






"""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"""







import unittest

import numpy as np

from transformers import ElectraConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor, random_attention_mask


if is_flax_available():
 from transformers.models.electra.modeling_flax_electra import (
     FlaxElectraForCausalLM,
     FlaxElectraForMaskedLM,
     FlaxElectraForMultipleChoice,
     FlaxElectraForPreTraining,
     FlaxElectraForQuestionAnswering,
     FlaxElectraForSequenceClassification,
     FlaxElectraForTokenClassification,
     FlaxElectraModel,
 )





class      UpperCamelCase_       (				unittest.TestCase     ):



  def __init__(					self       ,						snake_case__       ,						snake_case__=13       ,						snake_case__=7       ,						snake_case__=True       ,						snake_case__=True       ,						snake_case__=True       ,						snake_case__=True       ,						snake_case__=99       ,						snake_case__=24       ,						snake_case__=32       ,						snake_case__=5       ,						snake_case__=4       ,						snake_case__=37       ,						snake_case__="gelu"       ,						snake_case__=0.1       ,						snake_case__=0.1       ,						snake_case__=5_12       ,						snake_case__=16       ,						snake_case__=2       ,						snake_case__=0.02       ,						snake_case__=4       ,						)	->	int:



         """simple docstring"""





         UpperCAmelCase					=	parent
         UpperCAmelCase					=	batch_size
         UpperCAmelCase					=	seq_length
         UpperCAmelCase					=	is_training
         UpperCAmelCase					=	use_attention_mask
         UpperCAmelCase					=	use_token_type_ids
         UpperCAmelCase					=	use_labels
         UpperCAmelCase					=	vocab_size
         UpperCAmelCase					=	hidden_size
         UpperCAmelCase					=	embedding_size
         UpperCAmelCase					=	num_hidden_layers
         UpperCAmelCase					=	num_attention_heads
         UpperCAmelCase					=	intermediate_size
         UpperCAmelCase					=	hidden_act
         UpperCAmelCase					=	hidden_dropout_prob
         UpperCAmelCase					=	attention_probs_dropout_prob
         UpperCAmelCase					=	max_position_embeddings
         UpperCAmelCase					=	type_vocab_size
         UpperCAmelCase					=	type_sequence_label_size
         UpperCAmelCase					=	initializer_range
         UpperCAmelCase					=	num_choices



  def 						UpperCamelCase_ (					self )	->	Optional[Any]:



         """simple docstring"""





         UpperCAmelCase					=	ids_tensor([self.batch_size, self.seq_length]       ,						self.vocab_size )

         UpperCAmelCase					=	None
         if self.use_attention_mask:
                UpperCAmelCase					=	random_attention_mask([self.batch_size, self.seq_length] )

         UpperCAmelCase					=	None
         if self.use_token_type_ids:
                UpperCAmelCase					=	ids_tensor([self.batch_size, self.seq_length]       ,						self.type_vocab_size )

         UpperCAmelCase					=	ElectraConfig(
             vocab_size=self.vocab_size       ,						hidden_size=self.hidden_size       ,						embedding_size=self.embedding_size       ,						num_hidden_layers=self.num_hidden_layers       ,						num_attention_heads=self.num_attention_heads       ,						intermediate_size=self.intermediate_size       ,						hidden_act=self.hidden_act       ,						hidden_dropout_prob=self.hidden_dropout_prob       ,						attention_probs_dropout_prob=self.attention_probs_dropout_prob       ,						max_position_embeddings=self.max_position_embeddings       ,						type_vocab_size=self.type_vocab_size       ,						initializer_range=self.initializer_range       ,						)

         return config, input_ids, token_type_ids, attention_mask



  def 						UpperCamelCase_ (					self )	->	List[str]:



         """simple docstring"""





         UpperCAmelCase					=	self.prepare_config_and_inputs()
         UpperCAmelCase			,				UpperCAmelCase			,				UpperCAmelCase			,				UpperCAmelCase					=	config_and_inputs
         UpperCAmelCase					=	{"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """attention_mask""": attention_mask}
         return config, inputs_dict





@require_flax
class      UpperCamelCase_       (				a_      ,    unittest.TestCase     ):
  _A				:    str =		True

  _A				:    List[Any] =		(
      (
          FlaxElectraModel,
          FlaxElectraForCausalLM,
          FlaxElectraForMaskedLM,
          FlaxElectraForPreTraining,
          FlaxElectraForTokenClassification,
          FlaxElectraForQuestionAnswering,
          FlaxElectraForMultipleChoice,
          FlaxElectraForSequenceClassification,
      )
      if is_flax_available()
      else ()
  )



  def 						UpperCamelCase_ (					self )	->	str:



         """simple docstring"""





         UpperCAmelCase					=	FlaxElectraModelTester(self )



  @slow
  def 						UpperCamelCase_ (					self )	->	Tuple:



         """simple docstring"""





         for model_class_name in self.all_model_classes:
                if model_class_name == FlaxElectraForMaskedLM:
                       UpperCAmelCase					=	model_class_name.from_pretrained("""google/electra-small-generator""" )
                else:
                       UpperCAmelCase					=	model_class_name.from_pretrained("""google/electra-small-discriminator""" )
                UpperCAmelCase					=	model(np.ones((1, 1) ) )
                self.assertIsNotNone(snake_case__ )
