China was able to solve the equation once in the Han Dynasty, which was called "equation technique" in ancient times. In the Song and Yuan Dynasties, there was another achievement of world significance-magic. Then, when there is more than one unknown quantity, how to list the solutions of high-order simultaneous equations? There is an old math problem: "there are 864 steps in a straight field, but there are only 60 steps in the width of a cloud." How many steps are there? " ? A: Twenty-four steps wide and thirty-six steps. "That is to say, the area of a rectangular field is equal to 86 square steps, the sum of length and width is 60 steps, and how many steps is the length and width? This problem is formulated as an equation: xy = 864, x+y=60, where x and y represent the length and width of the domain respectively. This problem is a problem of binary quadratic equations, which is selected from the book Field-Mubi Multiplication and Division Algorithm written by Yang Hui, a mathematician in the Southern Song Dynasty. This shows that mathematicians in Song Dynasty have studied multivariate higher order equations in combination with production practice. So, are there three-dimensional cubic equations and four-dimensional quartic equations? Of course there is. As early as the Song and Yuan Dynasties, China mathematicians solved this problem satisfactorily.
Zhu Shijie, a mathematician in Yuan Dynasty, further developed the "Quaternary Method" on the basis of the numerical solution of univariate higher-order equations and the celestial sphere method founded by his contemporary mathematicians Qin and Li Zhi, and founded the method of solving binary, ternary and quartile higher-order equations by elimination.
Zhu Shijie's great invention is recorded in his masterpiece "Siyuan Jade Mirror".