code: 
  
  
  
  '''simple docstring'''
  
  
  
  def _lowercase   (  __A       ):
  
  
  
  	'''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."""       )
  
  	__UpperCamelCase				      =  {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."""       )
  
  	__UpperCamelCase				      =  len(__A       )
  
  	__UpperCamelCase				      =  0
  	__UpperCamelCase				      =  []
  	# put the x and x to the power values in a matrix
  	while count_of_line < x:
  		__UpperCamelCase				      =  0
  		__UpperCamelCase				      =  coordinates[count_of_line][0]
  		__UpperCamelCase				      =  []
  		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
  
  	__UpperCamelCase				      =  0
  	# put the y values into a vector
  	__UpperCamelCase				      =  []
  	while count_of_line < x:
  		vector.append(coordinates[count_of_line][1]       )
  		count_of_line += 1
  
  	__UpperCamelCase				      =  0
  
  	while count < x:
  		__UpperCamelCase				      =  0
  		while zahlen < x:
  			if count == zahlen:
  				zahlen += 1
  			if zahlen == x:
  				break
  			__UpperCamelCase				      =  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
  
  	__UpperCamelCase				      =  0
  	# make solutions
  	__UpperCamelCase				      =  []
  	while count < x:
  		solution.append(str(vector[count] / matrix[count][count]       )       )
  		count += 1
  
  	__UpperCamelCase				      =  0
  	__UpperCamelCase				      =  'f(x)='
  
  	while count < x:
  		__UpperCamelCase				      =  solution[count].split("""E"""       )
  		if len(__A       ) > 1:
  			__UpperCamelCase				      =  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]]))
  
  
  
  
  
  
style_context: 
  
  
  
  '''simple docstring'''
  
  
  
  from .stack import Stack
  
  
  
  
  
  
  
  def _lowercase   (  __A       ):
  
  
  
   '''simple docstring'''
  
  
  
   __UpperCamelCase				      =  Stack()
   __UpperCamelCase				      =  {"""(""": """)""", """[""": """]""", """{""": """}"""}
   for bracket in parentheses:
    if bracket in bracket_pairs:
     stack.push(__A       )
    elif bracket in (")", "]", "}"):
     if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
      return False
   return stack.is_empty()
  
  
  if __name__ == "__main__":
   from doctest import testmod
  
   testmod()
  
   a__						:			List[Any]										=			['((()))', '((())', '(()))']
   print('Balanced parentheses demonstration:\n')
   for example in examples:
    a__						:			int										=			'' if balanced_parentheses(example) else 'not '
    print(f'''{example} is {not_str}balanced''')
  
  
  
  
  
  