

'''simple docstring'''




from __future__ import annotations

from enum import Enum, unique
from typing import TypeVar

# Create a generic variable that can be 'Enum', or any subclass.
_a				: Optional[Any] 							=						TypeVar('T', bound='Enum')



@unique
class        lowercase_	(		_a ):

  '''simple docstring'''





  __lowerCAmelCase					: Tuple      =   80
  __lowerCAmelCase					: Any      =   70
  __lowerCAmelCase					: Any      =   60
  __lowerCAmelCase					: Tuple      =   50
  __lowerCAmelCase					: Optional[Any]      =   40
  __lowerCAmelCase					: Tuple      =   30
  __lowerCAmelCase					: Dict      =   20
  __lowerCAmelCase					: Optional[Any]      =   10




@unique
class        lowercase_	(		_a ):

  '''simple docstring'''





  __lowerCAmelCase					: List[Any]      =   24
  __lowerCAmelCase					: int      =   21
  __lowerCAmelCase					: Tuple      =   18
  __lowerCAmelCase					: List[str]      =   15
  __lowerCAmelCase					: Any      =   12
  __lowerCAmelCase					: Optional[int]      =   9
  __lowerCAmelCase					: Any      =   6
  __lowerCAmelCase					: Optional[int]      =   3
  __lowerCAmelCase					: Any      =   2
  __lowerCAmelCase					: List[Any]      =   1
  __lowerCAmelCase					: Tuple      =   -1
  __lowerCAmelCase					: Optional[Any]      =   -2
  __lowerCAmelCase					: Dict      =   -3
  __lowerCAmelCase					: Dict      =   -6
  __lowerCAmelCase					: Optional[int]      =   -9
  __lowerCAmelCase					: str      =   -12
  __lowerCAmelCase					: List[Any]      =   -15
  __lowerCAmelCase					: Optional[Any]      =   -18
  __lowerCAmelCase					: List[str]      =   -21
  __lowerCAmelCase					: List[str]      =   -24
  @classmethod
  def 						snake_case_			(     cls     )							->				Optional[int]:


    """simple docstring"""
    return {unit.name: unit.value for unit in cls if unit.value > 0}





  @classmethod
  def 						snake_case_			(     cls     )							->				Any:


    """simple docstring"""
    return {unit.name: unit.value for unit in cls if unit.value < 0}




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   str						):
  UpperCAmelCase													=	SIUnit.get_positive() if value > 0 else SIUnit.get_negative()
  for name_prefix, value_prefix in prefixes.items():
    UpperCAmelCase													=	value / (10**value_prefix)
    if numerical_part > 1:
      return f'''{numerical_part!s} {name_prefix}'''
  return str(SCREAMING_SNAKE_CASE						)


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Tuple						):
  for prefix in BinaryUnit:
    UpperCAmelCase													=	value / (2**prefix.value)
    if numerical_part > 1:
      return f'''{numerical_part!s} {prefix.name}'''
  return str(SCREAMING_SNAKE_CASE						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()





'''simple docstring'''




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   list[list[int]]						):
  if len(SCREAMING_SNAKE_CASE						) == 0 or not all(len(SCREAMING_SNAKE_CASE						) == 2 for pair in coordinates						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

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

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

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

  UpperCAmelCase													=	len(SCREAMING_SNAKE_CASE						)

  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(SCREAMING_SNAKE_CASE						)
    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(SCREAMING_SNAKE_CASE						) > 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]]))


