

def   UpperCamelCase(   lowercase_				)      ->							str:





  '''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."""				)

  snake_case_					= {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."""				)

  snake_case_					= len(lowercase_				)

  snake_case_					= 0
  snake_case_					= []
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    snake_case_					= 0
    snake_case_					= coordinates[count_of_line][0]
    snake_case_					= []
    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

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

  snake_case_					= 0

  while count < x:
    snake_case_					= 0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      snake_case_					= 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

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

  snake_case_					= 0
  snake_case_					= """f(x)="""

  while count < x:
    snake_case_					= solution[count].split("""E"""				)
    if len(lowercase_				) > 1:
      snake_case_					= 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]]))


def   UpperCamelCase(   lowercase_				)      ->							float:





  '''simple docstring'''





  return -num if num < 0 else num



def   UpperCamelCase(   lowercase_				)      ->							int:





  '''simple docstring'''





  if len(lowercase_				) == 0:
    raise ValueError("""abs_min() arg is an empty sequence"""				)
  snake_case_					= x[0]
  for i in x:
    if abs_val(lowercase_				) < abs_val(lowercase_				):
      snake_case_					= i
  return j



def   UpperCamelCase(   lowercase_				)      ->							int:





  '''simple docstring'''





  if len(lowercase_				) == 0:
    raise ValueError("""abs_max() arg is an empty sequence"""				)
  snake_case_					= x[0]
  for i in x:
    if abs(lowercase_				) > abs(lowercase_				):
      snake_case_					= i
  return j



def   UpperCamelCase(   lowercase_				)      ->							int:





  '''simple docstring'''





  if len(lowercase_				) == 0:
    raise ValueError("""abs_max_sort() arg is an empty sequence"""				)
  return sorted(lowercase_     ,   key=lowercase_				)[-1]



def   UpperCamelCase(   )      ->							List[Any]:





  '''simple docstring'''





  assert abs_val(0				) == 0
  assert abs_val(34				) == 34
  assert abs_val(-100000000000				) == 100000000000

  snake_case_					= [-3, -1, 2, -11]
  assert abs_max(lowercase_				) == -11
  assert abs_max_sort(lowercase_				) == -11
  assert abs_min(lowercase_				) == -1


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    test_abs_val()
    print(abs_val(-34))  # --> 34