code: 
  
  
  
  
  
  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.'	)
  
  		lowerCamelCase_  :    Dict   	=			{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.'	)
  
  		lowerCamelCase_  :    Dict   	=			len(lowerCAmelCase__	)
  
  		lowerCamelCase_  :    List[str]   	=			0
  		lowerCamelCase_  :    list[list[float]]   	=			[]
  		# put the x and x to the power values in a matrix
  		while count_of_line < x:
  				lowerCamelCase_  :    Union[str, Any]   	=			0
  				lowerCamelCase_  :    Optional[Any]   	=			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(lowerCAmelCase__	)
  				count_of_line += 1
  
  		lowerCamelCase_  :    Any   	=			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_  :    Optional[Any]   	=			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_  :    str   	=			0
  		# make solutions
  		lowerCamelCase_  :    list[str]   	=			[]
  		while count < x:
  				solution.append(str(vector[count] / matrix[count][count]	)	)
  				count += 1
  
  		lowerCamelCase_  :    Optional[int]   	=			0
  		lowerCamelCase_  :    Union[str, Any]   	=			'f(x)='
  
  		while count < x:
  				lowerCamelCase_  :    list[str]   	=			solution[count].split('E'	)
  				if len(lowerCAmelCase__	) > 1:
  						lowerCamelCase_  :    List[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]]))
  
style_context: 
  
  
  
  
  
  import unittest
  
  import requests
  
  from transformers import MODEL_FOR_VISION_2_SEQ_MAPPING, TF_MODEL_FOR_VISION_2_SEQ_MAPPING, is_vision_available
  from transformers.pipelines import pipeline
  from transformers.testing_utils import (
      is_pipeline_test,
      is_torch_available,
      require_tf,
      require_torch,
      require_vision,
      slow,
  )
  
  from .test_pipelines_common import ANY
  
  
  if is_torch_available():
  		from transformers.pytorch_utils import is_torch_greater_or_equal_than_1_11
  else:
  		_lowercase		:     Dict 					=False
  
  
  if is_vision_available():
  		from PIL import Image
  else:
  
  
  
  
  
  
  		class 	UpperCamelCase_     :
  
  
  
  							@staticmethod
  							def      __a    (		*lowerCamelCase    :    Any					,			**lowerCamelCase    :    List[Any]	):
  									pass
  
  
  
  
  
  
  @is_pipeline_test
  @require_vision
  class 	UpperCamelCase_     (     unittest.TestCase       ):
  					_a			:	int							=				MODEL_FOR_VISION_2_SEQ_MAPPING
  					_a			:	int							=				TF_MODEL_FOR_VISION_2_SEQ_MAPPING
  
  
  
  					def      __a    (		self    :    int					,			lowerCamelCase    :    Union[str, Any]					,			lowerCamelCase    :    Optional[int]					,			lowerCamelCase    :    Union[str, Any]	):
  							lowerCamelCase_  :    List[str]   	=			pipeline('image-to-text'					,			model=lowerCamelCase					,			tokenizer=lowerCamelCase					,			image_processor=lowerCamelCase	)
  							lowerCamelCase_  :    str   	=			[
  							    Image.open('./tests/fixtures/tests_samples/COCO/000000039769.png'	),
  							    './tests/fixtures/tests_samples/COCO/000000039769.png',
  							]
  							return pipe, examples
  
  
  
  					def      __a    (		self    :    List[Any]					,			lowerCamelCase    :    Any					,			lowerCamelCase    :    List[str]	):
  							lowerCamelCase_  :    str   	=			pipe(lowerCamelCase	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        [{'generated_text': ANY(lowerCamelCase	)}],
  							        [{'generated_text': ANY(lowerCamelCase	)}],
  							    ]					,			)
  
  
  
  					@require_tf
  					def      __a    (		self    :    Union[str, Any]	):
  							lowerCamelCase_  :    Tuple   	=			pipeline('image-to-text'					,			model='hf-internal-testing/tiny-random-vit-gpt2'					,			framework='tf'	)
  							lowerCamelCase_  :    Optional[int]   	=			'./tests/fixtures/tests_samples/COCO/000000039769.png'
  
  							lowerCamelCase_  :    Optional[int]   	=			pipe(lowerCamelCase	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        {
  							            'generated_text': 'growthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthGOGO'
  							        },
  							    ]					,			)
  
  							lowerCamelCase_  :    List[Any]   	=			pipe([image, image]	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        [
  							            {
  							                'generated_text': 'growthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthGOGO'
  							            }
  							        ],
  							        [
  							            {
  							                'generated_text': 'growthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthGOGO'
  							            }
  							        ],
  							    ]					,			)
  
  							lowerCamelCase_  :    str   	=			pipe(lowerCamelCase					,			max_new_tokens=1	)
  							self.assertEqual(
  							    lowerCamelCase					,			[{'generated_text': 'growth'}]					,			)
  
  
  
  					@require_torch
  					def      __a    (		self    :    Tuple	):
  							lowerCamelCase_  :    Union[str, Any]   	=			pipeline('image-to-text'					,			model='hf-internal-testing/tiny-random-vit-gpt2'	)
  							lowerCamelCase_  :    Any   	=			'./tests/fixtures/tests_samples/COCO/000000039769.png'
  
  							lowerCamelCase_  :    int   	=			pipe(lowerCamelCase	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        {
  							            'generated_text': 'growthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthGOGO'
  							        },
  							    ]					,			)
  
  							lowerCamelCase_  :    Tuple   	=			pipe([image, image]	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        [
  							            {
  							                'generated_text': 'growthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthGOGO'
  							            }
  							        ],
  							        [
  							            {
  							                'generated_text': 'growthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthgrowthGOGO'
  							            }
  							        ],
  							    ]					,			)
  
  
  
  					@require_torch
  					def      __a    (		self    :    Dict	):
  							lowerCamelCase_  :    Any   	=			pipeline('image-to-text'					,			model='hf-internal-testing/tiny-random-BlipForConditionalGeneration'	)
  							lowerCamelCase_  :    List[Any]   	=			'./tests/fixtures/tests_samples/COCO/000000039769.png'
  							lowerCamelCase_  :    List[Any]   	=			'a photo of'
  
  							lowerCamelCase_  :    Dict   	=			pipe(lowerCamelCase					,			prompt=lowerCamelCase	)
  							self.assertTrue(outputs[0]['generated_text'].startswith(lowerCamelCase	)	)
  
  
  
  					@slow
  					@require_torch
  					def      __a    (		self    :    Union[str, Any]	):
  							lowerCamelCase_  :    List[str]   	=			pipeline('image-to-text'					,			model='ydshieh/vit-gpt2-coco-en'	)
  							lowerCamelCase_  :    Any   	=			'./tests/fixtures/tests_samples/COCO/000000039769.png'
  
  							lowerCamelCase_  :    str   	=			pipe(lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'a cat laying on a blanket next to a cat laying on a bed '}]	)
  
  							lowerCamelCase_  :    Union[str, Any]   	=			pipe([image, image]	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        [{'generated_text': 'a cat laying on a blanket next to a cat laying on a bed '}],
  							        [{'generated_text': 'a cat laying on a blanket next to a cat laying on a bed '}],
  							    ]					,			)
  
  
  
  					@slow
  					@require_torch
  					def      __a    (		self    :    List[Any]	):
  							lowerCamelCase_  :    int   	=			pipeline('image-to-text'					,			model='Salesforce/blip-image-captioning-base'	)
  							lowerCamelCase_  :    Tuple   	=			'https://huggingface.co/datasets/sayakpaul/sample-datasets/resolve/main/pokemon.png'
  							lowerCamelCase_  :    List[Any]   	=			Image.open(requests.get(lowerCamelCase					,			stream=lowerCamelCase	).raw	)
  
  							lowerCamelCase_  :    Optional[Any]   	=			pipe(lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'a pink pokemon pokemon with a blue shirt and a blue shirt'}]	)
  
  
  
  					@slow
  					@require_torch
  					def      __a    (		self    :    List[str]	):
  							lowerCamelCase_  :    Optional[Any]   	=			pipeline('image-to-text'					,			model='microsoft/git-base-coco'	)
  							lowerCamelCase_  :    str   	=			'https://huggingface.co/datasets/sayakpaul/sample-datasets/resolve/main/pokemon.png'
  							lowerCamelCase_  :    Dict   	=			Image.open(requests.get(lowerCamelCase					,			stream=lowerCamelCase	).raw	)
  
  							lowerCamelCase_  :    Optional[int]   	=			pipe(lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'a cartoon of a purple character.'}]	)
  
  
  
  					@slow
  					@require_torch
  					def      __a    (		self    :    List[str]	):
  							lowerCamelCase_  :    List[Any]   	=			pipeline('image-to-text'					,			model='Salesforce/blip-image-captioning-base'	)
  							lowerCamelCase_  :    int   	=			'https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/ai2d-demo.jpg'
  							lowerCamelCase_  :    List[str]   	=			Image.open(requests.get(lowerCamelCase					,			stream=lowerCamelCase	).raw	)
  
  							lowerCamelCase_  :    int   	=			'a photography of'
  
  							lowerCamelCase_  :    Tuple   	=			pipe(lowerCamelCase					,			prompt=lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'a photography of a volcano'}]	)
  
  							with self.assertRaises(lowerCamelCase	):
  									lowerCamelCase_  :    Union[str, Any]   	=			pipe([image, image]					,			prompt=[prompt, prompt]	)
  
  
  
  					@slow
  					@require_torch
  					def      __a    (		self    :    int	):
  							lowerCamelCase_  :    Optional[int]   	=			pipeline('image-to-text'					,			model='microsoft/git-base-coco'	)
  							lowerCamelCase_  :    int   	=			'https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/ai2d-demo.jpg'
  							lowerCamelCase_  :    Optional[Any]   	=			Image.open(requests.get(lowerCamelCase					,			stream=lowerCamelCase	).raw	)
  
  							lowerCamelCase_  :    Optional[int]   	=			'a photo of a'
  
  							lowerCamelCase_  :    Optional[int]   	=			pipe(lowerCamelCase					,			prompt=lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'a photo of a tent with a tent and a tent in the background.'}]	)
  
  							with self.assertRaises(lowerCamelCase	):
  									lowerCamelCase_  :    List[Any]   	=			pipe([image, image]					,			prompt=[prompt, prompt]	)
  
  
  
  					@unittest.skipIf(
  					    not is_torch_greater_or_equal_than_1_11					,			reason='`Pix2StructImageProcessor` requires `torch>=1.11.0`.'	)
  					@slow
  					@require_torch
  					def      __a    (		self    :    Any	):
  							lowerCamelCase_  :    Union[str, Any]   	=			pipeline('image-to-text'					,			model='google/pix2struct-ai2d-base'	)
  							lowerCamelCase_  :    List[str]   	=			'https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/ai2d-demo.jpg'
  							lowerCamelCase_  :    Tuple   	=			Image.open(requests.get(lowerCamelCase					,			stream=lowerCamelCase	).raw	)
  
  							lowerCamelCase_  :    str   	=			'What does the label 15 represent? (1) lava (2) core (3) tunnel (4) ash cloud'
  
  							lowerCamelCase_  :    Union[str, Any]   	=			pipe(lowerCamelCase					,			prompt=lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'ash cloud'}]	)
  
  							with self.assertRaises(lowerCamelCase	):
  									lowerCamelCase_  :    Optional[Any]   	=			pipe([image, image]					,			prompt=[prompt, prompt]	)
  
  
  
  
  
  					@slow
  					@require_tf
  					def      __a    (		self    :    Dict	):
  							lowerCamelCase_  :    List[str]   	=			pipeline('image-to-text'					,			model='ydshieh/vit-gpt2-coco-en'					,			framework='tf'	)
  							lowerCamelCase_  :    Dict   	=			'./tests/fixtures/tests_samples/COCO/000000039769.png'
  
  							lowerCamelCase_  :    Optional[Any]   	=			pipe(lowerCamelCase	)
  							self.assertEqual(lowerCamelCase					,			[{'generated_text': 'a cat laying on a blanket next to a cat laying on a bed '}]	)
  
  							lowerCamelCase_  :    List[Any]   	=			pipe([image, image]	)
  							self.assertEqual(
  							    lowerCamelCase					,			[
  							        [{'generated_text': 'a cat laying on a blanket next to a cat laying on a bed '}],
  							        [{'generated_text': 'a cat laying on a blanket next to a cat laying on a bed '}],
  							    ]					,			)
  