"""simple docstring"""





from __future__ import annotations

from collections.abc import Callable

_UpperCamelCase     :		Union[str, Any]											=					list[list[float | int]]





def        a_  (   _lowerCAmelCase						:				Matrix     ,				_lowerCAmelCase						:				Matrix  ):





       '''simple docstring'''

       lowercase__    :	int     					=			len(a_  )
       lowercase__    :	Matrix     					=			[[0 for _ in range(size + 1  )] for _ in range(a_  )]
       lowercase__    :	int
       lowercase__    :	int
       lowercase__    :	int
       lowercase__    :	int
       lowercase__    :	int
       lowercase__    :	float

       for row in range(a_  ):
              for col in range(a_  ):
                     lowercase__    :	Any     					=			matrix[row][col]

              lowercase__    :	Optional[Any]     					=			vector[row][0]

       lowercase__    :	int     					=			0
       lowercase__    :	int     					=			0
       while row < size and col < size:
              # pivoting
              lowercase__    :	int     					=			max((abs(augmented[rowa][col]  ), rowa) for rowa in range(a_     ,				a_  )  )[
                  1
              ]
              if augmented[pivot_row][col] == 0:
                     col += 1
                     continue
              else:
                     lowercase__    :	str     					=			augmented[pivot_row], augmented[row]

              for rowa in range(row + 1     ,				a_  ):
                     lowercase__    :	Tuple     					=			augmented[rowa][col] / augmented[row][col]
                     lowercase__    :	Union[str, Any]     					=			0
                     for cola in range(col + 1     ,				size + 1  ):
                            augmented[rowa][cola] -= augmented[row][cola] * ratio

              row += 1
              col += 1

       # back substitution
       for col in range(1     ,				a_  ):
              for row in range(a_  ):
                     lowercase__    :	List[Any]     					=			augmented[row][col] / augmented[col][col]
                     for cola in range(a_     ,				size + 1  ):
                            augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
       return [
           [round(augmented[row][size] / augmented[row][row]     ,				10  )] for row in range(a_  )
       ]





def        a_  (   _lowerCAmelCase						:				list[int]  ):





       '''simple docstring'''

       lowercase__    :	int     					=			len(a_  )
       lowercase__    :	Matrix     					=			[[0 for _ in range(a_  )] for _ in range(a_  )]
       lowercase__    :	Matrix     					=			[[0] for _ in range(a_  )]
       lowercase__    :	Matrix
       lowercase__    :	int
       lowercase__    :	int
       lowercase__    :	int

       for x_val, y_val in enumerate(a_  ):
              for col in range(a_  ):
                     lowercase__    :	str     					=			(x_val + 1) ** (size - col - 1)
              lowercase__    :	Dict     					=			y_val

       lowercase__    :	Union[str, Any]     					=			solve(a_     ,				a_  )

       def interpolated_func(_lowerCAmelCase						:				int  ) -> int:
              return sum(
                  round(coeffs[x_val][0]  ) * (var ** (size - x_val - 1))
                  for x_val in range(a_  )  )

       return interpolated_func





def        a_  (   _lowerCAmelCase						:				int  ):





       '''simple docstring'''

       return (
           1
           - variable
           + variable**2
           - variable**3
           + variable**4
           - variable**5
           + variable**6
           - variable**7
           + variable**8
           - variable**9
           + variable**10
       )





def        a_  (   _lowerCAmelCase						:				Callable[[int], int] = question_function     ,				_lowerCAmelCase						:				int = 10  ):





       '''simple docstring'''

       lowercase__    :	list[int]     					=			[func(a_  ) for x_val in range(1     ,				order + 1  )]

       lowercase__    :	list[Callable[[int], int]]     					=			[
           interpolate(data_points[:max_coeff]  ) for max_coeff in range(1     ,				order + 1  )
       ]

       lowercase__    :	int     					=			0
       lowercase__    :	Callable[[int], int]
       lowercase__    :	int

       for poly in polynomials:
              lowercase__    :	Tuple     					=			1
              while func(a_  ) == poly(a_  ):
                     x_val += 1

              ret += poly(a_  )

       return ret


if __name__ == "__main__":
       print(f'''{solution() = }''')


"""simple docstring"""





from __future__ import annotations





def        a_  (   _lowerCAmelCase						:				float     ,				_lowerCAmelCase						:				float     ,				_lowerCAmelCase						:				float     ,				):





       '''simple docstring'''

       if (stress, tangential_force, area).count(0  ) != 1:
              raise ValueError('You cannot supply more or less than 2 values'  )
       elif stress < 0:
              raise ValueError('Stress cannot be negative'  )
       elif tangential_force < 0:
              raise ValueError('Tangential Force cannot be negative'  )
       elif area < 0:
              raise ValueError('Area cannot be negative'  )
       elif stress == 0:
              return (
                  "stress",
                  tangential_force / area,
              )
       elif tangential_force == 0:
              return (
                  "tangential_force",
                  stress * area,
              )
       else:
              return (
                  "area",
                  tangential_force / stress,
              )


if __name__ == "__main__":
       import doctest

       doctest.testmod()

