




"""simple docstring"""


from __future__ import annotations

import numpy as np


def 					UpperCAmelCase__       (snake_case__							:					np.ndarray    ):
  """simple docstring"""

  _snake_case		,					_snake_case							:		str								=  np.shape(snake_case__    )
  if rows != columns:
    _snake_case							:		Any								=  (
        """'table' has to be of square shaped array but got a """
        F"{rows}x{columns} array:\n{table}"
    )
    raise ValueError(snake_case__    )

  _snake_case							:		List[Any]								=  np.zeros((rows, columns)    )
  _snake_case							:		List[Any]								=  np.zeros((rows, columns)    )
  for i in range(snake_case__    ):
    for j in range(snake_case__    ):
      _snake_case							:		Optional[Any]								=  sum(lower[i][k] * upper[k][j] for k in range(snake_case__    )    )
      if upper[j][j] == 0:
        raise ArithmeticError("""No LU decomposition exists"""    )
      _snake_case							:		Any								=  (table[i][j] - total) / upper[j][j]
    _snake_case							:		Union[str, Any]								=  1
    for j in range(snake_case__		,   snake_case__    ):
      _snake_case							:		Optional[Any]								=  sum(lower[i][k] * upper[k][j] for k in range(snake_case__    )    )
      _snake_case							:		Tuple								=  table[i][j] - total
  return lower, upper


if __name__ == "__main__":
     import doctest

     doctest.testmod()






"""simple docstring"""
from math import factorial, radians






def 		lowercase							(     _snake_case						:      float     ,   _snake_case						:      int = 18     ,   _snake_case						:      int = 10     )     ->float:
	"""simple docstring"""





	__snake_case	:						Any						=				angle_in_degrees - ((angle_in_degrees // 360.0) * 360.0)

	# Converting from degrees to radians
	__snake_case	:						int						=				radians(_snake_case     )

	__snake_case	:						str						=				angle_in_radians
	__snake_case	:						Optional[int]						=				3
	__snake_case	:						List[Any]						=				-1

	for _ in range(_snake_case     ):
		result += (b * (angle_in_radians**a)) / factorial(_snake_case     )

		__snake_case	:						int						=				-b  # One positive term and the next will be negative and so on...
		a += 2  # Increased by 2 for every term.

	return round(_snake_case     ,   _snake_case     )


if __name__ == "__main__":
			__import__("""doctest""").testmod()





