


def  lowercase_						(						_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."		)

      lowerCamelCase__						:							List[str]       =    {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."		)

      lowerCamelCase__						:							Dict       =    len(_A		)

      lowerCamelCase__						:							Tuple       =    0
      lowerCamelCase__						:							list[list[float]]       =    []
      # put the x and x to the power values in a matrix
      while count_of_line < x:
            lowerCamelCase__						:							Any       =    0
            lowerCamelCase__						:							Optional[int]       =    coordinates[count_of_line][0]
            lowerCamelCase__						:							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

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

      lowerCamelCase__						:							List[str]       =    0

      while count < x:
            lowerCamelCase__						:							Union[str, Any]       =    0
            while zahlen < x:
                  if count == zahlen:
                        zahlen += 1
                  if zahlen == x:
                        break
                  lowerCamelCase__						:							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

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

      lowerCamelCase__						:							Optional[Any]       =    0
      lowerCamelCase__						:							int       =    "f(x)="

      while count < x:
            lowerCamelCase__						:							list[str]       =    solution[count].split("E"		)
            if len(_A		) > 1:
                  lowerCamelCase__						:							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]]))






import re
import tempfile
import unittest
from pathlib import Path

from datasets.utils.metadata import DatasetMetadata

def  lowercase_						(						_A     :       str		):

      """simple docstring"""




      lowerCamelCase__						:							Optional[Any]       =    min(re.search("^ +"       ,   _A		).end() if t.startswith(" "		) else 0 for t in string.splitlines()		)
      return "\n".join([line[indent_level:] for line in string.splitlines() if indent_level < len(_A		)]		)


A :       Optional[int]						=   "\\n---\nlanguage:\n- zh\n- en\ntask_ids:\n- sentiment-classification\n---\n# Begin of markdown\n\nSome cool dataset card\n"

A :       str						=   "\\n---\n---\n# Begin of markdown\n\nSome cool dataset card\n"


A :       Optional[Any]						=   "\\n# Begin of markdown\n\nSome cool dataset card\n"







class      _lowercase					(				unittest.TestCase):


       """simple docstring"""




       def 		lowerCAmelCase	(  self				:     List[Any]			):


             '''simple docstring'''



             with tempfile.TemporaryDirectory() as tmp_dir:
                   lowerCamelCase__						:							List[str]       =    Path(__lowerCamelCase			) / "README.md"
                   with open(__lowerCamelCase   , "w+"			) as readme_file:
                         readme_file.write(__lowerCamelCase			)
                   lowerCamelCase__						:							Dict       =    DatasetMetadata.from_readme(__lowerCamelCase			)
                   self.assertDictEqual(__lowerCamelCase   , {"language": ["zh", "en"], "task_ids": ["sentiment-classification"]}			)

                   with open(__lowerCamelCase   , "w+"			) as readme_file:
                         readme_file.write(__lowerCamelCase			)
                   lowerCamelCase__						:							Optional[Any]       =    DatasetMetadata.from_readme(__lowerCamelCase			)
                   self.assertDictEqual(__lowerCamelCase   , {}			)

                   with open(__lowerCamelCase   , "w+"			) as readme_file:
                         readme_file.write(__lowerCamelCase			)
                   lowerCamelCase__						:							int       =    DatasetMetadata.from_readme(__lowerCamelCase			)
                   self.assertEqual(__lowerCamelCase   , {}			)





       def 		lowerCAmelCase	(  self				:     Any			):


             '''simple docstring'''



             lowerCamelCase__						:							List[str]       =    _dedent(
                 "\\n            annotations_creators:\n            - found\n            language_creators:\n            - found\n            language:\n            - en\n            license:\n            - unknown\n            multilinguality:\n            - monolingual\n            pretty_name: Test Dataset\n            size_categories:\n            - 10K<n<100K\n            source_datasets:\n            - extended|other-yahoo-webscope-l6\n            task_categories:\n            - question-answering\n            task_ids:\n            - open-domain-qa\n            "			)
             assert DatasetMetadata.from_yaml_string(__lowerCamelCase			)

             lowerCamelCase__						:							Dict       =    _dedent(
                 "\\n            annotations_creators:\n            - found\n            language:\n            - en\n            license:\n            - unknown\n            multilinguality:\n            - monolingual\n            pretty_name: Test Dataset\n            size_categories:\n            - 10K<n<100K\n            source_datasets:\n            - extended|other-yahoo-webscope-l6\n            task_categories:\n            - question-answering\n            task_ids:\n            - open-domain-qa\n            task_ids:\n            - open-domain-qa\n            "			)
             with self.assertRaises(__lowerCamelCase			):
                   DatasetMetadata.from_yaml_string(__lowerCamelCase			)

             lowerCamelCase__						:							Optional[Any]       =    _dedent(
                 "\\n            annotations_creators:\n            - found\n            language_creators:\n            - found\n            language:\n            - en\n            license:\n            - unknown\n            multilinguality:\n            - monolingual\n            pretty_name: Test Dataset\n            size_categories:\n            - 10K<n<100K\n            source_datasets:\n            - extended|other-yahoo-webscope-l6\n            task_categories:\n            - text-classification\n            task_ids:\n            - multi-class-classification\n            paperswithcode_id:\n            - squad\n            configs:\n            - en\n            train-eval-index:\n            - config: en\n              task: text-classification\n              task_id: multi_class_classification\n              splits:\n                train_split: train\n                eval_split: test\n              col_mapping:\n                text: text\n                label: target\n              metrics:\n                - type: accuracy\n                  name: Accuracy\n            extra_gated_prompt: |\n              By clicking on “Access repository” below, you also agree to ImageNet Terms of Access:\n              [RESEARCHER_FULLNAME] (the \"Researcher\") has requested permission to use the ImageNet database (the \"Database\") at Princeton University and Stanford University. In exchange for such permission, Researcher hereby agrees to the following terms and conditions:\n              1. Researcher shall use the Database only for non-commercial research and educational purposes.\n            extra_gated_fields:\n              Company: text\n              Country: text\n              I agree to use this model for non-commerical use ONLY: checkbox\n            "			)
             assert DatasetMetadata.from_yaml_string(__lowerCamelCase			)


