"""⏎
Checks if a system of forces is in static equilibrium.⏎
⏎
python/black : true⏎
flake8 : passed⏎
mypy : passed⏎
"""⏎
⏎
from numpy import array, cos, sin, radians, cross  # type: ignore⏎
from typing import List⏎
⏎
⏎
def polar_force(⏎
    magnitude: float, angle: float, radian_mode: bool = False⏎
) -> List[float]:⏎
    """⏎
    Resolves force along rectangular components.⏎
    (force, angle) => (force_x, force_y)⏎
    >>> polar_force(10, 45)⏎
    [7.0710678118654755, 7.071067811865475]⏎
    >>> polar_force(10, 3.14, radian_mode=True)⏎
    [-9.999987317275394, 0.01592652916486828]⏎
    """⏎
    if radian_mode:⏎
        return [magnitude * cos(angle), magnitude * sin(angle)]⏎
    return [magnitude * cos(radians(angle)), magnitude * sin(radians(angle))]⏎
⏎
⏎
def in_static_equilibrium(⏎
    forces: array, location: array, eps: float = 10 ** -1⏎
) -> bool:⏎
    """⏎
    Check if a system is in equilibrium.⏎
    It takes two numpy.array objects.⏎
    forces ==>  [⏎
                        [force1_x, force1_y],⏎
                        [force2_x, force2_y],⏎
                        ....]⏎
    location ==>  [⏎
                        [x1, y1],⏎
                        [x2, y2],⏎
                        ....]⏎
    >>> force = array([[1, 1], [-1, 2]])⏎
    >>> location = array([[1, 0], [10, 0]])⏎
    >>> in_static_equilibrium(force, location)⏎
    False⏎
    """⏎
    # summation of moments is zero⏎
    moments: array = cross(location, forces)⏎
    sum_moments: float = sum(moments)⏎
    return abs(sum_moments) < eps⏎
⏎
⏎
if __name__ == "__main__":⏎
    # Test to check if it works⏎
    forces = array(⏎
        [polar_force(718.4, 180 - 30), polar_force(879.54, 45), polar_force(100, -90)]⏎
    )⏎
⏎
    location = array([[0, 0], [0, 0], [0, 0]])⏎
⏎
    assert in_static_equilibrium(forces, location)⏎
⏎
    # Problem 1 in image_data/2D_problems.jpg⏎
    forces = array(⏎
        [⏎
            polar_force(30 * 9.81, 15),⏎
            polar_force(215, 180 - 45),⏎
            polar_force(264, 90 - 30),⏎
        ]⏎
    )⏎
⏎
    location = array([[0, 0], [0, 0], [0, 0]])⏎
⏎
    assert in_static_equilibrium(forces, location)⏎
⏎
    # Problem in image_data/2D_problems_1.jpg⏎
    forces = array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])⏎
⏎
    location = array([[0, 0], [6, 0], [10, 0], [12, 0]])⏎
⏎
    assert in_static_equilibrium(forces, location)⏎
⏎
    import doctest⏎
⏎
    doctest.testmod()⏎