






snake_case__      :	Optional[int]       	=      {
    """a""": """AAAAA""",
    """b""": """AAAAB""",
    """c""": """AAABA""",
    """d""": """AAABB""",
    """e""": """AABAA""",
    """f""": """AABAB""",
    """g""": """AABBA""",
    """h""": """AABBB""",
    """i""": """ABAAA""",
    """j""": """BBBAA""",
    """k""": """ABAAB""",
    """l""": """ABABA""",
    """m""": """ABABB""",
    """n""": """ABBAA""",
    """o""": """ABBAB""",
    """p""": """ABBBA""",
    """q""": """ABBBB""",
    """r""": """BAAAA""",
    """s""": """BAAAB""",
    """t""": """BAABA""",
    """u""": """BAABB""",
    """v""": """BBBAB""",
    """w""": """BABAA""",
    """x""": """BABAB""",
    """y""": """BABBA""",
    """z""": """BABBB""",
    """ """: """ """,
}


snake_case__      :	int       	=      {value: key for key, value in encode_dict.items()}






def     _snake_case    (__lowercase):
			UpperCamelCase_									=     ''
			for letter in word.lower():
						if letter.isalpha() or letter == " ":
									encoded += encode_dict[letter]
						else:
									raise Exception('encode() accepts only letters of the alphabet and spaces')
			return encoded






def     _snake_case    (__lowercase):
			if set(__lowercase) - {"A", "B", " "} != set():
						raise Exception('decode() accepts only \'A\', \'B\' and spaces')
			UpperCamelCase_									=     ''
			for word in coded.split():
						while len(__lowercase) != 0:
									decoded += decode_dict[word[:5]]
									UpperCamelCase_									=     word[5:]
						decoded += " "
			return decoded.strip()


if __name__ == "__main__":
	from doctest import testmod

	testmod()













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






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase = "x"    ,      __lowercase = 10**-10    ,      __lowercase = 1    ,      ):
   UpperCamelCase_									=     symbols(__lowercase)
   UpperCamelCase_									=     lambdify(__lowercase    ,      __lowercase)
   UpperCamelCase_									=     lambdify(__lowercase    ,      diff(__lowercase    ,      __lowercase))

   UpperCamelCase_									=     starting_point

   while True:
      if diff_function(__lowercase) != 0:
         UpperCamelCase_									=     prev_guess - multiplicity * func(__lowercase) / diff_function(
             __lowercase)
      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_									=     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", 1_0, precision=0.005)}',
 )

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





