




"""simple docstring"""


def 					UpperCAmelCase__       (snake_case__							:					list[list]    ):
  """simple docstring"""

  _snake_case							:		Tuple								=  current_set.copy()
  for row_index, row in enumerate(snake_case__    ):
    _snake_case							:		Tuple								=  row[0]
    for column_index, column in enumerate(snake_case__    ):
      if magnitude == 0:
        _snake_case							:		List[Any]								=  column
        continue
      _snake_case							:		Tuple								=  column / magnitude
    # Subtract to cancel term
  _snake_case							:		Optional[Any]								=  current_set[0]
  _snake_case							:		List[str]								=  [first_row]
  _snake_case							:		str								=  current_set[1::]
  for row in current_set:
    _snake_case							:		int								=  []
    # If first term is 0, it is already in form we want, so we preserve it
    if row[0] == 0:
      final_set.append(snake_case__    )
      continue
    for column_index in range(len(snake_case__    )    ):
      temp_row.append(first_row[column_index] - row[column_index]    )
    final_set.append(snake_case__    )
  # Create next recursion iteration set
  if len(final_set[0]    ) != 3:
    _snake_case							:		Union[str, Any]								=  final_set[0]
    _snake_case							:		int								=  []
    _snake_case							:		str								=  []
    for row in final_set[1::]:
      current_first_column.append(row[0]    )
      next_iteration.append(row[1::]    )
    _snake_case							:		Optional[Any]								=  simplify(snake_case__    )
    for i in range(len(snake_case__    )    ):
      resultant[i].insert(0		,   current_first_column[i]    )
    resultant.insert(0		,   snake_case__    )
    _snake_case							:		List[str]								=  resultant
  return final_set


def 					UpperCAmelCase__       (snake_case__							:					list[list]    ):
  """simple docstring"""

  if len(snake_case__    ) == 0:
    raise IndexError("""solve_simultaneous() requires n lists of length n+1"""    )
  _snake_case							:		Union[str, Any]								=  len(snake_case__    ) + 1
  if any(len(snake_case__    ) != _length for item in equations    ):
    raise IndexError("""solve_simultaneous() requires n lists of length n+1"""    )
  for row in equations:
    if any(not isinstance(snake_case__		,   (int, float)    ) for column in row    ):
      raise ValueError("""solve_simultaneous() requires lists of integers"""    )
  if len(snake_case__    ) == 1:
    return [equations[0][-1] / equations[0][0]]
  _snake_case							:		Dict								=  equations.copy()
  if any(0 in row for row in data_set    ):
    _snake_case							:		Any								=  data_set.copy()
    _snake_case							:		int								=  []
    for row_index, row in enumerate(snake_case__    ):
      if 0 not in row:
        _snake_case							:		Optional[int]								=  data_set.pop(snake_case__    )
        break
    if not full_row:
      raise ValueError("""solve_simultaneous() requires at least 1 full equation"""    )
    data_set.insert(0		,   snake_case__    )
  _snake_case							:		str								=  data_set.copy()
  _snake_case							:		Union[str, Any]								=  simplify(snake_case__    )
  _snake_case							:		int								=  simplified[::-1]
  _snake_case							:		list								=  []
  for row in simplified:
    _snake_case							:		int								=  row[-1]
    if not solutions:
      if row[-2] == 0:
        solutions.append(0    )
        continue
      solutions.append(current_solution / row[-2]    )
      continue
    _snake_case							:		Dict								=  row.copy()[: len(snake_case__    ) - 1 :]
    while temp_row[0] == 0:
      temp_row.pop(0    )
    if len(snake_case__    ) == 0:
      solutions.append(0    )
      continue
    _snake_case							:		Optional[Any]								=  temp_row[1::]
    _snake_case							:		Dict								=  temp_row[::-1]
    for column_index, column in enumerate(snake_case__    ):
      current_solution -= column * solutions[column_index]
    solutions.append(snake_case__    )
  _snake_case							:		str								=  []
  for item in solutions:
    final.append(float(round(snake_case__		,   5    )    )    )
  return final[::-1]


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     A_						=				[
         [2, 1, 1, 1, 1, 4],
         [1, 2, 1, 1, 1, 5],
         [1, 1, 2, 1, 1, 6],
         [1, 1, 1, 2, 1, 7],
         [1, 1, 1, 1, 2, 8],
     ]
     print(solve_simultaneous(eq))
     print(solve_simultaneous([[4, 2]]))








"""simple docstring"""


from ..utils import DummyObject, requires_backends






class 					lowercase(     metaclass=__a ):







 '''simple docstring'''





 lowercase__ 					=					["note_seq"]


 def __init__(				self:		Dict,      *a_:		Union[str, Any],      **a_:		List[str]		):




   '''simple docstring'''



   requires_backends(self,      ["""note_seq"""]		)


 @classmethod
 def  UpperCamelCase_   (				cls:		Optional[int],      *a_:		Any,      **a_:		Optional[Any]		):




   '''simple docstring'''



   requires_backends(cls,      ["""note_seq"""]		)


 @classmethod
 def  UpperCamelCase_   (				cls:		Tuple,      *a_:		Optional[Any],      **a_:		List[str]		):




   '''simple docstring'''



   requires_backends(cls,      ["""note_seq"""]		)


