def       __magic_name__(  __UpperCAmelCase		)						->    list[list]:



      '''simple docstring'''

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



      '''simple docstring'''

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     snake_case__				= [
         [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]]))
from .testing import (
    are_the_same_tensors,
    execute_subprocess_async,
    require_bnb,
    require_cpu,
    require_cuda,
    require_huggingface_suite,
    require_mps,
    require_multi_gpu,
    require_multi_xpu,
    require_safetensors,
    require_single_gpu,
    require_single_xpu,
    require_torch_min_version,
    require_tpu,
    require_xpu,
    skip,
    slow,
)
from .training import RegressionDataset, RegressionModel, RegressionModelaXPU


from .scripts import test_script, test_sync, test_ops  # isort: skip