





def 			_a		(       UpperCAmelCase	)							->							Optional[int]:







   """simple docstring"""
   lowerCamelCase__  :		str     =				current_set.copy()
   for row_index, row in enumerate(UpperCAmelCase	):
      lowerCamelCase__  :		Tuple     =				row[0]
      for column_index, column in enumerate(UpperCAmelCase	):
         if magnitude == 0:
            lowerCamelCase__  :		Optional[Any]     =				column
            continue
         lowerCamelCase__  :		Union[str, Any]     =				column / magnitude
    # Subtract to cancel term
   lowerCamelCase__  :		List[str]     =				current_set[0]
   lowerCamelCase__  :		List[Any]     =				[first_row]
   lowerCamelCase__  :		Any     =				current_set[1::]
   for row in current_set:
      lowerCamelCase__  :		str     =				[]
      # 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__  :		Tuple     =				final_set[0]
      lowerCamelCase__  :		List[Any]     =				[]
      lowerCamelCase__  :		int     =				[]
      for row in final_set[1::]:
         current_first_column.append(row[0]	)
         next_iteration.append(row[1::]	)
      lowerCamelCase__  :		int     =				simplify(UpperCAmelCase	)
      for i in range(len(UpperCAmelCase	)	):
         resultant[i].insert(0     ,    current_first_column[i]	)
      resultant.insert(0     ,    UpperCAmelCase	)
      lowerCamelCase__  :		Any     =				resultant
   return final_set



def 			_a		(       UpperCAmelCase	)							->							Tuple:







   """simple docstring"""






   if len(UpperCAmelCase	) == 0:
      raise IndexError('''solve_simultaneous() requires n lists of length n+1'''	)
   lowerCamelCase__  :		int     =				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__  :		List[Any]     =				equations.copy()
   if any(0 in row for row in data_set	):
      lowerCamelCase__  :		Any     =				data_set.copy()
      lowerCamelCase__  :		List[str]     =				[]
      for row_index, row in enumerate(UpperCAmelCase	):
         if 0 not in row:
            lowerCamelCase__  :		Any     =				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__  :		Tuple     =				data_set.copy()
   lowerCamelCase__  :		Optional[Any]     =				simplify(UpperCAmelCase	)
   lowerCamelCase__  :		Optional[Any]     =				simplified[::-1]
   lowerCamelCase__  :		list     =				[]
   for row in simplified:
      lowerCamelCase__  :		int     =				row[-1]
      if not solutions:
         if row[-2] == 0:
            solutions.append(0	)
            continue
         solutions.append(current_solution / row[-2]	)
         continue
      lowerCamelCase__  :		Union[str, Any]     =				row.copy()[: len(UpperCAmelCase	) - 1 :]
      while temp_row[0] == 0:
         temp_row.pop(0	)
      if len(UpperCAmelCase	) == 0:
         solutions.append(0	)
         continue
      lowerCamelCase__  :		Dict     =				temp_row[1::]
      lowerCamelCase__  :		Any     =				temp_row[::-1]
      for column_index, column in enumerate(UpperCAmelCase	):
         current_solution -= column * solutions[column_index]
      solutions.append(UpperCAmelCase	)
   lowerCamelCase__  :		List[Any]     =				[]
   for item in solutions:
      final.append(float(round(UpperCAmelCase     ,    5	)	)	)
   return final[::-1]


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       _A   :       List[str]    					=    [
           [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 pytest
import requests

from datasets.utils.file_utils import http_head

from .utils import OfflineSimulationMode, RequestWouldHangIndefinitelyError, offline

@pytest.mark.integration
def   __lowercase       (			):







				"""simple docstring"""






				with offline(OfflineSimulationMode.CONNECTION_TIMES_OUT			):
								with pytest.raises(snake_case			):
												requests.request('''GET''',	'''https://huggingface.co'''			)
								with pytest.raises(requests.exceptions.ConnectTimeout			):
												requests.request('''GET''',	'''https://huggingface.co''',	timeout=1.0			)

@pytest.mark.integration
def   __lowercase       (			):







				"""simple docstring"""






				with offline(OfflineSimulationMode.CONNECTION_FAILS			):
								with pytest.raises(requests.exceptions.ConnectionError			):
												requests.request('''GET''',	'''https://huggingface.co'''			)

def   __lowercase       (			):







				"""simple docstring"""






				with offline(OfflineSimulationMode.HF_DATASETS_OFFLINE_SET_TO_1			):
								with pytest.raises(snake_case			):
												http_head('''https://huggingface.co'''			)






