def        SCREAMING_SNAKE_CASE_					(						snake_case__							)					->     str:
							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.'''							)

							lowerCAmelCase     		=		{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.'''							)

							lowerCAmelCase     		=		len(snake_case__							)

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

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

							lowerCAmelCase     		=		0

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

							lowerCAmelCase     		=		0
							lowerCAmelCase     		=		'''f(x)='''

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




import warnings

from .generation import FlaxGenerationMixin




class        lowercase_  (  UpperCamelCase_						):



	"""simple docstring"""





	warnings.warn(
	    """Importing `FlaxGenerationMixin` from `src/transformers/generation_flax_utils.py` is deprecated and will """
	    """be removed in Transformers v5. Import as `from transformers import FlaxGenerationMixin` instead."""				,					UpperCamelCase_				,					)



