

'''simple docstring'''

from __future__ import annotations

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




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_ = False     ):
 if radian_mode:
  return [magnitude * cos(UpperCAmelCase_     ), magnitude * sin(UpperCAmelCase_     )]
 return [magnitude * cos(radians(UpperCAmelCase_     )     ), magnitude * sin(radians(UpperCAmelCase_     )     )]




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_ = 10**-1     ):
 UpperCAmelCase	:     NDArray[floataa]						 =			cross(UpperCAmelCase_  ,	UpperCAmelCase_     )
 UpperCAmelCase	:     float						 =			sum(UpperCAmelCase_     )
 return abs(UpperCAmelCase_     ) < eps


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

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

 assert in_static_equilibrium(forces, location)

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

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

 assert in_static_equilibrium(forces, location)

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

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

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()







'''simple docstring'''

def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     int						 =			len(UpperCAmelCase_     )
 UpperCAmelCase	:     int						 =			len(UpperCAmelCase_     )
 UpperCAmelCase	:     int						 =			(
     first_str_length if first_str_length > second_str_length else second_str_length
 )
 UpperCAmelCase	:     list						 =			[]
 for char_count in range(UpperCAmelCase_     ):
  if char_count < first_str_length:
   output_list.append(first_str[char_count]     )
  if char_count < second_str_length:
   output_list.append(second_str[char_count]     )
 return "".join(UpperCAmelCase_     )


if __name__ == "__main__":
 print(alternative_string_arrange("AB", "XYZ"), end=" ")




