


from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403

def       lowercase_		(		_A			:    str    ,					_A			:    complex    ,					_A			:    str = "x"    ,					_A			:    float = 10**-10    ,					_A			:    int = 1    ,					):

      """simple docstring"""




      lowerCamelCase__		:				Optional[Any]    =  symbols(_A						)
      lowerCamelCase__		:				Union[str, Any]    =  lambdify(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  lambdify(_A    ,					diff(_A    ,					_A						)						)

      lowerCamelCase__		:				Any    =  starting_point

      while True:
            if diff_function(_A						) != 0:
                  lowerCamelCase__		:				List[Any]    =  prev_guess - multiplicity * func(_A						) / diff_function(
                      _A						)
            else:
                  raise ZeroDivisionError("Could not find root"						) from None

            # Precision is checked by comparing the difference of consecutive guesses
            if abs(next_guess - prev_guess						) < precision:
                  return next_guess

            lowerCamelCase__		:				Dict    =  next_guess


# Let's Execute
if __name__ == "__main__":
    # Find root of trigonometric function
    # Find value of pi
    print(f'The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}')

    # Find root of polynomial
    # Find fourth Root of 5
    print(f'The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}')

    # Find value of e
    print(
        "The root of log(y) - 1 = 0 is ",
        f'{newton_raphson("log(y) - 1", 2, variable="y")}',
    )

    # Exponential Roots
    print(
        "The root of exp(x) - 1 = 0 is",
        f'{newton_raphson("exp(x) - 1", 10, precision=0.0_0_5)}',
    )

    # Find root of cos(x)
    print(f'The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}')






class 			_lowercase :


       """simple docstring"""




       def __init__(   self							:			List[Any]					,      __lowerCamelCase							:			int       ):


             '''simple docstring'''



             lowerCamelCase__		:				Optional[Any]    =  size
             lowerCamelCase__		:				List[str]    =  [0] * size
             lowerCamelCase__		:				str    =  [0] * size





       @staticmethod
       def 						lowerCAmelCase     (   __lowerCamelCase							:			int       ):


             '''simple docstring'''



             return index | (index + 1)





       @staticmethod
       def 						lowerCAmelCase     (   __lowerCamelCase							:			int       ):


             '''simple docstring'''



             return (index & (index + 1)) - 1





       def 						lowerCAmelCase     (   self							:			int					,      __lowerCamelCase							:			int					,      __lowerCamelCase							:			int       ):


             '''simple docstring'''



             lowerCamelCase__		:				Union[str, Any]    =  value
             while index < self.size:
                   lowerCamelCase__		:				Tuple    =  self.get_prev(__lowerCamelCase       ) + 1
                   if current_left_border == index:
                         lowerCamelCase__		:				Optional[Any]    =  value
                   else:
                         lowerCamelCase__		:				str    =  max(__lowerCamelCase					,      __lowerCamelCase					,      __lowerCamelCase       )
                   lowerCamelCase__		:				Dict    =  self.get_next(__lowerCamelCase       )





       def 						lowerCAmelCase     (   self							:			List[Any]					,      __lowerCamelCase							:			int					,      __lowerCamelCase							:			int       ):


             '''simple docstring'''



             right -= 1  # Because of right is exclusive
             lowerCamelCase__		:				str    =  0
             while left <= right:
                   lowerCamelCase__		:				Optional[Any]    =  self.get_prev(__lowerCamelCase       )
                   if left <= current_left:
                         lowerCamelCase__		:				Optional[Any]    =  max(__lowerCamelCase					,      self.tree[right]       )
                         lowerCamelCase__		:				Any    =  current_left
                   else:
                         lowerCamelCase__		:				Optional[Any]    =  max(__lowerCamelCase					,      self.arr[right]       )
                         right -= 1
             return result


if __name__ == "__main__":
    import doctest

    doctest.testmod()


