
def 		lowercase_     (  A__						)				->				Optional[Any]:
    """simple docstring"""

    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."						)

    snake_case						=   {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."						)

    snake_case						=   len(UpperCAmelCase_						)

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

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

    snake_case						=   0

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

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

    snake_case						=   0
    snake_case						=   "f(x)="

    while count < x:
        snake_case						=   solution[count].split("E"						)
        if len(UpperCAmelCase_						) > 1:
            snake_case						=   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_flax_available,
    is_tf_available,
    is_torch_available,
)


SCREAMING_SNAKE_CASE_       :						Union[str, Any]					=    {'configuration_gptj': ['GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP', 'GPTJConfig', 'GPTJOnnxConfig']}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 SCREAMING_SNAKE_CASE_       :						Optional[int]					=    [
     'GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST',
     'GPTJForCausalLM',
     'GPTJForQuestionAnswering',
     'GPTJForSequenceClassification',
     'GPTJModel',
     'GPTJPreTrainedModel',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 SCREAMING_SNAKE_CASE_       :						List[str]					=    [
     'TFGPTJForCausalLM',
     'TFGPTJForQuestionAnswering',
     'TFGPTJForSequenceClassification',
     'TFGPTJModel',
     'TFGPTJPreTrainedModel',
 ]

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 SCREAMING_SNAKE_CASE_       :						Tuple					=    [
     '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

 SCREAMING_SNAKE_CASE_       :						List[str]					=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)






