





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






def lowerCamelCase__    (							snake_case_	:  str       ,      snake_case_	:  complex       ,      snake_case_	:  str = "x"       ,      snake_case_	:  float = 10**-10       ,      snake_case_	:  int = 1       ,      )      ->				complex:
   __snake_case							       =   symbols(snake_case_       )
   __snake_case							       =   lambdify(snake_case_       ,      snake_case_       )
   __snake_case							       =   lambdify(snake_case_       ,      diff(snake_case_       ,      snake_case_       )       )

   __snake_case							       =   starting_point

   while True:
      if diff_function(snake_case_       ) != 0:
         __snake_case							       =   prev_guess - multiplicity * func(snake_case_       ) / diff_function(
             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

      __snake_case							       =   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=0.0_05)}',
    )

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









"""simple docstring"""
def 				snake_case      (   A__	,A__						):
			# "extended trapezoidal rule"
			# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
			UpperCAmelCase_     : Dict			     =					(boundary[1] - boundary[0]) / steps
			UpperCAmelCase_     : Optional[int]			     =					boundary[0]
			UpperCAmelCase_     : str			     =					boundary[1]
			UpperCAmelCase_     : Tuple			     =					make_points(A__	,A__	,A__						)
			UpperCAmelCase_     : List[str]			     =					0.0
			y += (h / 2.0) * f(A__						)
			for i in x_i:
						# print(i)
						y += h * f(A__						)
			y += (h / 2.0) * f(A__						)
			return y

def 				snake_case      (   A__	,A__	,A__						):
			UpperCAmelCase_     : Union[str, Any]			     =					a + h
			while x < (b - h):
						yield x
						UpperCAmelCase_     : Optional[Any]			     =					x + h

def 				snake_case      (   A__						):  # enter your function here
			UpperCAmelCase_     : Dict			     =					(x - 0) * (x - 0)
			return y

def 				snake_case      (   ):
			UpperCAmelCase_     : Dict			     =					0.0  # Lower bound of integration
			UpperCAmelCase_     : Optional[int]			     =					1.0  # Upper bound of integration
			UpperCAmelCase_     : Dict			     =					10.0  # define number of steps or resolution
			UpperCAmelCase_     : List[Any]			     =					[a, b]  # define boundary of integration
			UpperCAmelCase_     : Union[str, Any]			     =					method_a(A__	,A__						)
			print(F"""y = {y}"""						)


if __name__ == "__main__":
			main()



