





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

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

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

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

       _UpperCamelCase														=    len(lowerCAmelCase       )

       _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(lowerCAmelCase       )
              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(lowerCAmelCase       ) > 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"""




from typing import TYPE_CHECKING

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


A__   :						Optional[Any] 							=     {"""configuration_vilt""": ["""VILT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """ViltConfig"""]}

try:
    if not is_vision_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A__   :						List[Any] 							=     ["""ViltFeatureExtractor"""]
    A__   :						Any 							=     ["""ViltImageProcessor"""]
    A__   :						int 							=     ["""ViltProcessor"""]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A__   :						str 							=     [
        """VILT_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """ViltForImageAndTextRetrieval""",
        """ViltForImagesAndTextClassification""",
        """ViltForTokenClassification""",
        """ViltForMaskedLM""",
        """ViltForQuestionAnswering""",
        """ViltLayer""",
        """ViltModel""",
        """ViltPreTrainedModel""",
    ]


if TYPE_CHECKING:
    from .configuration_vilt import VILT_PRETRAINED_CONFIG_ARCHIVE_MAP, ViltConfig

    try:
        if not is_vision_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .feature_extraction_vilt import ViltFeatureExtractor
        from .image_processing_vilt import ViltImageProcessor
        from .processing_vilt import ViltProcessor

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_vilt import (
            VILT_PRETRAINED_MODEL_ARCHIVE_LIST,
            ViltForImageAndTextRetrieval,
            ViltForImagesAndTextClassification,
            ViltForMaskedLM,
            ViltForQuestionAnswering,
            ViltForTokenClassification,
            ViltLayer,
            ViltModel,
            ViltPreTrainedModel,
        )


else:
    import sys

    A__   :						Any 							=     _LazyModule(__name__, globals()["""__file__"""], _import_structure)



