

'''simple docstring'''



def    a__       (  a__      ,    a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      len(__snake_case						)
     __SCREAMING_SNAKE_CASE     =      [[0] * n for i in range(__snake_case						)]
     for i in range(__snake_case						):
          __SCREAMING_SNAKE_CASE     =      y_points[i]

     for i in range(2      ,    __snake_case						):
          for j in range(__snake_case      ,    __snake_case						):
               __SCREAMING_SNAKE_CASE     =      (
                   (xa - x_points[j - i + 1]) * q[j][i - 1]
                   - (xa - x_points[j]) * q[j - 1][i - 1]
               ) / (x_points[j] - x_points[j - i + 1])

     return [q[n - 1][n - 1], q]


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        _lowerCAmelCase			(  __snake_case  : float ,							__snake_case  : float ,							__snake_case  : bool = False			)     ->     list[float]:
     if radian_mode:
          return [magnitude * cos(__snake_case			), magnitude * sin(__snake_case			)]
     return [magnitude * cos(radians(__snake_case			)			), magnitude * sin(radians(__snake_case			)			)]






def        _lowerCAmelCase			(  __snake_case  : NDArray[floataa] ,							__snake_case  : NDArray[floataa] ,							__snake_case  : float = 10**-1			)     ->     bool:
     __A						: NDArray[floataa]      =       cross(__snake_case ,							__snake_case			)
     __A						: float      =       sum(__snake_case			)
     return abs(__snake_case			) < eps


if __name__ == "__main__":
  # Test to check if it works
  lowercase__    :      List[Any]						=    array(
      [
          polar_force(718.4, 1_80 - 30),
          polar_force(879.54, 45),
          polar_force(1_00, -90),
      ]
  )

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

  assert in_static_equilibrium(forces, location)

  # Problem 1 in image_data/2D_problems.jpg
  lowercase__    :      Dict						=    array(
      [
          polar_force(30 * 9.81, 15),
          polar_force(2_15, 1_80 - 45),
          polar_force(2_64, 90 - 30),
      ]
  )

  lowercase__    :      Any						=    array([[0, 0], [0, 0], [0, 0]])

  assert in_static_equilibrium(forces, location)

  # Problem in image_data/2D_problems_1.jpg
  lowercase__    :      Optional[int]						=    array([[0, -20_00], [0, -12_00], [0, 1_56_00], [0, -1_24_00]])

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

  assert in_static_equilibrium(forces, location)

  import doctest

  doctest.testmod()