






'''simple docstring'''





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




def      __A					(     _lowercase					,			_lowercase					,			_lowercase = "x"					,			_lowercase = 10**-10					,			_lowercase = 1					,			):

					'''simple docstring'''







					_A								= symbols(_UpperCamelCase )
					_A								= lambdify(_UpperCamelCase					,			_UpperCamelCase )
					_A								= lambdify(_UpperCamelCase					,			diff(_UpperCamelCase					,			_UpperCamelCase ) )

					_A								= starting_point

					while True:
										if diff_function(_UpperCamelCase ) != 0:
															_A								= 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

										_A								= 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)}')











import math




def      __A					(     _lowercase ):

					'''simple docstring'''







					_A								= []
					_A								= 2
					_A								= int(math.sqrt(_lowercase ) )  # Size of every segment
					_A								= [True] * (end + 1)
					_A								= []

					while start <= end:
										if temp[start] is True:
															in_prime.append(_lowercase )
															for i in range(start * start					,			end + 1					,			_lowercase ):
																				_A								= False
										start += 1
					prime += in_prime

					_A								= end + 1
					_A								= min(2 * end					,			_lowercase )

					while low <= n:
										_A								= [True] * (high - low + 1)
										for each in in_prime:
															_A								= math.floor(low / each ) * each
															if t < low:
																				t += each

															for j in range(_lowercase					,			high + 1					,			_lowercase ):
																				_A								= False

										for j in range(len(_lowercase ) ):
															if temp[j] is True:
																				prime.append(j + low )

										_A								= high + 1
										_A								= min(high + end					,			_lowercase )

					return prime


print(sieve(10**6))



