

"""simple docstring"""




def 		A    (       snake_case__      ):




			'''simple docstring'''


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

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

			SCREAMING_SNAKE_CASE__									= {x for x, _ in coordinates}
			if len(snake_case__      ) == 1:
						return f"""x={coordinates[0][0]}"""

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

			SCREAMING_SNAKE_CASE__									= len(snake_case__      )

			SCREAMING_SNAKE_CASE__									= 0
			SCREAMING_SNAKE_CASE__									= []
			# put the x and x to the power values in a matrix
			while count_of_line < x:
						SCREAMING_SNAKE_CASE__									= 0
						SCREAMING_SNAKE_CASE__									= coordinates[count_of_line][0]
						SCREAMING_SNAKE_CASE__									= []
						while count_in_line < x:
									count_line.append(a ** (x - (count_in_line + 1))      )
									count_in_line += 1
						matrix.append(snake_case__      )
						count_of_line += 1

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

			SCREAMING_SNAKE_CASE__									= 0

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

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

			SCREAMING_SNAKE_CASE__									= 0
			SCREAMING_SNAKE_CASE__									= """f(x)="""

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





"""simple docstring"""




import os
import pickle
import tempfile
import unittest
from typing import Callable, Optional

import numpy as np

from transformers import (
    BatchEncoding,
    BertTokenizer,
    BertTokenizerFast,
    PreTrainedTokenizer,
    PreTrainedTokenizerFast,
    TensorType,
    TokenSpan,
    is_tokenizers_available,
)
from transformers.models.gpta.tokenization_gpta import GPTaTokenizer
from transformers.testing_utils import CaptureStderr, require_flax, require_tf, require_tokenizers, require_torch, slow


if is_tokenizers_available():
						from tokenizers import Tokenizer
						from tokenizers.models import WordPiece





class 				lowerCamelCase  (unittest.TestCase     ):

			def    SCREAMING_SNAKE_CASE			(   self			:  Union[str, Any]      ,			__UpperCAmelCase			:  str    )				->      int:
						SCREAMING_SNAKE_CASE__									= list(tokenizer_class.max_model_input_sizes.keys()    )
						for model_name in sa_models[:1]:
									SCREAMING_SNAKE_CASE__									= tokenizer_class.from_pretrained(__UpperCAmelCase    )
									self.assertIsNotNone(__UpperCAmelCase    )
									self.assertIsInstance(__UpperCAmelCase      ,			__UpperCAmelCase    )
									self.assertIsInstance(__UpperCAmelCase      ,			__UpperCAmelCase    )

									for special_tok in tokenizer.all_special_tokens:
												self.assertIsInstance(__UpperCAmelCase      ,			__UpperCAmelCase    )
												SCREAMING_SNAKE_CASE__									= tokenizer.convert_tokens_to_ids(__UpperCAmelCase    )
												self.assertIsInstance(__UpperCAmelCase      ,			__UpperCAmelCase    )

			def    SCREAMING_SNAKE_CASE			(   self			:  Dict      ,			__UpperCAmelCase			:  BatchEncoding      ,			__UpperCAmelCase			:  Optional[Callable] = None    )				->      Tuple:
						SCREAMING_SNAKE_CASE__									= pickle.dumps(__UpperCAmelCase    )
						self.assertIsNotNone(__UpperCAmelCase    )

						SCREAMING_SNAKE_CASE__									= pickle.loads(__UpperCAmelCase    )

						# Ensure is_fast is correctly restored
						self.assertEqual(be_restored.is_fast      ,			be_original.is_fast    )

						# Ensure encodings are potentially correctly restored
						if be_original.is_fast:
									self.assertIsNotNone(be_restored.encodings    )
						else:
									self.assertIsNone(be_restored.encodings    )

						# Ensure the keys are the same
						for original_v, restored_v in zip(be_original.values()      ,			be_restored.values()    ):
									if equal_op:
												self.assertTrue(equal_op(__UpperCAmelCase      ,			__UpperCAmelCase    )    )
									else:
												self.assertEqual(__UpperCAmelCase      ,			__UpperCAmelCase    )

			@slow
			def    SCREAMING_SNAKE_CASE			(   self			:  str    )				->      Optional[Any]:
						self.check_tokenizer_from_pretrained(__UpperCAmelCase    )

			def    SCREAMING_SNAKE_CASE			(   self			:  Tuple    )				->      Optional[int]:
						self.assertEqual(TensorType("""tf"""    )      ,			TensorType.TENSORFLOW    )
						self.assertEqual(TensorType("""pt"""    )      ,			TensorType.PYTORCH    )
						self.assertEqual(TensorType("""np"""    )      ,			TensorType.NUMPY    )

			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  Dict    )				->      List[str]:
						import numpy as np

						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )
						SCREAMING_SNAKE_CASE__									= BertTokenizerFast.from_pretrained("""bert-base-cased"""    )

						# Python no tensor
						with self.subTest("""BatchEncoding (Python, return_tensors=None)"""    ):
									self.assert_dump_and_restore(tokenizer_p("""Small example to encode"""    )    )

						with self.subTest("""BatchEncoding (Python, return_tensors=NUMPY)"""    ):
									self.assert_dump_and_restore(
									    tokenizer_p("""Small example to encode"""      ,			return_tensors=TensorType.NUMPY    )      ,			np.array_equal    )

						with self.subTest("""BatchEncoding (Rust, return_tensors=None)"""    ):
									self.assert_dump_and_restore(tokenizer_r("""Small example to encode"""    )    )

						with self.subTest("""BatchEncoding (Rust, return_tensors=NUMPY)"""    ):
									self.assert_dump_and_restore(
									    tokenizer_r("""Small example to encode"""      ,			return_tensors=TensorType.NUMPY    )      ,			np.array_equal    )

			@require_tf
			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  Dict    )				->      int:
						import tensorflow as tf

						def tf_array_equals(__UpperCAmelCase			:  Optional[int]      ,			__UpperCAmelCase			:  str    ):
									return tf.reduce_all(tf.equal(__UpperCAmelCase      ,			__UpperCAmelCase    )    )

						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )
						SCREAMING_SNAKE_CASE__									= BertTokenizerFast.from_pretrained("""bert-base-cased"""    )

						with self.subTest("""BatchEncoding (Python, return_tensors=TENSORFLOW)"""    ):
									self.assert_dump_and_restore(
									    tokenizer_p("""Small example to encode"""      ,			return_tensors=TensorType.TENSORFLOW    )      ,			__UpperCAmelCase    )

						with self.subTest("""BatchEncoding (Rust, return_tensors=TENSORFLOW)"""    ):
									self.assert_dump_and_restore(
									    tokenizer_r("""Small example to encode"""      ,			return_tensors=TensorType.TENSORFLOW    )      ,			__UpperCAmelCase    )

			@require_torch
			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  Optional[int]    )				->      Optional[int]:
						import torch

						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )
						SCREAMING_SNAKE_CASE__									= BertTokenizerFast.from_pretrained("""bert-base-cased"""    )

						with self.subTest("""BatchEncoding (Python, return_tensors=PYTORCH)"""    ):
									self.assert_dump_and_restore(
									    tokenizer_p("""Small example to encode"""      ,			return_tensors=TensorType.PYTORCH    )      ,			torch.equal    )

						with self.subTest("""BatchEncoding (Rust, return_tensors=PYTORCH)"""    ):
									self.assert_dump_and_restore(
									    tokenizer_r("""Small example to encode"""      ,			return_tensors=TensorType.PYTORCH    )      ,			torch.equal    )

			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  Any    )				->      int:
						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )
						SCREAMING_SNAKE_CASE__									= BertTokenizerFast.from_pretrained("""bert-base-cased"""    )

						with self.subTest("""Python Tokenizer"""    ):
									self.assertFalse(tokenizer_p("""Small example to_encode"""    ).is_fast    )

						with self.subTest("""Rust Tokenizer"""    ):
									self.assertTrue(tokenizer_r("""Small example to_encode"""    ).is_fast    )

			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  Optional[int]    )				->      Optional[Any]:
						SCREAMING_SNAKE_CASE__									= BertTokenizerFast.from_pretrained("""bert-base-cased"""    )
						SCREAMING_SNAKE_CASE__									= tokenizer_r(["""Test""", """\xad""", """test"""]      ,			is_split_into_words=__UpperCAmelCase    )

						self.assertEqual(encoded.word_to_tokens(0    )      ,			TokenSpan(start=1      ,			end=2    )    )
						self.assertEqual(encoded.word_to_tokens(1    )      ,			__UpperCAmelCase    )
						self.assertEqual(encoded.word_to_tokens(2    )      ,			TokenSpan(start=2      ,			end=3    )    )

			def    SCREAMING_SNAKE_CASE			(   self			:  Optional[Any]    )				->      Optional[int]:
						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""np"""    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(2, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(2,)    )
						# test converting the converted
						with CaptureStderr() as cs:
									SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""np"""    )
						self.assertFalse(len(cs.err    )      ,			msg=F"""should have no warning, but got {cs.err}"""    )

						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""np"""      ,			prepend_batch_axis=__UpperCAmelCase    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(1, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(1,)    )

			@require_torch
			def    SCREAMING_SNAKE_CASE			(   self			:  Dict    )				->      Optional[Any]:
						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""pt"""    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(2, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(2,)    )
						# test converting the converted
						with CaptureStderr() as cs:
									SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""pt"""    )
						self.assertFalse(len(cs.err    )      ,			msg=F"""should have no warning, but got {cs.err}"""    )

						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""pt"""      ,			prepend_batch_axis=__UpperCAmelCase    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(1, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(1,)    )

			@require_tf
			def    SCREAMING_SNAKE_CASE			(   self			:  Any    )				->      int:
						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""tf"""    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(2, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(2,)    )
						# test converting the converted
						with CaptureStderr() as cs:
									SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""tf"""    )
						self.assertFalse(len(cs.err    )      ,			msg=F"""should have no warning, but got {cs.err}"""    )

						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""tf"""      ,			prepend_batch_axis=__UpperCAmelCase    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(1, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(1,)    )

			@require_flax
			def    SCREAMING_SNAKE_CASE			(   self			:  int    )				->      Tuple:
						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""jax"""    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(2, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(2,)    )
						# test converting the converted
						with CaptureStderr() as cs:
									SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""jax"""    )
						self.assertFalse(len(cs.err    )      ,			msg=F"""should have no warning, but got {cs.err}"""    )

						SCREAMING_SNAKE_CASE__									= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}    )
						SCREAMING_SNAKE_CASE__									= batch.convert_to_tensors(tensor_type="""jax"""      ,			prepend_batch_axis=__UpperCAmelCase    )
						self.assertEqual(tensor_batch["""inputs"""].shape      ,			(1, 3)    )
						self.assertEqual(tensor_batch["""labels"""].shape      ,			(1,)    )

			def    SCREAMING_SNAKE_CASE			(   self			:  List[Any]    )				->      List[Any]:
						SCREAMING_SNAKE_CASE__									= [{"""input_ids""": np.array([0, 1, 2]    )}, {"""input_ids""": np.array([0, 1, 2, 3]    )}]
						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )

						SCREAMING_SNAKE_CASE__									= tokenizer.pad(__UpperCAmelCase      ,			padding=__UpperCAmelCase    )
						self.assertTrue(isinstance(batch["""input_ids"""]      ,			np.ndarray    )    )
						self.assertEqual(batch["""input_ids"""].tolist()      ,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )
						SCREAMING_SNAKE_CASE__									= tokenizer.pad(__UpperCAmelCase      ,			padding=__UpperCAmelCase      ,			return_tensors="""np"""    )
						self.assertTrue(isinstance(batch["""input_ids"""]      ,			np.ndarray    )    )
						self.assertEqual(batch["""input_ids"""].tolist()      ,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )

			@require_torch
			def    SCREAMING_SNAKE_CASE			(   self			:  Dict    )				->      Optional[int]:
						import torch

						SCREAMING_SNAKE_CASE__									= [{"""input_ids""": torch.tensor([0, 1, 2]    )}, {"""input_ids""": torch.tensor([0, 1, 2, 3]    )}]
						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )

						SCREAMING_SNAKE_CASE__									= tokenizer.pad(__UpperCAmelCase      ,			padding=__UpperCAmelCase    )
						self.assertTrue(isinstance(batch["""input_ids"""]      ,			torch.Tensor    )    )
						self.assertEqual(batch["""input_ids"""].tolist()      ,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )
						SCREAMING_SNAKE_CASE__									= tokenizer.pad(__UpperCAmelCase      ,			padding=__UpperCAmelCase      ,			return_tensors="""pt"""    )
						self.assertTrue(isinstance(batch["""input_ids"""]      ,			torch.Tensor    )    )
						self.assertEqual(batch["""input_ids"""].tolist()      ,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )

			@require_tf
			def    SCREAMING_SNAKE_CASE			(   self			:  List[Any]    )				->      Dict:
						import tensorflow as tf

						SCREAMING_SNAKE_CASE__									= [{"""input_ids""": tf.constant([0, 1, 2]    )}, {"""input_ids""": tf.constant([0, 1, 2, 3]    )}]
						SCREAMING_SNAKE_CASE__									= BertTokenizer.from_pretrained("""bert-base-cased"""    )

						SCREAMING_SNAKE_CASE__									= tokenizer.pad(__UpperCAmelCase      ,			padding=__UpperCAmelCase    )
						self.assertTrue(isinstance(batch["""input_ids"""]      ,			tf.Tensor    )    )
						self.assertEqual(batch["""input_ids"""].numpy().tolist()      ,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )
						SCREAMING_SNAKE_CASE__									= tokenizer.pad(__UpperCAmelCase      ,			padding=__UpperCAmelCase      ,			return_tensors="""tf"""    )
						self.assertTrue(isinstance(batch["""input_ids"""]      ,			tf.Tensor    )    )
						self.assertEqual(batch["""input_ids"""].numpy().tolist()      ,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]    )

			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  Optional[Any]    )				->      Optional[int]:
						SCREAMING_SNAKE_CASE__									= Tokenizer(WordPiece(unk_token="""[UNK]"""    )    )
						PreTrainedTokenizerFast(tokenizer_object=__UpperCAmelCase    )





			@require_tokenizers
			def    SCREAMING_SNAKE_CASE			(   self			:  str    )				->      int:
						SCREAMING_SNAKE_CASE__									= Tokenizer(WordPiece(unk_token="""[UNK]"""    )    )
						with tempfile.TemporaryDirectory() as tmpdirname:
									bert_tokenizer.save(os.path.join(__UpperCAmelCase      ,			"""tokenizer.json"""    )    )
									PreTrainedTokenizerFast(tokenizer_file=os.path.join(__UpperCAmelCase      ,			"""tokenizer.json"""    )    )


