




"""simple docstring"""

from typing import TYPE_CHECKING

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


__lowerCamelCase								=						{
    "configuration_bart": ["BART_PRETRAINED_CONFIG_ARCHIVE_MAP", "BartConfig", "BartOnnxConfig"],
    "tokenization_bart": ["BartTokenizer"],
}

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCamelCase								=						["BartTokenizerFast"]

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

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

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCamelCase								=						[
						    "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

						__lowerCamelCase								=						_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)








"""simple docstring"""

def 				a (						__snake_case     :				list[list[int]]  ):



				'''simple docstring'''





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

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

				UpperCAmelCase_					:Optional[Any]      			=      {x for x, _ in coordinates}
				if len(__snake_case  ) == 1:
								return f'x={coordinates[0][0]}'

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

				UpperCAmelCase_					:List[Any]      			=      len(__snake_case  )

				UpperCAmelCase_					:str      			=      0
				UpperCAmelCase_					:list[list[float]]      			=      []
				# put the x and x to the power values in a matrix
				while count_of_line < x:
								UpperCAmelCase_					:str      			=      0
								UpperCAmelCase_					:Optional[int]      			=      coordinates[count_of_line][0]
								UpperCAmelCase_					:list[float]      			=      []
								while count_in_line < x:
												count_line.append(a ** (x - (count_in_line + 1))  )
												count_in_line += 1
								matrix.append(__snake_case  )
								count_of_line += 1

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

				UpperCAmelCase_					:Dict      			=      0

				while count < x:
								UpperCAmelCase_					:Any      			=      0
								while zahlen < x:
												if count == zahlen:
																zahlen += 1
												if zahlen == x:
																break
												UpperCAmelCase_					:str      			=      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_					:Tuple      			=      0
				# make solutions
				UpperCAmelCase_					:list[str]      			=      []
				while count < x:
								solution.append(str(vector[count] / matrix[count][count]  )  )
								count += 1

				UpperCAmelCase_					:Optional[int]      			=      0
				UpperCAmelCase_					:Optional[Any]      			=      '''f(x)='''

				while count < x:
								UpperCAmelCase_					:list[str]      			=      solution[count].split('''E'''  )
								if len(__snake_case  ) > 1:
												UpperCAmelCase_					:List[Any]      			=      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]]))


