






def    _lowerCamelCase	(	__lowerCamelCase					)   -> str:

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

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

     UpperCAmelCase__			:     Tuple										= {x for x, _ in coordinates}
     if len(__lowerCamelCase					) == 1:
          return F"x={coordinates[0][0]}"

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

     UpperCAmelCase__			:     Tuple										= len(__lowerCamelCase					)

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

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

     UpperCAmelCase__			:     Optional[Any]										= 0

     while count < x:
          UpperCAmelCase__			:     Optional[int]										= 0
          while zahlen < x:
               if count == zahlen:
                    zahlen += 1
               if zahlen == x:
                    break
               UpperCAmelCase__			:     List[str]										= 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

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

     UpperCAmelCase__			:     Union[str, Any]										= 0
     UpperCAmelCase__			:     Tuple										= """f(x)="""

     while count < x:
          UpperCAmelCase__			:     list[str]										= solution[count].split("""E"""					)
          if len(__lowerCamelCase					) > 1:
               UpperCAmelCase__			:     List[Any]										= 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]]))














import concurrent.futures
import json
import os
import shutil
import tempfile
import unittest

from transformers import AutoTokenizer, PreTrainedTokenizerFast
from transformers.testing_utils import require_tokenizers

from ..test_tokenization_common import TokenizerTesterMixin







@require_tokenizers
class 							UpperCAmelCase_     (		__lowerCamelCase       ,			unittest.TestCase		):
     __lowerCamelCase										=     PreTrainedTokenizerFast
     __lowerCamelCase										=     False
     __lowerCamelCase										=     True
     __lowerCamelCase										=     'tokenizer_file'




     def      __UpperCAmelCase     (							self		):
          UpperCAmelCase__			:     Union[str, Any]										= False  # because we don't have pretrained_vocab_files_map
          super().setUp()
          UpperCAmelCase__			:     Dict										= True

          UpperCAmelCase__			:     int										= ["""robot-test/dummy-tokenizer-fast""", """robot-test/dummy-tokenizer-wordlevel"""]
          UpperCAmelCase__			:     List[Any]										= """SaulLu/dummy-tokenizer-bytelevel-bpe"""

          # Inclusion of 2 tokenizers to test different types of models (Unigram and WordLevel for the moment)
          UpperCAmelCase__			:     int										= [(PreTrainedTokenizerFast, model_path, {}) for model_path in model_paths]

          UpperCAmelCase__			:     Union[str, Any]										= PreTrainedTokenizerFast.from_pretrained(model_paths[0]		)
          tokenizer.save_pretrained(self.tmpdirname		)




     def      __UpperCAmelCase     (							self		):
          # We disable this test for PreTrainedTokenizerFast because it is the only tokenizer that is not linked to any
          # model
          pass




     def      __UpperCAmelCase     (							self		):
          # We disable this test for PreTrainedTokenizerFast because it is the only tokenizer that is not linked to any
          # model
          pass




     def      __UpperCAmelCase     (							self		):
          # We disable this test for PreTrainedTokenizerFast because it is the only tokenizer that is not linked to any
          # model
          pass




     def      __UpperCAmelCase     (							self		):
          # PreTrainedTokenizerFast doesn't have tokenizer_file in its signature
          pass




     def      __UpperCAmelCase     (							self		):
          UpperCAmelCase__			:     Optional[int]										= self.tmpdirname
          # Here we want to test the 2 available tokenizers that use 2 different types of models: Unigram and WordLevel.
          for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
               with self.subTest(f"{tokenizer.__class__.__name__} ({pretrained_name})"		):
                    try:
                         UpperCAmelCase__			:     str										= tempfile.mkdtemp()
                         UpperCAmelCase__			:     Any										= self.rust_tokenizer_class.from_pretrained(_lowerCAmelCase  ,	**_lowerCAmelCase		)

                         tokenizer.save_pretrained(self.tmpdirname		)
                         super().test_training_new_tokenizer()
                    finally:
                         # Even if the test fails, we must be sure that the folder is deleted and that the default tokenizer
                         # is restored
                         shutil.rmtree(self.tmpdirname		)
                         UpperCAmelCase__			:     str										= tmpdirname_orig




     def      __UpperCAmelCase     (							self		):
          UpperCAmelCase__			:     Tuple										= self.tmpdirname
          # Here we want to test the 2 available tokenizers that use 2 different types of models: Unigram and WordLevel.
          for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
               with self.subTest(f"{tokenizer.__class__.__name__} ({pretrained_name})"		):
                    try:
                         UpperCAmelCase__			:     Optional[Any]										= tempfile.mkdtemp()
                         UpperCAmelCase__			:     Any										= self.rust_tokenizer_class.from_pretrained(_lowerCAmelCase  ,	**_lowerCAmelCase		)

                         tokenizer.save_pretrained(self.tmpdirname		)
                         super().test_training_new_tokenizer_with_special_tokens_change()
                    finally:
                         # Even if the test fails, we must be sure that the folder is deleted and that the default tokenizer
                         # is restored
                         shutil.rmtree(self.tmpdirname		)
                         UpperCAmelCase__			:     str										= tmpdirname_orig




     def      __UpperCAmelCase     (							self		):
          UpperCAmelCase__			:     Tuple										= self.rust_tokenizer_class.from_pretrained(self.bytelevel_bpe_model_name		)

          UpperCAmelCase__			:     Dict										= ("""a""" for _ in range(1000		))
          UpperCAmelCase__			:     int										= tokenizer.train_new_from_iterator(text_iterator=_lowerCAmelCase  ,	length=1000  ,	vocab_size=50		)

          UpperCAmelCase__			:     Optional[Any]										= new_tokenizer.encode("""a🤗"""		)
          self.assertEqual(_lowerCAmelCase  ,	[64, 172, 253, 97, 245]		)







@require_tokenizers
class 							UpperCAmelCase_     (		unittest.TestCase		):




     def      __UpperCAmelCase     (							self		):
          UpperCAmelCase__			:     List[str]										= AutoTokenizer.from_pretrained("""bert-base-cased"""		)
          UpperCAmelCase__			:     List[Any]										= json.loads(tokenizer._tokenizer.to_str()		)
          UpperCAmelCase__			:     Optional[Any]										= len(_lowerCAmelCase		)

          with tempfile.TemporaryDirectory() as tmp_dir:
               # Hack to save this in the tokenizer_config.json
               UpperCAmelCase__			:     Tuple										= ["""tokenizer.4.0.0.json"""]
               tokenizer.save_pretrained(_lowerCAmelCase		)
               json.dump(_lowerCAmelCase  ,	open(os.path.join(_lowerCAmelCase  ,	"""tokenizer.4.0.0.json"""		)  ,	"""w"""		)		)

               # This should pick the new tokenizer file as the version of Transformers is > 4.0.0
               UpperCAmelCase__			:     Optional[int]										= AutoTokenizer.from_pretrained(_lowerCAmelCase		)
               self.assertEqual(len(_lowerCAmelCase		)  ,	len(_lowerCAmelCase		) + 1		)
               UpperCAmelCase__			:     Any										= json.loads(new_tokenizer._tokenizer.to_str()		)
               self.assertIn("""huggingface"""  ,	json_tokenizer["""model"""]["""vocab"""]		)

               # Will need to be adjusted if we reach v42 and this test is still here.
               # Should pick the old tokenizer file as the version of Transformers is < 4.0.0
               shutil.move(os.path.join(_lowerCAmelCase  ,	"""tokenizer.4.0.0.json"""		)  ,	os.path.join(_lowerCAmelCase  ,	"""tokenizer.42.0.0.json"""		)		)
               UpperCAmelCase__			:     Union[str, Any]										= ["""tokenizer.42.0.0.json"""]
               tokenizer.save_pretrained(_lowerCAmelCase		)
               UpperCAmelCase__			:     Optional[Any]										= AutoTokenizer.from_pretrained(_lowerCAmelCase		)
               self.assertEqual(len(_lowerCAmelCase		)  ,	len(_lowerCAmelCase		)		)
               UpperCAmelCase__			:     List[Any]										= json.loads(new_tokenizer._tokenizer.to_str()		)
               self.assertNotIn("""huggingface"""  ,	json_tokenizer["""model"""]["""vocab"""]		)




     def      __UpperCAmelCase     (							self		):
          # This repo has two tokenizer files, one for v4.0.0 and above with an added token, one for versions lower.
          UpperCAmelCase__			:     List[str]										= """hf-internal-testing/test-two-tokenizers"""

          # This should pick the new tokenizer file as the version of Transformers is > 4.0.0
          UpperCAmelCase__			:     int										= AutoTokenizer.from_pretrained(_lowerCAmelCase		)
          self.assertEqual(len(_lowerCAmelCase		)  ,	28997		)
          UpperCAmelCase__			:     List[Any]										= json.loads(tokenizer._tokenizer.to_str()		)
          self.assertIn("""huggingface"""  ,	json_tokenizer["""model"""]["""vocab"""]		)

          # Testing an older version by monkey-patching the version in the module it's used.
          import transformers as old_transformers

          UpperCAmelCase__			:     Any										= """3.0.0"""
          UpperCAmelCase__			:     Optional[int]										= old_transformers.models.auto.AutoTokenizer.from_pretrained(_lowerCAmelCase		)
          self.assertEqual(len(_lowerCAmelCase		)  ,	28996		)
          UpperCAmelCase__			:     Optional[int]										= json.loads(old_tokenizer._tokenizer.to_str()		)
          self.assertNotIn("""huggingface"""  ,	json_tokenizer["""model"""]["""vocab"""]		)







@require_tokenizers
class 							UpperCAmelCase_     (		unittest.TestCase		):




     def      __UpperCAmelCase     (							self		):
          # See https://github.com/huggingface/transformers/pull/12550
          # and https://github.com/huggingface/tokenizers/issues/537
          UpperCAmelCase__			:     int										= PreTrainedTokenizerFast.from_pretrained("""robot-test/dummy-tokenizer-wordlevel"""		)
          UpperCAmelCase__			:     List[str]										= """The Matrix is a 1999 science fiction action film."""

          with concurrent.futures.ThreadPoolExecutor() as executor:
               UpperCAmelCase__			:     List[str]										= [executor.submit(self.fetch  ,	_lowerCAmelCase  ,	_lowerCAmelCase		) for i in range(10		)]
               UpperCAmelCase__			:     Dict										= [future.result() for future in futures]
               self.assertEqual(_lowerCAmelCase  ,	[[1, 10, 0, 8, 0, 18, 0, 0, 0, 2] for i in range(10		)]		)




     def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
          return tokenizer.encode(_lowerCAmelCase  ,	truncation="""longest_first"""  ,	padding="""longest"""		)






