吴方法与和式几何研究  

Research on Wu's Method and Japanese Geometry

作　　者：徐泽林[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《自然科学史研究》2008年第4期471-484,共14页Studies in The History of Natural Sciences

基　　金：国家自然科学基金项目"数学天文交流对创新的作用"(项目编号:10561006);天津市教委科研基金(项目编号:20011204)

摘　　要：分析了宋元数学中几何代数化的数学特征,指出宋元数学传统独特之处在于其抽象化和形式化的代数演算,考察了和算对天元术与代数化几何传统的受容过程以及和式几何发展情形,讨论了和算在多项式方程组消元理论方面的成就及其对于现代计算代数的意义,通过具体案例介绍吴方法与Grbner基方法等数学机械化方法在和式几何研究中的实践与作用。In anaqlysing the mathematical characteristics of algebraical geometry in Song and Yuan Dynasties, this paper Points out that the unique character of Song and Yuan metamathematics consists in its abstract and formalized algebraic operation, explores the process of Wasan absorbing the Tianyuan method and algebraical geometry as well as the development of Japanese geometry, discusses the accomplishment in the field of eliminant of polynomial equation in Wasan and its significance to modern computational algebra, and finally introduces by concrete case the function of the mathematical mechanization including Wu＇s mothod and Grobner basis-method in Japanese geometry.

关 键 词：吴方法 Grobner基方法 宋元数学 和式几何解伏题 

分 类 号：O112[理学—数学]