1248, Ye Li, a mathematician in the Jin Dynasty, systematically introduced the establishment of quadratic equation in his works "Measuring the Round Sea Mirror" and "An Ancient Analysis", while Zhu Shijie, a mathematician in the Yuan Dynasty,
Astrology is a general method of using unknown equations, which is basically consistent with the method of equations in modern algebra. In ancient mathematics, equation and solution are two important interrelated problems.
The calculation process of Ye Li and Zhu Shijie's celestial skills
In Ye Li's art of heaven, first "set Tianyuan as a certain", that is, set an unknown number, and then list Tianyuan styles according to the conditions of the problem. Write a word "Yuan" next to the primary term of the unknown and a word "Tai" next to the constant term, arranged in order of high power and low power. You can also subtract two Tianyuan expressions to cancel the same number. Tianyuan book has the embryonic form of modern notation of equations, which is called semi-symbolic algebra by modern historians. The saying that "yuan" represents the unknown has been used to this day.
He defined the unknown as "Tian" yuan and the constant as "Tai" (Tai Chi), and listed the equations. For example, the equation 2x2+32x+256=0. He expressed the polynomial on the left side of the equal sign as "Tianyuan type". Then he put the constant term on the top layer and arranged the coefficients in ascending order of power. When two polynomials are added, the corresponding Tianyuan formula is added at the same level, which is $ Canada, too much, too much, and so on.
Yuan by Tianyuan style, "yuan" word by going up one flight of stairs. These Tianyuan algorithms are consistent with the current polynomial operations. After the polynomials are listed, the numerical solution is obtained by "increasing multiplication and opening method"