東洋 數學에서 多項方程式의 解

Abstract

Since Jiuzhang Suanshu, mathematical structures in the traditional East Asian mathematics have been revealed by practical problems. Since then, polynomial equations are mostly the type of $p(x) = a_0$ where $p(x)$ has no constant term and $a_0$ is a positive number. This restriction for the polynomial equations hinders the systematic development of theory of equations. Since tianyuanshu (天元術) was introduced in the 11th century, the polynomial equations took the form of $p(x)=0$, but it was not universally adopted. In the mean time, East Asian mathematicians were occupied by kaifangfa so that the concept of zeros of polynomials was not materialized. We also show that Suanxue Qimeng inflicted distinct developments of the theory of equations in three countries of East Asia.