Tianyuanshu is a method to solve the unary equation, which may sprout in the Tang Dynasty at the earliest. There is a method of "taking from the square" in Wang Xiaotong's Ji Gu Shu Jing in the early Tang Dynasty, which is used to solve the cubic equation of x3+AX2+BX+Cκ 0 type.
In the Northern Song Dynasty, Jia Xian improved the method of "taking from the prescription", created the method of "increasing multiplication and increasing prescription", extended the method of recipe science to any high-order recipe science, and put forward the "original map of recipe science method", which became the "Yang Hui Triangle".
12nd century Mathematicians in the Northern Song Dynasty first studied the solution of general positive coefficient or negative coefficient equations, and Qin extended the "multiplication and multiplication method" to the method of finding the positive root of any higher order equation.
Extended data
Zhu Shijie traveled around the world as a mathematician for more than 20 years, and many people came to learn from him. When I went to Guangling (now Yangzhou), "under the door, there were many people."
He fully inherited the mathematical achievements of predecessors, not only absorbed the celestial science in the north, but also absorbed the positive and negative formulas, various daily algorithms and popular songs in the south. On this basis, he conducted creative research, and for the purpose of summarizing and popularizing all kinds of mathematical knowledge at that time, he wrote "Enlightenment of Arithmetic" (3 volumes), and also wrote "Siyuan-Siyuan Encounter" (3 volumes), which was published in: 65433.
The Enlightenment of Arithmetic, from simple to deep, from one-digit multiplication to the latest mathematical achievement at that time-Tiandao, suddenly formed a complete system.
The book clearly puts forward the multiplication rule of positive and negative numbers, gives the concept and basic properties of reciprocal, summarizes some new multiplication formulas and radical operation rules, summarizes some quick formulas of multiplication and division, and applies the method of setting auxiliary unknowns to solving linear equations.
The main content of Siyuan Encounter is quaternary technology, that is, the establishment and solution of multivariate higher order equations. Qin's numerical solution of higher-order equations and his celestial skills are all included.
References:
Baidu Encyclopedia-Zhu Shijie