





def        lowerCAmelCase_       (							UpperCamelCase_     )   ->						str:


       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."     )

       UpperCamelCase_      				=     {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."     )

       UpperCamelCase_      				=     len(UpperCamelCase_     )

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

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

       UpperCamelCase_      				=     0

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

       UpperCamelCase_      				=     0
       UpperCamelCase_      				=     'f(x)='

       while count < x:
              UpperCamelCase_      				=     solution[count].split("E"     )
              if len(UpperCamelCase_     ) > 1:
                     UpperCamelCase_      				=     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]]))







# as due to their complexity multi-gpu tests could impact other tests, and to aid debug we have those in a separate module.

import os
import sys

from transformers.testing_utils import TestCasePlus, execute_subprocess_async, get_gpu_count, require_torch_gpu, slow

from .utils import load_json


class 				__SCREAMING_SNAKE_CASE							(		lowerCamelCase  ):

					@classmethod
					def 	lowercase_							(				cls					):







						'''simple docstring'''




						return cls





					@slow
					@require_torch_gpu
					def 	lowercase_							(				self					):







						'''simple docstring'''




						lowerCamelCase_							:		Dict							   =							self.get_auto_remove_tmp_dir()
						lowerCamelCase_							:		Tuple							   =							f"\n            --model_name Helsinki-NLP/opus-mt-en-ro\n            --save_dir {output_dir}\n            --data_dir {self.test_file_dir_str}/test_data/wmt_en_ro\n            --num_beams 2\n            --task translation\n        ".split()

						# we want this test to run even if there is only one GPU, but if there are more we use them all
						lowerCamelCase_							:		List[Any]							   =							get_gpu_count()
						lowerCamelCase_							:		Union[str, Any]							   =							f"\n            -m torch.distributed.launch\n            --nproc_per_node={n_gpu}\n            {self.test_file_dir}/run_distributed_eval.py\n        ".split()
						lowerCamelCase_							:		int							   =							[sys.executable] + distributed_args + args
						execute_subprocess_async(__lowercase ,       env=self.get_env()					)

						lowerCamelCase_							:		Any							   =							os.path.join(__lowercase ,       'test_bleu.json'					)
						lowerCamelCase_							:		List[Any]							   =							load_json(__lowercase					)
						# print(metrics)
						self.assertGreaterEqual(metrics['bleu'] ,       25					)
