




"""simple docstring"""







def     __snake_case   (							_lowercase						):


    """simple docstring"""







    if len(_lowercase						) == 0 or not all(len(_lowercase						) == 2 for pair in coordinates						):
        raise ValueError('''The program cannot work out a fitting polynomial.'''						)

    if len({tuple(_lowercase						) for pair in coordinates}						) != len(_lowercase						):
        raise ValueError('''The program cannot work out a fitting polynomial.'''						)

    UpperCamelCase										=  {x for x, _ in coordinates}
    if len(_lowercase						) == 1:
        return f'x={coordinates[0][0]}'

    if len(_lowercase						) != len(_lowercase						):
        raise ValueError('''The program cannot work out a fitting polynomial.'''						)

    UpperCamelCase										=  len(_lowercase						)

    UpperCamelCase										=  0
    UpperCamelCase										=  []
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        UpperCamelCase										=  0
        UpperCamelCase										=  coordinates[count_of_line][0]
        UpperCamelCase										=  []
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))						)
            count_in_line += 1
        matrix.append(_lowercase						)
        count_of_line += 1

    UpperCamelCase										=  0
    # put the y values into a vector
    UpperCamelCase										=  []
    while count_of_line < x:
        vector.append(coordinates[count_of_line][1]						)
        count_of_line += 1

    UpperCamelCase										=  0

    while count < x:
        UpperCamelCase										=  0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            UpperCamelCase										=  matrix[zahlen][count] / matrix[count][count]
            for counting_columns, item in enumerate(matrix[count]						):
                # manipulating all the values in the matrix
                matrix[zahlen][counting_columns] -= item * bruch
            # manipulating the values in the vector
            vector[zahlen] -= vector[count] * bruch
            zahlen += 1
        count += 1

    UpperCamelCase										=  0
    # make solutions
    UpperCamelCase										=  []
    while count < x:
        solution.append(str(vector[count] / matrix[count][count]						)						)
        count += 1

    UpperCamelCase										=  0
    UpperCamelCase										=  '''f(x)='''

    while count < x:
        UpperCamelCase										=  solution[count].split('''E'''						)
        if len(_lowercase						) > 1:
            UpperCamelCase										=  f'{remove_e[0]}*10^{remove_e[1]}'
        solved += f'x^{x - (count + 1)}*{solution[count]}'
        if count + 1 != x:
            solved += "+"
        count += 1

    return solved


if __name__ == "__main__":
  print(points_to_polynomial([]))
  print(points_to_polynomial([[]]))
  print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
  print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
  print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
  print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
  print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
  print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
  print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
  print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





"""simple docstring"""







import torch

from transformers import PreTrainedModel

from .custom_configuration import CustomConfig, NoSuperInitConfig

class 							snake_case_ (				lowerCamelCase_ ):







   """simple docstring"""




   A_										=					CustomConfig







   def __init__(		self					,				lowerCamelCase_)							->      List[Any]:
       super().__init__(lowerCamelCase_)
       UpperCamelCase										=  torch.nn.Linear(config.hidden_size					,				config.hidden_size)







   def      UpperCAmelCase__ (		self					,				lowerCamelCase_)							->      Optional[Any]:
       return self.linear(lowerCamelCase_)







   def      UpperCAmelCase__ (		self					,				lowerCamelCase_)							->      List[str]:
       pass

class 							snake_case_ (				lowerCamelCase_ ):







   """simple docstring"""




   A_										=					NoSuperInitConfig







   def __init__(		self					,				lowerCamelCase_)							->      Optional[int]:
       super().__init__(lowerCamelCase_)
       UpperCamelCase										=  torch.nn.Linear(config.attribute					,				config.attribute)







   def      UpperCAmelCase__ (		self					,				lowerCamelCase_)							->      int:
       return self.linear(lowerCamelCase_)







   def      UpperCAmelCase__ (		self					,				lowerCamelCase_)							->      Any:
       pass