
def 					__lowerCAmelCase    (    a__						) ->						str:
				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    							=					{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    							=					len(a__						)

				__a    							=					0
				__a    							=					[]
				# put the x and x to the power values in a matrix
				while count_of_line < x:
								__a    							=					0
								__a    							=					coordinates[count_of_line][0]
								__a    							=					[]
								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    							=					0
				# put the y values into a vector
				__a    							=					[]
				while count_of_line < x:
								vector.append(coordinates[count_of_line][1]						)
								count_of_line += 1

				__a    							=					0

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

				__a    							=					0
				__a    							=					'''f(x)='''

				while count < x:
								__a    							=					solution[count].split('''E'''						)
								if len(a__						) > 1:
												__a    							=					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, 1_1]]))
					print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
					print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))








# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
					import tensorflow as tf







class     __A(				TensorFormatter[Mapping, '''tf.Tensor''', Mapping]    ):




				def __init__(  self	,  _snake_case=None	,  **_snake_case       )					->   Dict:


								'''simple docstring'''




								super().__init__(features=_snake_case       )
								__a    							=					tf_tensor_kwargs
								import tensorflow as tf  # noqa: import tf at initialization




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   Optional[Any]:


								'''simple docstring'''




								import tensorflow as tf

								if isinstance(_snake_case	,  _snake_case       ) and column:
												if all(
												    isinstance(_snake_case	,  tf.Tensor       ) and x.shape == column[0].shape and x.dtype == column[0].dtype for x in column       ):
																return tf.stack(_snake_case       )
												elif all(
												    isinstance(_snake_case	,  (tf.Tensor, tf.RaggedTensor)       ) and x.ndim == 1 and x.dtype == column[0].dtype
												    for x in column       ):
																# only rag 1-D tensors, otherwise some dimensions become ragged even though they were consolidated
																return tf.ragged.stack(_snake_case       )

								return column




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   Optional[Any]:


								'''simple docstring'''




								import tensorflow as tf

								if value is None:
												return value

								__a    							=					{}

								if isinstance(_snake_case	,  (np.number, np.ndarray)       ) and np.issubdtype(value.dtype	,  np.integer       ):
												__a    							=					{'''dtype''': tf.intaa}
								elif isinstance(_snake_case	,  (np.number, np.ndarray)       ) and np.issubdtype(value.dtype	,  np.floating       ):
												__a    							=					{'''dtype''': tf.floataa}
								elif config.PIL_AVAILABLE and "PIL" in sys.modules:
												import PIL.Image

												if isinstance(_snake_case	,  PIL.Image.Image       ):
																__a    							=					np.asarray(_snake_case       )

								return tf.convert_to_tensor(_snake_case	,  **{**default_dtype, **self.tf_tensor_kwargs}       )




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   str:


								'''simple docstring'''




								import tensorflow as tf

								# support for torch, tf, jax etc.
								if config.TORCH_AVAILABLE and "torch" in sys.modules:
												import torch

												if isinstance(_snake_case	,  torch.Tensor       ):
																return self._tensorize(data_struct.detach().cpu().numpy()[()]       )
								if hasattr(_snake_case	,  '''__array__'''       ) and not isinstance(_snake_case	,  tf.Tensor       ):
												__a    							=					data_struct.__array__()
								# support for nested types like struct of list of struct
								if isinstance(_snake_case	,  np.ndarray       ):
												if data_struct.dtype == object:  # tf tensors cannot be instantied from an array of objects
																return self._consolidate([self.recursive_tensorize(_snake_case       ) for substruct in data_struct]       )
								elif isinstance(_snake_case	,  (list, tuple)       ):
												return self._consolidate([self.recursive_tensorize(_snake_case       ) for substruct in data_struct]       )
								return self._tensorize(_snake_case       )




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   Tuple:


								'''simple docstring'''




								return map_nested(self._recursive_tensorize	,  _snake_case	,  map_list=_snake_case       )




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   Mapping:


								'''simple docstring'''




								__a    							=					self.numpy_arrow_extractor().extract_row(_snake_case       )
								__a    							=					self.python_features_decoder.decode_row(_snake_case       )
								return self.recursive_tensorize(_snake_case       )




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   "tf.Tensor":


								'''simple docstring'''




								__a    							=					self.numpy_arrow_extractor().extract_column(_snake_case       )
								__a    							=					self.python_features_decoder.decode_column(_snake_case	,  pa_table.column_names[0]       )
								__a    							=					self.recursive_tensorize(_snake_case       )
								__a    							=					self._consolidate(_snake_case       )
								return column




				def        SCREAMING_SNAKE_CASE_	(  self	,  _snake_case       )					->   Mapping:


								'''simple docstring'''




								__a    							=					self.numpy_arrow_extractor().extract_batch(_snake_case       )
								__a    							=					self.python_features_decoder.decode_batch(_snake_case       )
								__a    							=					self.recursive_tensorize(_snake_case       )
								for column_name in batch:
												__a    							=					self._consolidate(batch[column_name]       )
								return batch