ex2.ipynb

Kernel: Python 2 (system-wide)

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(-12,12,0.001)
y = x**3 - 9*(x**2) -23 * x -15

def find_roots(y):
    z = np.diff(np.heaviside(y,0))
    return np.argwhere(z!=0)

print('the roots of the fuction are:',x[find_roots(y)])

plt.plot(x,y)

('the roots of the fuction are:', array([[11.177]]))

[<matplotlib.lines.Line2D at 0x7f53aa382210>]

x = np.arange(0,10,0.001)
y = x**5 -25*x**4 + 230*x**3 -950*x**2+1689*x-945

plt.plot(x,y)

print('the roots of the fuction are:',np.round(x[find_roots(y)]))

x = np.round(x[find_roots(y)])
y = np.zeros(np.shape(x)[0])
plt.plot(x,y,'r.')

('the roots of the fuction are:', array([[1.],
       [3.],
       [5.],
       [7.],
       [9.]]))

[<matplotlib.lines.Line2D at 0x7f53aa35d810>]

x = np.linspace(0,6.28,1000)
plt.plot(np.sin(x),np.cos(x))
plt.plot(np.sin(x)*0.2-0.4,np.cos(x)*0.2 + 0.4,'g')
plt.plot(np.sin(x)*0.2+0.4,np.cos(x)*0.2 + 0.4,'orange')
plt.plot(-np.cos(x/2)*0.2,-np.sin(x/2)*0.2,'r')

x = np.arange(0,7*6.28,0.001)
r = x/np.max(x)
r = r/5
plt.plot(np.cos(x)*r + 0.4,np.sin(x)*r + 0.4,'darkorchid')


t = np.arange(-1,1,0.0001)
x = 0.5*np.sin(t)*np.cos(t)*np.log(abs(t)) - 0.6
y = 0.5*abs(t)**0.4 * np.cos(t) - 0.25

plt.plot(x,y,'sienna')

[<matplotlib.lines.Line2D at 0x7f53a12d8990>]