


"""simple docstring"""



from __future__ import annotations

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







def   __lowerCAmelCase						(						lowercase  :  str						,							lowercase  :  List[Any]						,							lowercase  :  Tuple = False			)     ->						list[float]:


				"""simple docstring"""





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







def   __lowerCAmelCase						(						lowercase  :  str						,							lowercase  :  int						,							lowercase  :  str = 10**-1			)     ->						bool:


				"""simple docstring"""





				snake_case   :				Optional[Any]				 =   cross(lowercase						,							lowercase			)
				snake_case   :				Dict				 =   sum(lowercase			)
				return abs(lowercase			) < eps


if __name__ == "__main__":
		# Test to check if it works
		__snake_case             =   array(
		    [
		        polar_force(7_18.4, 180 - 30),
		        polar_force(8_79.54, 45),
		        polar_force(100, -90),
		    ]
		)

		__snake_case             =   array([[0, 0], [0, 0], [0, 0]])

		assert in_static_equilibrium(forces, location)

		# Problem 1 in image_data/2D_problems.jpg
		__snake_case             =   array(
		    [
		        polar_force(30 * 9.81, 15),
		        polar_force(215, 180 - 45),
		        polar_force(264, 90 - 30),
		    ]
		)

		__snake_case             =   array([[0, 0], [0, 0], [0, 0]])

		assert in_static_equilibrium(forces, location)

		# Problem in image_data/2D_problems_1.jpg
		__snake_case             =   array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

		__snake_case             =   array([[0, 0], [6, 0], [10, 0], [12, 0]])

		assert in_static_equilibrium(forces, location)

		import doctest

		doctest.testmod()









"""simple docstring"""



def   __lowerCAmelCase						(						lowercase  :  int			)     ->						int:


    """simple docstring"""





    if not isinstance(lowercase						,							lowercase			):
        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()





