And Historical Count Of The Origin Of The Elimination Method Visits

The article makes an investigation into the source of the elimination method in Wasan and its developing procedure. The phases of its origin,establishment,abundance and maturity are respectively arranged in chronological order and are carried out by wide-ranging comparative studies. In the author's perspective, tianyuanshu(天元术)and the tradition of algebraic geometry in mathematics of Song and Yuan Dynasties has played great significance in Wasan elimination during the process of its transmission and application.It is a pivotal issue in the shape of Wasan elimination that Wasanka has created pangshufa(旁书法)on the basis of tianyuanshu which shares the feature in its symbolic character method of oriental culture.Meanwhile,the author inspects and contrasts the performance of Guan and its contemporary school in area Tokyo and Osaka in terms of elimination methods.After that, analysis and summation of elimination features and its regular pattern are also obtained so as to explain the original relations among these methods.In the end,the author compares the elimination methods in Wasan and its counterpart of Zhu shijie's in order to illustrate the advance of Wasan and its influence to the algebra of Song and Yuan Dynasties.The article is mainly divided into four parts:In part one, it mainly introduces the contents and methods of Tianyuanshu in Wasan works Gujinsuanfaji(《古今算法记》)and analyses the relations between Gujinsuanfaji and Suanxueqimeng(《算学启�'�》).The author places great emphasis on the absorption of Tianyuanshu in Wasan.In part two,it is mainly on the in-depth analysis about Yanduan(演段)and Fukudai(解伏题)in Faweisuanfa(《发微算法》)and Faweisuanfayanduanyanjie(《发微算法演段谚解》).It discusses the contribution and its features of Guan in elimination and inspects the methods in the contemporary typical Wasan works in area Tokyo and Osaka,such as Suanfamingjie(《算法明解》),Mingyuansuanfa(《明元算法》),Hehansuanfa(《�'�汉算法》)and Yijisuanfa(《一极算法》).Lateral comparison has been made to show the similarities and differences between two schools.In part three,it is mainly on the elimination methods in Jiefutizhifa(《解伏题之法》),Dachengsuanjing(《大成算经》)and Suanfafahui(《算法发挥》).Then it leads to the conclusion that the methods above are the sign of Wasan maturity.In part four, the author summarizes the features and laws of Wasan elimination and gives the longitudinal comparison between Wasan elimination and Four elements elimination.In consequence,it reveals the advancement of Wasan in the aspects of algebraic system and degree of mechanization.