3737.sagews

def pol1(x, a):
    """
     Algoritmo pol1
    """
    n = a.shape[0]
    px = a[n-1]
    for j in range(n-2, -1, -1):
        px = px + a[j] * x^(n-j-1)
    return px

def pol2(x, a):
    """ 
    Algoritmo pol2
    """
    n = a.shape[0]
    px = a[n-1]
    xp = 1
    for j in range(n-2, -1, -1):
        xp = xp*x
        px = px + a[j] * xp
    return px

def horner(x, a):
    """
     Algoritmo di Horner
    """
    n = a.shape[0]
    px = a[0]
    for i in range(1, n):
        px = a[i] + px*x
    return px

import numpy as np
import matplotlib.pylab as plt

p = np.array([1,-6,15,-20,15,-6,1])
x = np.linspace(0.995,1.005,1000)
# rappresentazione compatta
y = (x-1)**6

# Algoritmo di horner

yh = horner(x,p)
# Algoritmo  1

y1 = pol1(x,p)

# Algoritmo  2

y2 = pol2(x,p)

plt.plot(x,y,'-b',lw=2)

plt.plot(x,yh,'og')

plt.plot(x,y1,'*r')

plt.plot(x,y2,'vm')
plt.savefig('polfig.png')