关于“大衍术”源流的算例分析

通过分析秦九韶《数学九章》“治历演纪”题算例,证明了所谓“通其率”算法在中算史上是确实存在的。指出历家相传有一种解一次同余式的一般性算法程序,秦氏称之为大衍术,并将之规范为大衍求一术,而历家推演历元的“方程术”与大衍术在算理上是一致的。并给出了“方程术”演算程序的一种推测。

AN ANALYSIS OF THE TEXT ON THE ORIGIN AND DEVELOPMENT OF THE DAYAN METHOD

Analysing the problem Zhili Yanji (searching the number of years between the beginning of the grand cycle and the year given by calendar makers , called Shangyan Jinian , in making calendars) in the book Shushu Jiuzhang (Mathematical Treatise in Nine Sections , A. D. 1247) by the celebrated Song mathematician Qin Jiushao , this paper proves that a mathematical method , known as Tongqilu , existed indeed in the history of mathematics in China. It also points out that the calendar makers had a traditional calculation program handed down for solving congruences called Dayanshu by Qin Jiushao who improved it into a standardized method named Dayan qiuyishu (lit. the great extension method of searching unity) . The authors consider that the mathematical principles of Dayanshu and Fangchengshu (a part of the method for searching Shangyuan Jinian)are identical. The paper goes a step fur- ther to conjecture how the calculation program of Fangchengshu worked.