
'''simple docstring'''



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




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				current_set.copy()
   for row_index, row in enumerate(SCREAMING_SNAKE_CASE_						):
      _SCREAMING_SNAKE_CASE      =				row[0]
      for column_index, column in enumerate(SCREAMING_SNAKE_CASE_						):
         if magnitude == 0:
            _SCREAMING_SNAKE_CASE      =				column
            continue
         _SCREAMING_SNAKE_CASE      =				column / magnitude
    # Subtract to cancel term
   _SCREAMING_SNAKE_CASE      =				current_set[0]
   _SCREAMING_SNAKE_CASE      =				[first_row]
   _SCREAMING_SNAKE_CASE      =				current_set[1::]
   for row in current_set:
      _SCREAMING_SNAKE_CASE      =				[]
      # If first term is 0, it is already in form we want, so we preserve it
      if row[0] == 0:
         final_set.append(SCREAMING_SNAKE_CASE_						)
         continue
      for column_index in range(len(SCREAMING_SNAKE_CASE_						)						):
         temp_row.append(first_row[column_index] - row[column_index]						)
      final_set.append(SCREAMING_SNAKE_CASE_						)
   # Create next recursion iteration set
   if len(final_set[0]						) != 3:
      _SCREAMING_SNAKE_CASE      =				final_set[0]
      _SCREAMING_SNAKE_CASE      =				[]
      _SCREAMING_SNAKE_CASE      =				[]
      for row in final_set[1::]:
         current_first_column.append(row[0]						)
         next_iteration.append(row[1::]						)
      _SCREAMING_SNAKE_CASE      =				simplify(SCREAMING_SNAKE_CASE_						)
      for i in range(len(SCREAMING_SNAKE_CASE_						)						):
         resultant[i].insert(0    ,      current_first_column[i]						)
      resultant.insert(0    ,      SCREAMING_SNAKE_CASE_						)
      _SCREAMING_SNAKE_CASE      =				resultant
   return final_set
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     list:




   """simple docstring"""
   if len(SCREAMING_SNAKE_CASE_						) == 0:
      raise IndexError("""solve_simultaneous() requires n lists of length n+1"""						)
   _SCREAMING_SNAKE_CASE      =				len(SCREAMING_SNAKE_CASE_						) + 1
   if any(len(SCREAMING_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(SCREAMING_SNAKE_CASE_    ,      (int, float)						) for column in row						):
         raise ValueError("""solve_simultaneous() requires lists of integers"""						)
   if len(SCREAMING_SNAKE_CASE_						) == 1:
      return [equations[0][-1] / equations[0][0]]
   _SCREAMING_SNAKE_CASE      =				equations.copy()
   if any(0 in row for row in data_set						):
      _SCREAMING_SNAKE_CASE      =				data_set.copy()
      _SCREAMING_SNAKE_CASE      =				[]
      for row_index, row in enumerate(SCREAMING_SNAKE_CASE_						):
         if 0 not in row:
            _SCREAMING_SNAKE_CASE      =				data_set.pop(SCREAMING_SNAKE_CASE_						)
            break
      if not full_row:
         raise ValueError("""solve_simultaneous() requires at least 1 full equation"""						)
      data_set.insert(0    ,      SCREAMING_SNAKE_CASE_						)
   _SCREAMING_SNAKE_CASE      =				data_set.copy()
   _SCREAMING_SNAKE_CASE      =				simplify(SCREAMING_SNAKE_CASE_						)
   _SCREAMING_SNAKE_CASE      =				simplified[::-1]
   _SCREAMING_SNAKE_CASE      =				[]
   for row in simplified:
      _SCREAMING_SNAKE_CASE      =				row[-1]
      if not solutions:
         if row[-2] == 0:
            solutions.append(0						)
            continue
         solutions.append(current_solution / row[-2]						)
         continue
      _SCREAMING_SNAKE_CASE      =				row.copy()[: len(SCREAMING_SNAKE_CASE_						) - 1 :]
      while temp_row[0] == 0:
         temp_row.pop(0						)
      if len(SCREAMING_SNAKE_CASE_						) == 0:
         solutions.append(0						)
         continue
      _SCREAMING_SNAKE_CASE      =				temp_row[1::]
      _SCREAMING_SNAKE_CASE      =				temp_row[::-1]
      for column_index, column in enumerate(SCREAMING_SNAKE_CASE_						):
         current_solution -= column * solutions[column_index]
      solutions.append(SCREAMING_SNAKE_CASE_						)
   _SCREAMING_SNAKE_CASE      =				[]
   for item in solutions:
      final.append(float(round(SCREAMING_SNAKE_CASE_    ,      5						)						)						)
   return final[::-1]


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     UpperCamelCase__      :		Union[str, Any]       							=  [
         [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'''



def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     int:




   """simple docstring"""

   if not isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						):
      raise ValueError("""multiplicative_persistence() only accepts integral values"""						)
   if num < 0:
      raise ValueError("""multiplicative_persistence() does not accept negative values"""						)

   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _SCREAMING_SNAKE_CASE      =				[int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _SCREAMING_SNAKE_CASE      =				1
      for i in range(0    ,      len(SCREAMING_SNAKE_CASE_						)						):
         total *= numbers[i]

      _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     int:




   """simple docstring"""

   if not isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						):
      raise ValueError("""additive_persistence() only accepts integral values"""						)
   if num < 0:
      raise ValueError("""additive_persistence() does not accept negative values"""						)

   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _SCREAMING_SNAKE_CASE      =				[int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _SCREAMING_SNAKE_CASE      =				0
      for i in range(0    ,      len(SCREAMING_SNAKE_CASE_						)						):
         total += numbers[i]

      _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps


if __name__ == "__main__":
     import doctest

     doctest.testmod()






