


def   _UpperCamelCase				(						lowerCAmelCase_   )						->list[list]:
   UpperCAmelCase							=     current_set.copy()
   for row_index, row in enumerate(lowerCAmelCase_   ):
      UpperCAmelCase							=     row[0]
      for column_index, column in enumerate(lowerCAmelCase_   ):
         if magnitude == 0:
            UpperCAmelCase							=     column
            continue
         UpperCAmelCase							=     column / magnitude
    # Subtract to cancel term
   UpperCAmelCase							=     current_set[0]
   UpperCAmelCase							=     [first_row]
   UpperCAmelCase							=     current_set[1::]
   for row in current_set:
      UpperCAmelCase							=     []
      # If first term is 0, it is already in form we want, so we preserve it
      if row[0] == 0:
         final_set.append(lowerCAmelCase_   )
         continue
      for column_index in range(len(lowerCAmelCase_   )   ):
         temp_row.append(first_row[column_index] - row[column_index]   )
      final_set.append(lowerCAmelCase_   )
   # Create next recursion iteration set
   if len(final_set[0]   ) != 3:
      UpperCAmelCase							=     final_set[0]
      UpperCAmelCase							=     []
      UpperCAmelCase							=     []
      for row in final_set[1::]:
         current_first_column.append(row[0]   )
         next_iteration.append(row[1::]   )
      UpperCAmelCase							=     simplify(lowerCAmelCase_   )
      for i in range(len(lowerCAmelCase_   )   ):
         resultant[i].insert(0  ,						current_first_column[i]   )
      resultant.insert(0  ,						lowerCAmelCase_   )
      UpperCAmelCase							=     resultant
   return final_set
def   _UpperCamelCase				(						lowerCAmelCase_   )						->list:
   if len(lowerCAmelCase_   ) == 0:
      raise IndexError("""solve_simultaneous() requires n lists of length n+1"""   )
   UpperCAmelCase							=     len(lowerCAmelCase_   ) + 1
   if any(len(lowerCAmelCase_   ) != _length for item in equations   ):
      raise IndexError("""solve_simultaneous() requires n lists of length n+1"""   )
   for row in equations:
      if any(not isinstance(lowerCAmelCase_  ,						(int, float)   ) for column in row   ):
         raise ValueError("""solve_simultaneous() requires lists of integers"""   )
   if len(lowerCAmelCase_   ) == 1:
      return [equations[0][-1] / equations[0][0]]
   UpperCAmelCase							=     equations.copy()
   if any(0 in row for row in data_set   ):
      UpperCAmelCase							=     data_set.copy()
      UpperCAmelCase							=     []
      for row_index, row in enumerate(lowerCAmelCase_   ):
         if 0 not in row:
            UpperCAmelCase							=     data_set.pop(lowerCAmelCase_   )
            break
      if not full_row:
         raise ValueError("""solve_simultaneous() requires at least 1 full equation"""   )
      data_set.insert(0  ,						lowerCAmelCase_   )
   UpperCAmelCase							=     data_set.copy()
   UpperCAmelCase							=     simplify(lowerCAmelCase_   )
   UpperCAmelCase							=     simplified[::-1]
   UpperCAmelCase							=     []
   for row in simplified:
      UpperCAmelCase							=     row[-1]
      if not solutions:
         if row[-2] == 0:
            solutions.append(0   )
            continue
         solutions.append(current_solution / row[-2]   )
         continue
      UpperCAmelCase							=     row.copy()[: len(lowerCAmelCase_   ) - 1 :]
      while temp_row[0] == 0:
         temp_row.pop(0   )
      if len(lowerCAmelCase_   ) == 0:
         solutions.append(0   )
         continue
      UpperCAmelCase							=     temp_row[1::]
      UpperCAmelCase							=     temp_row[::-1]
      for column_index, column in enumerate(lowerCAmelCase_   ):
         current_solution -= column * solutions[column_index]
      solutions.append(lowerCAmelCase_   )
   UpperCAmelCase							=     []
   for item in solutions:
      final.append(float(round(lowerCAmelCase_  ,						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 pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu






@require_cpu
class   __lowercase				(  unittest.TestCase  ):





      def        _lowercase				(		self						:					Any       )    ->   Union[str, Any]:






         """simple docstring"""







         UpperCAmelCase							=     torch.nn.Linear(1_0					,       1_0       )
         UpperCAmelCase							=     torch.optim.SGD(model.parameters()					,       0.1       )
         UpperCAmelCase							=     Accelerator()
         UpperCAmelCase							=     accelerator.prepare(__lowerCamelCase       )
         try:
            pickle.loads(pickle.dumps(__lowerCamelCase       )       )
         except Exception as e:
            self.fail(F"""Accelerated optimizer pickling failed with {e}"""       )
         AcceleratorState._reset_state()



