

def        _lowercase  (					a_					:       list[list[int]]					)					->						str:




					'''simple docstring'''







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

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

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

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

					__magic_name__				=     len(a_					)

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

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

					__magic_name__				=     0

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

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

					__magic_name__				=     0
					__magic_name__				=     'f(x)='

					while count < x:
										__magic_name__				=     solution[count].split('E'					)
										if len(a_					) > 1:
															__magic_name__				=     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 __future__ import annotations

from collections.abc import Iterator
from typing import Any

class 					__UpperCamelCase					:







	def __init__( self:			Optional[Any]	,			__UpperCamelCase:			Any   ):

						'''simple docstring'''





						__magic_name__				=     data
						__magic_name__				=     None







	def __str__( self:			Optional[int]   ):

						'''simple docstring'''





						return F'{self.data}'




class 					__UpperCamelCase					:







	def __init__( self:			List[Any]   ):

						'''simple docstring'''





						__magic_name__				=     None
						__magic_name__				=     None







	def __iter__( self:			str   ):

						'''simple docstring'''





						__magic_name__				=     self.front
						while node:
											yield node.data
											__magic_name__				=     node.next







	def __len__( self:			Any   ):

						'''simple docstring'''





						return len(tuple(iter(self   )   )   )







	def __str__( self:			List[str]   ):

						'''simple docstring'''





						return " <- ".join(str(__UpperCamelCase   ) for item in self   )







	def 						_SCREAMING_SNAKE_CASE				( self:			Any   ):

						'''simple docstring'''





						return len(self   ) == 0







	def 						_SCREAMING_SNAKE_CASE				( self:			Any	,			__UpperCamelCase:			Any   ):

						'''simple docstring'''





						__magic_name__				=     Node(__UpperCamelCase   )
						if self.is_empty():
											__magic_name__				=     __magic_name__				=     node
						else:
											assert isinstance(self.rear	,			__UpperCamelCase   )
											__magic_name__				=     node
											__magic_name__				=     node







	def 						_SCREAMING_SNAKE_CASE				( self:			Any   ):

						'''simple docstring'''





						if self.is_empty():
											raise IndexError('dequeue from empty queue'   )
						assert isinstance(self.front	,			__UpperCamelCase   )
						__magic_name__				=     self.front
						__magic_name__				=     self.front.next
						if self.front is None:
											__magic_name__				=     None
						return node.data







	def 						_SCREAMING_SNAKE_CASE				( self:			Tuple   ):

						'''simple docstring'''





						__magic_name__				=     __magic_name__				=     None


if __name__ == "__main__":
						from doctest import testmod

						testmod()




