

"""simple docstring"""



def 			_snake_case  (     UpperCAmelCase_	:       Any      ):





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

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

     A__				      =	{x for x, _ in coordinates}
     if len(lowercase_      ) == 1:
          return F"""x={coordinates[0][0]}"""

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

     A__				      =	len(lowercase_      )

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

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

     A__				      =	0

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

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

     A__				      =	0
     A__				      =	"""f(x)="""

     while count < x:
          A__				      =	solution[count].split("""E"""      )
          if len(lowercase_      ) > 1:
               A__				      =	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]]))









def   UpperCamelCase(   lowercase_				)      ->							str:





  '''simple docstring'''





  return "".join(chr(ord(lowercase_				) + 32				) if """A""" <= char <= """Z""" else char for char in word				)


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

    testmod()