
def 		SCREAMING_SNAKE_CASE__      ( __lowerCAmelCase							):
    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."							)

    snake_case__  =			{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."							)

    snake_case__  =			len(__lowerCAmelCase							)

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

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

    snake_case__  =			0

    while count < x:
        snake_case__  =			0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            snake_case__  =			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

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

    snake_case__  =			0
    snake_case__  =			"f(x)="

    while count < x:
        snake_case__  =			solution[count].split("E"							)
        if len(__lowerCAmelCase							) > 1:
            snake_case__  =			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 os
import tempfile
import unittest
from typing import List

from transformers.models.esm.tokenization_esm import VOCAB_FILES_NAMES, EsmTokenizer
from transformers.testing_utils import require_tokenizers
from transformers.tokenization_utils import PreTrainedTokenizer
from transformers.tokenization_utils_base import PreTrainedTokenizerBase




@require_tokenizers
class    _SCREAMING_SNAKE_CASE					( unittest.TestCase	):
      _A  :						Optional[Any]      		=       EsmTokenizer
      def A_     (     self	):
          super().setUp()
          snake_case__  =			tempfile.mkdtemp()
          # fmt: off
          snake_case__  =			["<cls>", "<pad>", "<eos>", "<unk>", "L", "A", "G", "V", "S", "E", "R", "T", "I", "D", "P", "K", "Q", "N", "F", "Y", "M", "H", "W", "C", "X", "B", "U", "Z", "O", ".", "-", "<null_1>", "<mask>"]  # noqa: E501
          # fmt: on
          snake_case__  =			os.path.join(self.tmpdirname						,		VOCAB_FILES_NAMES["vocab_file"]	)
          with open(self.vocab_file						,		"w"						,		encoding="utf-8"	) as vocab_writer:
              vocab_writer.write("".join([x + "\n" for x in vocab_tokens]	)	)
      def A_     (     self						,		**lowerCamelCase	):
          return [self.get_tokenizer(**lowerCamelCase	)]
      def A_     (     self						,		**lowerCamelCase	):
          return self.tokenizer_class.from_pretrained(self.tmpdirname						,		**lowerCamelCase	)
      def A_     (     self	):
          snake_case__  =			self.tokenizer_class(self.vocab_file	)

          snake_case__  =			tokenizer.tokenize("LAGVS"	)
          self.assertListEqual(lowerCamelCase						,		["L", "A", "G", "V", "S"]	)
          self.assertListEqual(tokenizer.convert_tokens_to_ids(lowerCamelCase	)						,		[4, 5, 6, 7, 8]	)
      def A_     (     self	):
          snake_case__  =			self.tokenizer_class(self.vocab_file	)

          snake_case__  =			"LAGVS"
          self.assertListEqual(tokenizer.encode(lowerCamelCase	)						,		[0, 4, 5, 6, 7, 8, 2]	)
      def A_     (     self	):
          snake_case__  =			self.tokenizer_class(self.vocab_file	)

          snake_case__  =			["LAGVS", "WCB"]
          snake_case__  =			tokenizer(lowerCamelCase						,		padding=lowerCamelCase	)["input_ids"]

          self.assertListEqual(lowerCamelCase						,		[[0, 4, 5, 6, 7, 8, 2], [0, 22, 23, 25, 2]]	)
      def A_     (     self	):
          snake_case__  =			self.tokenizer_class(self.vocab_file	)

          snake_case__  =			["LAGVS", "WCB"]
          snake_case__  =			tokenizer(lowerCamelCase						,		padding=lowerCamelCase	)["input_ids"]

          self.assertListEqual(lowerCamelCase						,		[[0, 4, 5, 6, 7, 8, 2], [0, 22, 23, 25, 2, 1, 1]]	)



      def A_     (     self	):
          snake_case__  =			self.get_tokenizers(fast=lowerCamelCase	)
          for tokenizer in tokenizers:
              with self.subTest(F"""{tokenizer.__class__.__name__}"""	):
                  snake_case__  =			"<unk>"
                  snake_case__  =			"<mask>"

                  snake_case__  =			tokenizer.tokenize(lowerCamelCase	)
                  snake_case__  =			tokenizer.tokenize(lowerCamelCase	)

                  self.assertEqual(len(lowerCamelCase	)						,		1	)
                  self.assertEqual(len(lowerCamelCase	)						,		1	)
                  self.assertEqual(token_a[0]						,		lowerCamelCase	)
                  self.assertEqual(token_a[0]						,		lowerCamelCase	)



