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

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

	lowercase					  =   {x for x, _ in coordinates}
	if len(__SCREAMING_SNAKE_CASE							) == 1:
		return F'''x={coordinates[0][0]}'''

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

	lowercase					  =   len(__SCREAMING_SNAKE_CASE							)

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

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

	lowercase					  =   0

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

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

	lowercase					  =   0
	lowercase					  =   'f(x)='

	while count < x:
		lowercase					  =   solution[count].split('E'							)
		if len(__SCREAMING_SNAKE_CASE							) > 1:
			lowercase					  =   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]]))



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase     				=			{
    '''configuration_dpr''': ['''DPR_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''DPRConfig'''],
    '''tokenization_dpr''': [
        '''DPRContextEncoderTokenizer''',
        '''DPRQuestionEncoderTokenizer''',
        '''DPRReaderOutput''',
        '''DPRReaderTokenizer''',
    ],
}


try:
	if not is_tokenizers_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase     				=			[
	    '''DPRContextEncoderTokenizerFast''',
	    '''DPRQuestionEncoderTokenizerFast''',
	    '''DPRReaderTokenizerFast''',
	]

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase     				=			[
	    '''DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''DPRContextEncoder''',
	    '''DPRPretrainedContextEncoder''',
	    '''DPRPreTrainedModel''',
	    '''DPRPretrainedQuestionEncoder''',
	    '''DPRPretrainedReader''',
	    '''DPRQuestionEncoder''',
	    '''DPRReader''',
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase     				=			[
	    '''TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST''',
	    '''TFDPRContextEncoder''',
	    '''TFDPRPretrainedContextEncoder''',
	    '''TFDPRPretrainedQuestionEncoder''',
	    '''TFDPRPretrainedReader''',
	    '''TFDPRQuestionEncoder''',
	    '''TFDPRReader''',
	]


if TYPE_CHECKING:
	from .configuration_dpr import DPR_PRETRAINED_CONFIG_ARCHIVE_MAP, DPRConfig
	from .tokenization_dpr import (
	    DPRContextEncoderTokenizer,
	    DPRQuestionEncoderTokenizer,
	    DPRReaderOutput,
	    DPRReaderTokenizer,
	)

	try:
		if not is_tokenizers_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_dpr_fast import (
		    DPRContextEncoderTokenizerFast,
		    DPRQuestionEncoderTokenizerFast,
		    DPRReaderTokenizerFast,
		)

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_dpr import (
		    DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    DPRContextEncoder,
		    DPRPretrainedContextEncoder,
		    DPRPreTrainedModel,
		    DPRPretrainedQuestionEncoder,
		    DPRPretrainedReader,
		    DPRQuestionEncoder,
		    DPRReader,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_dpr import (
		    TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TFDPRContextEncoder,
		    TFDPRPretrainedContextEncoder,
		    TFDPRPretrainedQuestionEncoder,
		    TFDPRPretrainedReader,
		    TFDPRQuestionEncoder,
		    TFDPRReader,
		)

else:
	import sys

	UpperCAmelCase     				=			_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

