




'''simple docstring'''







def 					lowerCamelCase__							(			__lowercase							):
     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 :			Tuple					   = {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 :			Dict					   = len(__lowercase							)

     snake_case :			int					   = 0
     snake_case :			list[list[float]]					   = []
     # put the x and x to the power values in a matrix
     while count_of_line < x:
          snake_case :			Optional[int]					   = 0
          snake_case :			Any					   = coordinates[count_of_line][0]
          snake_case :			list[float]					   = []
          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 :			Tuple					   = 0
     # put the y values into a vector
     snake_case :			list[float]					   = []
     while count_of_line < x:
          vector.append(coordinates[count_of_line][1]							)
          count_of_line += 1

     snake_case :			Tuple					   = 0

     while count < x:
          snake_case :			Union[str, Any]					   = 0
          while zahlen < x:
               if count == zahlen:
                    zahlen += 1
               if zahlen == x:
                    break
               snake_case :			Optional[int]					   = 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 :			str					   = 0
     # make solutions
     snake_case :			list[str]					   = []
     while count < x:
          solution.append(str(vector[count] / matrix[count][count]							)							)
          count += 1

     snake_case :			Optional[Any]					   = 0
     snake_case :			Union[str, Any]					   = """f(x)="""

     while count < x:
          snake_case :			list[str]					   = solution[count].split("""E"""							)
          if len(__lowercase							) > 1:
               snake_case :			List[str]					   = 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'''







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


lowercase			:      Tuple			=					{"""configuration_bert_generation""": ["""BertGenerationConfig"""]}

try:
      if not is_sentencepiece_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase			:      Tuple			=					["""BertGenerationTokenizer"""]

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase			:      List[Any]			=					[
          """BertGenerationDecoder""",
          """BertGenerationEncoder""",
          """BertGenerationPreTrainedModel""",
          """load_tf_weights_in_bert_generation""",
      ]


if TYPE_CHECKING:
      from .configuration_bert_generation import BertGenerationConfig

      try:
            if not is_sentencepiece_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_bert_generation import BertGenerationTokenizer

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_bert_generation import (
                BertGenerationDecoder,
                BertGenerationEncoder,
                BertGenerationPreTrainedModel,
                load_tf_weights_in_bert_generation,
            )

else:
      import sys

      lowercase			:      Optional[Any]			=					_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



