


'''simple docstring'''






def 						_A					(lowerCAmelCase__	:Tuple		) ->	Optional[int]:




     '''simple docstring'''



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

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

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

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

     _a         =				len(UpperCamelCase__		)

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

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

     _a         =				0

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

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

     _a         =				0
     _a         =				'f(x)='

     while count < x:
          _a         =				solution[count].split('E'		)
          if len(UpperCamelCase__		) > 1:
               _a         =				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, 1_1]]))
 print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
 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_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCamelCase				:     Dict								=  {
    """configuration_camembert""": ["""CAMEMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """CamembertConfig""", """CamembertOnnxConfig"""],
}

try:
    if not is_sentencepiece_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCamelCase				:     Optional[Any]								=  ["""CamembertTokenizer"""]

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCamelCase				:     Optional[Any]								=  ["""CamembertTokenizerFast"""]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCamelCase				:     int								=  [
        """CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """CamembertForCausalLM""",
        """CamembertForMaskedLM""",
        """CamembertForMultipleChoice""",
        """CamembertForQuestionAnswering""",
        """CamembertForSequenceClassification""",
        """CamembertForTokenClassification""",
        """CamembertModel""",
        """CamembertPreTrainedModel""",
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCamelCase				:     str								=  [
        """TF_CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """TFCamembertForCausalLM""",
        """TFCamembertForMaskedLM""",
        """TFCamembertForMultipleChoice""",
        """TFCamembertForQuestionAnswering""",
        """TFCamembertForSequenceClassification""",
        """TFCamembertForTokenClassification""",
        """TFCamembertModel""",
        """TFCamembertPreTrainedModel""",
    ]


if TYPE_CHECKING:
    from .configuration_camembert import CAMEMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, CamembertConfig, CamembertOnnxConfig

    try:
        if not is_sentencepiece_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_camembert import CamembertTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_camembert_fast import CamembertTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_camembert import (
            CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
            CamembertForCausalLM,
            CamembertForMaskedLM,
            CamembertForMultipleChoice,
            CamembertForQuestionAnswering,
            CamembertForSequenceClassification,
            CamembertForTokenClassification,
            CamembertModel,
            CamembertPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_camembert import (
            TF_CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFCamembertForCausalLM,
            TFCamembertForMaskedLM,
            TFCamembertForMultipleChoice,
            TFCamembertForQuestionAnswering,
            TFCamembertForSequenceClassification,
            TFCamembertForTokenClassification,
            TFCamembertModel,
            TFCamembertPreTrainedModel,
        )

else:
    import sys

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