





def 		lowerCAmelCase_    (  __UpperCAmelCase:			str		,   __UpperCAmelCase:			str      )      ->	float:

    def get_matched_characters(__UpperCAmelCase:			str		,   __UpperCAmelCase:			str      ) -> str:
        UpperCamelCase__							:				Tuple          =      []
        UpperCamelCase__							:				Any          =      min(len(_stra      )		,   len(_stra      )      ) // 2
        for i, l in enumerate(_stra      ):
            UpperCamelCase__							:				Tuple          =      int(max(0		,   i - limit      )      )
            UpperCamelCase__							:				Dict          =      int(min(i + limit + 1		,   len(_stra      )      )      )
            if l in _stra[left:right]:
                matched.append(__UpperCAmelCase      )
                UpperCamelCase__							:				List[str]          =      f"{_stra[0:_stra.index(__UpperCAmelCase      )]} {_stra[_stra.index(__UpperCAmelCase      ) + 1:]}"

        return "".join(__UpperCAmelCase      )

    # matching characters
    UpperCamelCase__							:				str          =      get_matched_characters(__UpperCAmelCase		,   __UpperCAmelCase      )
    UpperCamelCase__							:				Optional[int]          =      get_matched_characters(__UpperCAmelCase		,   __UpperCAmelCase      )
    UpperCamelCase__							:				List[Any]          =      len(__UpperCAmelCase      )

    # transposition
    UpperCamelCase__							:				List[str]          =      (
        len([(ca, ca) for ca, ca in zip(__UpperCAmelCase		,   __UpperCAmelCase      ) if ca != ca]      ) // 2
    )

    if not match_count:
        UpperCamelCase__							:				List[Any]          =      0.0
    else:
        UpperCamelCase__							:				Union[str, Any]          =      (
            1
            / 3
            * (
                match_count / len(__UpperCAmelCase      )
                + match_count / len(__UpperCAmelCase      )
                + (match_count - transpositions) / match_count
            )
        )

    # common prefix up to 4 characters
    UpperCamelCase__							:				Optional[Any]          =      0
    for ca, ca in zip(stra[:4]		,   stra[:4]      ):
        if ca == ca:
            prefix_len += 1
        else:
            break

    return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(jaro_winkler('hello', 'world'))








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




def 		lowerCAmelCase_    (  __UpperCAmelCase:			str		,   __UpperCAmelCase:			complex		,   __UpperCAmelCase:			str = "x"		,   __UpperCAmelCase:			float = 10**-10		,   __UpperCAmelCase:			int = 1		,   )      ->	complex:
    UpperCamelCase__							:				Optional[int]          =      symbols(__UpperCAmelCase      )
    UpperCamelCase__							:				Dict          =      lambdify(__UpperCAmelCase		,   __UpperCAmelCase      )
    UpperCamelCase__							:				List[str]          =      lambdify(__UpperCAmelCase		,   diff(__UpperCAmelCase		,   __UpperCAmelCase      )      )

    UpperCamelCase__							:				int          =      starting_point

    while True:
        if diff_function(__UpperCAmelCase      ) != 0:
            UpperCamelCase__							:				Optional[int]          =      prev_guess - multiplicity * func(__UpperCAmelCase      ) / diff_function(
                __UpperCAmelCase      )
        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

        UpperCamelCase__							:				Tuple          =      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=0.005)}''',
  )

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

