


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray

def 			lowerCAmelCase__					(     a__:						Dict     ,    a__:						Optional[Any]     ,    a__:						List[str] = False			)    ->						Any:


							'''simple docstring'''





							if radian_mode:
														return [magnitude * cos(a__			), magnitude * sin(a__			)]
							return [magnitude * cos(radians(a__			)			), magnitude * sin(radians(a__			)			)]

def 			lowerCAmelCase__					(     a__:						List[str]     ,    a__:						Tuple     ,    a__:						Tuple = 1_0**-1			)    ->						Union[str, Any]:


							'''simple docstring'''





							_UpperCAmelCase											=     cross(a__     ,    a__			)
							_UpperCAmelCase											=     sum(a__			)
							return abs(a__			) < eps


if __name__ == "__main__":
		# Test to check if it works
		lowerCAmelCase__    :List[Any]       =				array(
		    [
		        polar_force(718.4, 1_8_0 - 3_0),
		        polar_force(879.54, 4_5),
		        polar_force(1_0_0, -9_0),
		    ]
		)

		lowerCAmelCase__    :NDArray[floataa]       =				array([[0, 0], [0, 0], [0, 0]])

		assert in_static_equilibrium(forces, location)

		# Problem 1 in image_data/2D_problems.jpg
		lowerCAmelCase__    :Dict       =				array(
		    [
		        polar_force(3_0 * 9.81, 1_5),
		        polar_force(2_1_5, 1_8_0 - 4_5),
		        polar_force(2_6_4, 9_0 - 3_0),
		    ]
		)

		lowerCAmelCase__    :Optional[int]       =				array([[0, 0], [0, 0], [0, 0]])

		assert in_static_equilibrium(forces, location)

		# Problem in image_data/2D_problems_1.jpg
		lowerCAmelCase__    :int       =				array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

		lowerCAmelCase__    :str       =				array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

		assert in_static_equilibrium(forces, location)

		import doctest

		doctest.testmod()







'''simple docstring'''






def   UpperCamelCase__ (						lowerCAmelCase    ):





      """simple docstring"""


      if not isinstance(lowerCAmelCase				,      lowerCAmelCase    ):
            raise ValueError("""Input must be an integer"""    )
      if input_num <= 0:
            raise ValueError("""Input must be positive"""    )
      return sum(
          divisor for divisor in range(1				,      input_num // 2 + 1    ) if input_num % divisor == 0    )


if __name__ == "__main__":
      import doctest

      doctest.testmod()






