




"""simple docstring"""

from typing import TYPE_CHECKING

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


__lowerCamelCase								=						{"configuration_gptj": ["GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP", "GPTJConfig", "GPTJOnnxConfig"]}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __lowerCamelCase								=						[
          "GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST",
          "GPTJForCausalLM",
          "GPTJForQuestionAnswering",
          "GPTJForSequenceClassification",
          "GPTJModel",
          "GPTJPreTrainedModel",
      ]

try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __lowerCamelCase								=						[
          "TFGPTJForCausalLM",
          "TFGPTJForQuestionAnswering",
          "TFGPTJForSequenceClassification",
          "TFGPTJModel",
          "TFGPTJPreTrainedModel",
      ]

try:
      if not is_flax_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __lowerCamelCase								=						[
          "FlaxGPTJForCausalLM",
          "FlaxGPTJModel",
          "FlaxGPTJPreTrainedModel",
      ]


if TYPE_CHECKING:
      from .configuration_gptj import GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTJConfig, GPTJOnnxConfig

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_gptj import (
                GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST,
                GPTJForCausalLM,
                GPTJForQuestionAnswering,
                GPTJForSequenceClassification,
                GPTJModel,
                GPTJPreTrainedModel,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_gptj import (
                TFGPTJForCausalLM,
                TFGPTJForQuestionAnswering,
                TFGPTJForSequenceClassification,
                TFGPTJModel,
                TFGPTJPreTrainedModel,
            )

      try:
            if not is_flax_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_flax_gptj import FlaxGPTJForCausalLM, FlaxGPTJModel, FlaxGPTJPreTrainedModel

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]]))


