中国、日本以及西方的消元方法的比较研究

作为一项数学史课题，本项目以消元方法为研究对象，以吴文俊数学机械化理论创立思想为切入点，从算法与历史的角度出发，主要选取中国宋元数学的天元术与四元术、日本江户时代和算的解伏题之法、西方十八世纪的多项式乘数法以及现代吴文俊机械化理论中求解非线性代数方程组的吴消元法进行比较研究，对于不同文化背景下这几种消元方法的算法本质及构建原理进行解析，探讨算法之间的传承关系与沿革影响；并将西方消元方法的发展轨迹与中算传统（中、日）的消元理论结合起来进行系统考察、比较研究；将消元法的整个历史演变与现代吴文俊数学机械化理论中的消去法联系在一起进行综合考量；以算法和历史两个维度视角，为历史上不同文化背景下产生的消元方法与现代消元方法建立联系。

As a research topic of history of mathematics, this project start from the roots of Wu's method, taking the elimination menthods as the core of research, try to study the Tianyuan method and Siyuan method in Song and Yuan dynasties in China, Kaifukudai noho of Wasan in Japan, Bezout’s polynomial multiplier in the West and Wu's elimination method. The principle of the algorithm, the connection and differences among these methods which originated from different cultural background will be analysed. Moreover, we will conduct the comparative study on the development process of western elimination theory, elimination methods in Song and Yuan dynasties in China and in Edo period in Japan, explore the relationship of transfer and inheritance between the historical evolution process of elimination methods and the Wu's elimination method. From the two perspectives of algorithm and history, the connection between the modern elimination methods and elimination methods which originated in different cultural background in history will be established.