



"""simple docstring"""


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







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






				'''simple docstring'''



				_UpperCAmelCase					=    symbols(_SCREAMING_SNAKE_CASE				)
				_UpperCAmelCase					=    lambdify(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)
				_UpperCAmelCase					=    lambdify(_SCREAMING_SNAKE_CASE					,     diff(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)				)

				_UpperCAmelCase					=    starting_point

				while True:
								if diff_function(_SCREAMING_SNAKE_CASE				) != 0:
												_UpperCAmelCase					=    prev_guess - multiplicity * func(_SCREAMING_SNAKE_CASE				) / diff_function(
												    _SCREAMING_SNAKE_CASE				)
								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", 10, precision=0.005)}''',
					)

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








"""simple docstring"""


class 			_a :
			"""simple docstring"""



			def __init__(		self     :    Tuple				,   __UpperCamelCase     :    list[int]   )->None:
							_UpperCAmelCase					=    len(__UpperCamelCase   )
							_UpperCAmelCase					=    [0] * len_array

							if len_array > 0:
											_UpperCAmelCase					=    array[0]

							for i in range(1				,   __UpperCamelCase   ):
											_UpperCAmelCase					=    self.prefix_sum[i - 1] + array[i]



			def  lowercase__						(		self     :    str				,   __UpperCamelCase     :    int				,   __UpperCamelCase     :    int   )->int:
							if start == 0:
											return self.prefix_sum[end]

							return self.prefix_sum[end] - self.prefix_sum[start - 1]



			def  lowercase__						(		self     :    Any				,   __UpperCamelCase     :    int   )->bool:
							_UpperCAmelCase					=    {0}
							for sum_item in self.prefix_sum:
											if sum_item - target_sum in sums:
															return True

											sums.add(__UpperCamelCase   )

							return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()



