


def 							UpperCamelCase_  (				__snake_case			:						Optional[Any]     )->      Optional[Any]:




      '''simple docstring'''
      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.'     )

      __magic_name__ 		=			{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.'     )

      __magic_name__ 		=			len(lowerCAmelCase__     )

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

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

      __magic_name__ 		=			0

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

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

      __magic_name__ 		=			0
      __magic_name__ 		=			'f(x)='

      while count < x:
            __magic_name__ 		=			solution[count].split('E'     )
            if len(lowerCAmelCase__     ) > 1:
                  __magic_name__ 		=			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]]))





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase :				str						    =       {
    '''configuration_bart''': ['''BART_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''BartConfig''', '''BartOnnxConfig'''],
    '''tokenization_bart''': ['''BartTokenizer'''],
}

try:
					if not is_tokenizers_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase :				Optional[int]						    =       ['''BartTokenizerFast''']

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase :				Any						    =       [
					    '''BART_PRETRAINED_MODEL_ARCHIVE_LIST''',
					    '''BartForCausalLM''',
					    '''BartForConditionalGeneration''',
					    '''BartForQuestionAnswering''',
					    '''BartForSequenceClassification''',
					    '''BartModel''',
					    '''BartPretrainedModel''',
					    '''PretrainedBartModel''',
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase :				Tuple						    =       [
					    '''TFBartForConditionalGeneration''',
					    '''TFBartForSequenceClassification''',
					    '''TFBartModel''',
					    '''TFBartPretrainedModel''',
					]

try:
					if not is_flax_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase :				List[Any]						    =       [
					    '''FlaxBartDecoderPreTrainedModel''',
					    '''FlaxBartForCausalLM''',
					    '''FlaxBartForConditionalGeneration''',
					    '''FlaxBartForQuestionAnswering''',
					    '''FlaxBartForSequenceClassification''',
					    '''FlaxBartModel''',
					    '''FlaxBartPreTrainedModel''',
					]

if TYPE_CHECKING:
					from .configuration_bart import BART_PRETRAINED_CONFIG_ARCHIVE_MAP, BartConfig, BartOnnxConfig
					from .tokenization_bart import BartTokenizer

					try:
										if not is_tokenizers_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_bart_fast import BartTokenizerFast

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_bart import (
										    BART_PRETRAINED_MODEL_ARCHIVE_LIST,
										    BartForCausalLM,
										    BartForConditionalGeneration,
										    BartForQuestionAnswering,
										    BartForSequenceClassification,
										    BartModel,
										    BartPretrainedModel,
										    PretrainedBartModel,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_bart import (
										    TFBartForConditionalGeneration,
										    TFBartForSequenceClassification,
										    TFBartModel,
										    TFBartPretrainedModel,
										)

					try:
										if not is_flax_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_flax_bart import (
										    FlaxBartDecoderPreTrainedModel,
										    FlaxBartForCausalLM,
										    FlaxBartForConditionalGeneration,
										    FlaxBartForQuestionAnswering,
										    FlaxBartForSequenceClassification,
										    FlaxBartModel,
										    FlaxBartPreTrainedModel,
										)

else:
					import sys

					UpperCamelCase :				Optional[int]						    =       _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

