Mold Cross-computing Algorithms

The theory of modules is increasingly important in modern mathematics. It unifies many mathematical structures, and is the basic tools in commutative algebra. Computation of the intersection of modules plays a very crucial role in many application fields.The question is how to do we compute efficiently the intersection of the ideals and sub-module ? In fact, we have various different approaches to compute the intersection of two modules in the theoretic sense. Our goal is to apply some methods in Computer Algebra to deal the related problems.This paper introduces firstly the basic concepts and modules-related parts of knowledge, including Ideals and modules and Gr?ebner bases. One presents an approach to compute intersection of modules, which is relatively easy to be implemented in the computer System.This paper is based on modules, The main result of this paper:1.Apply the theory of Gr?ebner basis to improve the method for computing intersection of ideals , and the algorithm is also presented.2.Apply the theory of modules to improve the method for computing intersection of Modules.3. Implement all the algorithms in this paper in Maple System.Several examples are illustrated our improvements.