regular chains and primitive of polynomials.2. spread the primitivism of polynomials, defining the C-primitive of polynomials and draw some important conclusions.3. A detailed discuss of the properties of the U-set,and based the properties of the U-set and characteristic set method, we improve the well-known extension theorem and use a new method to prove closure theorem.4. Be given some examples to explain the improved expansion theorem more effectively in determining whether partial solutions could extend to complete solution...