Mathematical graphics (1.46) high-order equation curve

This section reminds everyone of the mathematics they have learned in high school. The equation with the maximum number of unknowns in the equation is greater than twice. It is called a high-order equation. The idea of high-order equation solution is to convert high-order equations into low-frequency equations through appropriate methods. There is no universal algebraic solution and root-seeking formula for a single-dimensional high-order equation of five or more times (that is, it cannot be solved through a finite number of four arithmetic operations and multiplication and open arithmetic operations ), this is called Abel's theorem. However, in this section, I did not aim to find the root of the equation, but to plot the curve of N functions.

The general form of high-order equations can be written as follows: x ^ N + bnx ^ n-1 + ------- b1x + b0 = 0 we have learned in mathematics, and the curve of the quadratic equation is a parabolic, the curve of the cubic equation is an S-shape, then the curve of the n Cheng will have a N-1 bend, here will show several n Cheng curves, where n is 2 to 5. for related software, see: Mathematical graphics visualization tool. Use script code with custom syntax to generate mathematical graphics. quadratic function:

#http://www.bb.ustc.edu.cn/jpkc/xiaoji/wjf/kj/vertices = 360x = from (-5) to (5)y = 3*x*x + 4*x + 1

Three functions:

#http://www.bb.ustc.edu.cn/jpkc/xiaoji/wjf/kj/vertices = 360x = from (-2) to (4)y = x^3 - 4*x*x + 5*x + 6

Four functions:

#http://www.bb.ustc.edu.cn/jpkc/xiaoji/wjf/kj/vertices = 360x = from (-2) to (4)y = x^4 - x^3*5 + 5*x*x + 6*x + 1

Five functions:

#http://www.bb.ustc.edu.cn/jpkc/xiaoji/wjf/kj/vertices = 360x = from (-2) to (3.4)y = -x^5 + x^4*3 + x^3*3 - 6*x*x + 2

 

Mathematical graphics (1.46) high-order equation curve