# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

from legendre import legendre

import numpy as np

def legnewton(n,xold,kmax=200,tol=1.e-8):

for k in range(1,kmax):

val, dval = legendre(n,xold)

xnew = xold - val/dval

xdiff = xnew - xold

if abs(xdiff/xnew) < tol:

break

xold = xnew

else:

xnew = None

return xnew

def legroots(n):

roots = np.zeros(n)

npos = n//2

for i in range(npos):

xold = np.cos(np.pi*(4*i+3)/(4*n+2))

root = legnewton(n,xold)

roots[i] = -root

roots[-1-i] = root

return roots

if __name__ == '__main__':

roots = legroots(9); print(roots)