update

README.md

@@ -50,6 +50,31 @@ y2 = -2 + x^1
 y3 = -2 + 5x - 8x^2 + 3x^3
 ```
 
+```py
+from lumpur.num.polynomial import Polynomial
+from lumpur.viz.plot.polynomial import plot_polynomial
+
+p1 = Polynomial([-1, 1])
+p2 = Polynomial([-3, 1])
+p3 = Polynomial([-5, 1])
+p4 = Polynomial([-7, 1])
+p = p1 * p2 * p3 * p4
+dp = p.differentiate()
+d2p = dp.differentiate()
+d3p = d2p.differentiate()
+d4p = d3p.differentiate()
+d5p = d4p.differentiate()
+x = [0.1*i for i in range(10, 71)]
+
+plot_polynomial(x, p, label='p')
+plot_polynomial(x, dp, label='dpdx')
+plot_polynomial(x, d2p, label='d2p/dx2')
+plot_polynomial(x, d3p, label='d3p/dx3')
+plot_polynomial(x, d4p, label='d4p/dx4')
+```
+<img src="https://raw.githubusercontent.com/dudung/lumpur/refs/heads/main/docs/images/polynomial.png" width="300" />
+
+
 ### circular decision boundary
 $$
 0.41 - 0.8x - 1.2y + x^2 + y^2 = 0