
"""simple docstring"""
import math
def 				a__   (   a   :				int		):

  """simple docstring"""







  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5       ,     int(math.sqrt(__A		) + 1		)       ,     6		):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True
def 				a__   (   a   :				float = 0.1		):

  """simple docstring"""







  _snake_case     :						Optional[Any]						=   3
  _snake_case     :						Union[str, Any]						=   3

  while primes / (2 * j - 1) >= ratio:
    for i in range(j * j + j + 1       ,     (j + 2) * (j + 2)       ,     j + 1		):
      primes += is_prime(__A		)
    j += 2
  return j


if __name__ == "__main__":
    import doctest

    doctest.testmod()

"""simple docstring"""
from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray
def 				a__   (   a   :				float       ,     a   :				float       ,     a   :				bool = False		):

  """simple docstring"""







  if radian_mode:
    return [magnitude * cos(a		), magnitude * sin(a		)]
  return [magnitude * cos(radians(a		)		), magnitude * sin(radians(a		)		)]
def 				a__   (   a   :				NDArray[floataa]       ,     a   :				NDArray[floataa]       ,     a   :				float = 10**-1		):

  """simple docstring"""







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


if __name__ == "__main__":
    # Test to check if it works
    _a      :			Tuple					=							array(
        [
            polar_force(718.4, 180 - 30),
            polar_force(879.54, 45),
            polar_force(100, -90),
        ]
    )

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

    assert in_static_equilibrium(forces, location)

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

    _a      :			List[Any]					=							array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    _a      :			List[str]					=							array([[0, -2_000], [0, -1_200], [0, 15_600], [0, -12_400]])

    _a      :			Optional[int]					=							array([[0, 0], [6, 0], [10, 0], [12, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()

