#! /usr/bin/env python3
#
def solve_example ( ):

  from sympy import N
  from sympy import solve
  from sympy import symbols
  import sympy

  print ( '' )
  print ( 'newton_example():' )
  print ( '  sympy version: ' + sympy.__version__ )
  print ( '  We plan to apply the Newton method to a function f(x).' )
  print ( '  We have f(x) = x^(1/3) exp(-x^2).' )
  print ( '  We want a formula for the derivative of f(x).' )
  print ( '  We also seek the second derivative.' )

  x = symbols ( 'x' )

  humps = 100 / ( ( 10 * x - 3 )**2 + 1 ) \
        + 100 / ( ( 10 * x - 9 )**2 + 4 ) \
        - 6

  solution = solve ( humps, x )
  print ( solution )
  print ( '' )
  n = len(solution)
  for i in range ( 0, n ):
    print ( (solution[0]).evalf() )

  return

if ( __name__ == "__main__" ):
  solve_example ( )