






"""simple docstring"""






UpperCAmelCase_     :				List[str]         =				'''
# Transformers installation
! pip install transformers datasets
# To install from source instead of the last release, comment the command above and uncomment the following one.
# ! pip install git+https://github.com/huggingface/transformers.git
'''

UpperCAmelCase_     :				List[str]         =				[{'''type''': '''code''', '''content''': INSTALL_CONTENT}]
UpperCAmelCase_     :				Union[str, Any]         =				{
    '''{processor_class}''': '''FakeProcessorClass''',
    '''{model_class}''': '''FakeModelClass''',
    '''{object_class}''': '''FakeObjectClass''',
}










"""simple docstring"""






from __future__ import annotations

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



def       _A    (__a					,       __a					,       __a = False							)				-> list[float]:
    """simple docstring"""






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



def       _A    (__a					,       __a					,       __a = 10**-1							)				-> bool:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_   :						NDArray[floataa]							=	cross(__a					,       __a							)
    SCREAMING_SNAKE_CASE_   :						float							=	sum(__a							)
    return abs(__a							) < eps


if __name__ == "__main__":
  # Test to check if it works
  UpperCAmelCase_     :				Union[str, Any]         =				array(
      [
          polar_force(7_1_8.4, 180 - 30),
          polar_force(8_7_9.5_4, 45),
          polar_force(100, -90),
      ]
  )

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

  assert in_static_equilibrium(forces, location)

  # Problem 1 in image_data/2D_problems.jpg
  UpperCAmelCase_     :				Union[str, Any]         =				array(
      [
          polar_force(30 * 9.8_1, 15),
          polar_force(215, 180 - 45),
          polar_force(264, 90 - 30),
      ]
  )

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

  assert in_static_equilibrium(forces, location)

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

  UpperCAmelCase_     :				Any         =				array([[0, 0], [6, 0], [10, 0], [12, 0]])

  assert in_static_equilibrium(forces, location)

  import doctest

  doctest.testmod()


