






"""simple docstring"""


def 			snake_case  (A_      :list[list[int]]      ):







  '''simple docstring'''

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

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

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

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

  a     :			List[Any]				=   len(A_      )

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

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

  a     :			List[str]				=   0

  while count < x:
    a     :			Tuple				=   0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      a     :			Dict				=   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

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

  a     :			Any				=   0
  a     :			Any				=   'f(x)='

  while count < x:
    a     :			list[str]				=   solution[count].split('E'      )
    if len(A_      ) > 1:
      a     :			str				=   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_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


_UpperCamelCase				:    List[Any]     =						{
    'configuration_openai': ['OPENAI_GPT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'OpenAIGPTConfig'],
    'tokenization_openai': ['OpenAIGPTTokenizer'],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _UpperCamelCase				:    Any     =						['OpenAIGPTTokenizerFast']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _UpperCamelCase				:    int     =						[
       'OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'OpenAIGPTDoubleHeadsModel',
       'OpenAIGPTForSequenceClassification',
       'OpenAIGPTLMHeadModel',
       'OpenAIGPTModel',
       'OpenAIGPTPreTrainedModel',
       'load_tf_weights_in_openai_gpt',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _UpperCamelCase				:    List[str]     =						[
       'TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFOpenAIGPTDoubleHeadsModel',
       'TFOpenAIGPTForSequenceClassification',
       'TFOpenAIGPTLMHeadModel',
       'TFOpenAIGPTMainLayer',
       'TFOpenAIGPTModel',
       'TFOpenAIGPTPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_openai import OPENAI_GPT_PRETRAINED_CONFIG_ARCHIVE_MAP, OpenAIGPTConfig
   from .tokenization_openai import OpenAIGPTTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_openai_fast import OpenAIGPTTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_openai import (
          OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          OpenAIGPTDoubleHeadsModel,
          OpenAIGPTForSequenceClassification,
          OpenAIGPTLMHeadModel,
          OpenAIGPTModel,
          OpenAIGPTPreTrainedModel,
          load_tf_weights_in_openai_gpt,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_openai import (
          TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFOpenAIGPTDoubleHeadsModel,
          TFOpenAIGPTForSequenceClassification,
          TFOpenAIGPTLMHeadModel,
          TFOpenAIGPTMainLayer,
          TFOpenAIGPTModel,
          TFOpenAIGPTPreTrainedModel,
      )

else:
   import sys

   _UpperCamelCase				:    Union[str, Any]     =						_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




