Improving And Some Applications Of The Groebner Basis Algorithm

Improving and some applications of the Groebner basis algorithm.The main results of this paper are the following:(1) The algorithm of the Groebner Basis has been improved;(2) Some applications of Groebner Basis are given.In this paper we study the the algorithm of the Groebner Basis and improve the algoithm appropriately.By improving the algoithm,we can skip S polynomial and make the algorithm more directly.The improved algorithm:By improving the algorithm,we can get the Groebner Basis.We investigate some application problems which are common in nature. By studying the common applications we can lie the foundation for the deeper studying of the use of the Groebner Basis in the future.