code: 
  '''simple docstring'''
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       Tuple		)    ->						str:
  		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."""		)
  
  		_lowerCAmelCase       :  List[str]   				=					{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."""		)
  
  		_lowerCAmelCase       :  str   				=					len(_UpperCAmelCase		)
  
  		_lowerCAmelCase       :  str   				=					0
  		_lowerCAmelCase       :  List[Any]   				=					[]
  		# put the x and x to the power values in a matrix
  		while count_of_line < x:
  				_lowerCAmelCase       :  int   				=					0
  				_lowerCAmelCase       :  Optional[Any]   				=					coordinates[count_of_line][0]
  				_lowerCAmelCase       :  Any   				=					[]
  				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
  
  		_lowerCAmelCase       :  Optional[int]   				=					0
  		# put the y values into a vector
  		_lowerCAmelCase       :  List[str]   				=					[]
  		while count_of_line < x:
  				vector.append(coordinates[count_of_line][1]		)
  				count_of_line += 1
  
  		_lowerCAmelCase       :  List[str]   				=					0
  
  		while count < x:
  				_lowerCAmelCase       :  int   				=					0
  				while zahlen < x:
  						if count == zahlen:
  								zahlen += 1
  						if zahlen == x:
  								break
  						_lowerCAmelCase       :  int   				=					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
  
  		_lowerCAmelCase       :  Optional[Any]   				=					0
  		# make solutions
  		_lowerCAmelCase       :  Optional[int]   				=					[]
  		while count < x:
  				solution.append(str(vector[count] / matrix[count][count]		)		)
  				count += 1
  
  		_lowerCAmelCase       :  Tuple   				=					0
  		_lowerCAmelCase       :  Optional[int]   				=					"""f(x)="""
  
  		while count < x:
  				_lowerCAmelCase       :  str   				=					solution[count].split("""E"""		)
  				if len(_UpperCAmelCase		) > 1:
  						_lowerCAmelCase       :  Dict   				=					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]]))
  
  
  
style_context: 
  '''simple docstring'''
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available
  
  
  UpperCamelCase_     			=       {
      """configuration_deformable_detr""": ["""DEFORMABLE_DETR_PRETRAINED_CONFIG_ARCHIVE_MAP""", """DeformableDetrConfig"""],
  }
  
  try:
       if not is_vision_available():
            raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
       pass
  else:
       UpperCamelCase_     			=       ["""DeformableDetrFeatureExtractor"""]
       UpperCamelCase_     			=       ["""DeformableDetrImageProcessor"""]
  
  try:
       if not is_torch_available():
            raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
       pass
  else:
       UpperCamelCase_     			=       [
           """DEFORMABLE_DETR_PRETRAINED_MODEL_ARCHIVE_LIST""",
           """DeformableDetrForObjectDetection""",
           """DeformableDetrModel""",
           """DeformableDetrPreTrainedModel""",
       ]
  
  
  if TYPE_CHECKING:
       from .configuration_deformable_detr import DEFORMABLE_DETR_PRETRAINED_CONFIG_ARCHIVE_MAP, DeformableDetrConfig
  
       try:
            if not is_vision_available():
                 raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
            pass
       else:
            from .feature_extraction_deformable_detr import DeformableDetrFeatureExtractor
            from .image_processing_deformable_detr import DeformableDetrImageProcessor
  
       try:
            if not is_torch_available():
                 raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
            pass
       else:
            from .modeling_deformable_detr import (
                DEFORMABLE_DETR_PRETRAINED_MODEL_ARCHIVE_LIST,
                DeformableDetrForObjectDetection,
                DeformableDetrModel,
                DeformableDetrPreTrainedModel,
            )
  
  else:
       import sys
  
       UpperCamelCase_     			=       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
  
  
  