





def      lowerCAmelCase_ (       __a		)     ->		list[list]:







  """simple docstring"""





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





def      lowerCAmelCase_ (       __a		)     ->		list:







  """simple docstring"""





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








import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
__A									=				"."


if __name__ == "__main__":
     __A									=				os.path.join(REPO_PATH, "utils/documentation_tests.txt")
     __A									=				[]
     __A									=				[]
     with open(doctest_file_path) as fp:
          for line in fp:
               __A									=				line.strip()
               __A									=				os.path.join(REPO_PATH, line)
               if not (os.path.isfile(path) or os.path.isdir(path)):
                    non_existent_paths.append(line)
               all_paths.append(path)
     if len(non_existent_paths) > 0:
          __A									=				"\n".join(non_existent_paths)
          raise ValueError(f'`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}')
     if all_paths != sorted(all_paths):
          raise ValueError("Files in `utils/documentation_tests.txt` are not in alphabetical order.")

