from numpy import *
import matplotlib.pyplot as plt
from sympy import *

a=0.5
h = 10**(-arange(0,6,0.1).reshape((-1,1)) )
plt.loglog(h, abs(sin(a)*h/2), \
           h, abs(cos(a)*h**2/6), \
           h, abs(18*cos(a)*h**4), \
           h, abs(sin(a)*h**2/12))
plt.legend(['Newton','Symmetrisk Newton', 'Fire punkter','Andrederiverte'])
plt.show()

x = arange(0,6,0.05)
f = lambda x : (-x**2+10*x-5)/4
plt.plot(x,f(x))
plt.plot(array([1,3]),array([f(1),f(3)]))
plt.plot(array([1,5]),array([f(1),f(5)]))
plt.plot(array([3,5]),array([f(3),f(5)]))
plt.show()

A = Matrix([[-2,-1,1,2,1],[4,1,1,4,0],[-8,-1,1,8,0],[16,1,1,16,0]])
C,c=A.rref()
print(C)