# 2.4.py
# created on 21:02 2015-03-28
# $Id: 2.4.py 1.3 2016/11/13 06:27:20 s Exp $

from fractions import Fraction

def f(x):
  return -1 + x + x**2

def fd(x):
  return 1 + 2 * x

# main

# calculate
x0 = 1
x1 = x0 - f(x0) / fd(x0)
x2 = x1 - f(x1) / fd(x1)
x3 = x2 - f(x2) / fd(x2)
x4 = x3 - f(x3) / fd(x3)

# output
print('2.4.py')
print('in float')
print('{:>10}{:>10}{:>10}{:>10}'.format('n', 'lambda(n)', 'f(lambda)', 'f\'(lambda)'))
print(40 * '-')
print('{:10d}{:10.7f}{:10.7f}{:10.7f}'.format(0, x0, f(x0), fd(x0)))
print('{:10d}{:10.7f}{:10.7f}{:10.7f}'.format(1, x1, f(x1), fd(x1)))
print('{:10d}{:10.7f}{:10.7f}{:10.7f}'.format(2, x2, f(x2), fd(x2)))
print('{:10d}{:10.7f}{:10.7f}{:10.7f}'.format(3, x3, f(x3), fd(x3)))
print('{:10d}{:10.7f}{:10.7f}{:10.7f}'.format(4, x4, f(x4), fd(x4)))
print(40 * '-')

# main #2
x0 = Fraction(1, 1)
x1 = x0 - Fraction(f(x0), fd(x0))
x2 = x1 - Fraction(f(x1), fd(x1))
x3 = x2 - Fraction(f(x2), fd(x2))
x4 = x3 - Fraction(f(x3), fd(x3))

# output #2
fmt = '{:10d}{:21s}{:9.7f}'
print()
print('in fraction')
print('{:>10}{:21}{}'.format('n', ' lambda(n)', 'lambda(n)'))
print(40 * '-')
print(fmt.format(0, ' ' + str(x0), float(x0)))
print(fmt.format(1, ' ' + str(x1), float(x1)))
print(fmt.format(2, ' ' + str(x2), float(x2)))
print(fmt.format(3, ' ' + str(x3), float(x3)))
print(fmt.format(4, ' ' + str(x4), float(x4)))
print(40 * '-')

# end of program
#
# below is output
#
# 2.4.py
# in float
#          n lambda(n) f(lambda)f'(lambda)
# ----------------------------------------
#          0 1.0000000 1.0000000 3.0000000
#          1 0.6666667 0.1111111 2.3333333
#          2 0.6190476 0.0022676 2.2380952
#          3 0.6180344 0.0000010 2.2360689
#          4 0.6180340 0.0000000 2.2360680
# ----------------------------------------
# 
# in fraction
#          n lambda(n)           lambda(n)
# ----------------------------------------
#          0 1                   1.0000000
#          1 2/3                 0.6666667
#          2 13/21               0.6190476
#          3 610/987             0.6180344
#          4 1346269/2178309     0.6180340
# ----------------------------------------
# end of output