



"""simple docstring"""






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






def   snake_case__     (	__lowerCamelCase       :					str							,	__lowerCamelCase       :					complex							,	__lowerCamelCase       :					str = "x"							,	__lowerCamelCase       :					float = 10**-10							,	__lowerCamelCase       :					int = 1							,	):
			"""simple docstring"""
			lowerCamelCase__	:	Any				=symbols(__lowerCamelCase			)
			lowerCamelCase__	:	Optional[int]				=lambdify(__lowerCamelCase							,	__lowerCamelCase			)
			lowerCamelCase__	:	List[str]				=lambdify(__lowerCamelCase							,	diff(__lowerCamelCase							,	__lowerCamelCase			)			)

			lowerCamelCase__	:	Optional[Any]				=starting_point

			while True:
						if diff_function(__lowerCamelCase			) != 0:
									lowerCamelCase__	:	Tuple				=prev_guess - multiplicity * func(__lowerCamelCase			) / diff_function(
									    __lowerCamelCase			)
						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__	:	int				=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)}')









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					list[int]			):
			"""simple docstring"""
			if not numbers:
						return 0

			if not isinstance(__lowerCamelCase							,	(list, tuple)			) or not all(
			    isinstance(__lowerCamelCase							,	__lowerCamelCase			) for number in numbers			):
						raise ValueError('''numbers must be an iterable of integers'''			)

			lowerCamelCase__	:	Any				=numbers[0]

			for i in range(1							,	len(__lowerCamelCase			)			):
						# update the maximum and minimum subarray products
						lowerCamelCase__	:	Dict				=numbers[i]
						if number < 0:
									lowerCamelCase__			,     lowerCamelCase__	:	List[Any]				=min_till_now, max_till_now
						lowerCamelCase__	:	Optional[int]				=max(__lowerCamelCase							,	max_till_now * number			)
						lowerCamelCase__	:	Dict				=min(__lowerCamelCase							,	min_till_now * number			)

						# update the maximum product found till now
						lowerCamelCase__	:	Tuple				=max(__lowerCamelCase							,	__lowerCamelCase			)

			return max_prod




