拟环的算法研究

The study of algorithm for quasi-rings

计算机代数系统(简称CAS)是指符号数学的软件设计,而计算机代数则是指对CAS的算法研究.近些年随着CAS及其算法研究的迅速发展,该研究涉及到越来越多的数学领域.利用矩阵数据变换、矩阵分块等方法有效实现了某些代数系统的代数计算.特别地,建立了矩阵同构、拟环及多元代数系统的验证方法.这些结果不仅对矩阵、拟环及多元代数系统研究进行了验算,而且丰富和完善了现有CAS中的一些算法.

Computer algebra system （CAS） is a software program that facilitates symbolic mathematics. The study of algorithm for CAS is known as computer algebra. Now ,the study of the CAS and its algorithm is on the rapid development with more and more mathematical fields involved. In this paper, several algorithm for CAS are established by using matrix-data conversion and partition of matrices. Particularly, a new theory and its algorithm for quasi-rings, isomorphism of matrix and multivariate algebra are presented. These results not only investigate the arithmetic in detail for quasi-rings,matrix and multivariate algebra, but well complement the prevailing algorithm for CAS.