






'''simple docstring'''


def 	__magic_name__( _A					):
						'''simple docstring'''





						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 	__magic_name__( _A					):
						'''simple docstring'''





						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()
			lowerCamelCase_				: Optional[int]    	=							[
			    [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'''


from typing import Optional

import pyspark

from .. import Features, NamedSplit
from ..download import DownloadMode
from ..packaged_modules.spark.spark import Spark
from .abc import AbstractDatasetReader
class    _SCREAMING_SNAKE_CASE							(		SCREAMING_SNAKE_CASE	):


			'''simple docstring'''





			def __init__(   self							:						Tuple ,      lowercase							:						pyspark.sql.DataFrame ,      lowercase							:						Optional[NamedSplit] = None ,      lowercase							:						Optional[Features] = None ,      lowercase							:						bool = True ,      lowercase							:						str = None ,      lowercase							:						bool = False ,      lowercase							:						str = None ,      lowercase							:						bool = True ,      lowercase							:						str = "arrow" ,      **lowercase							:						Any ,      )							->    Optional[int]:

									'''simple docstring'''







									super().__init__(
									    split=lowercase ,      features=lowercase ,      cache_dir=lowercase ,      keep_in_memory=lowercase ,      streaming=lowercase ,      **lowercase ,      )
									UpperCamelCase__         = load_from_cache_file
									UpperCamelCase__         = file_format
									UpperCamelCase__         = Spark(
									    df=lowercase ,      features=lowercase ,      cache_dir=lowercase ,      working_dir=lowercase ,      **lowercase ,      )







			def 				A      (   self							:						int			)							->    Any:

									'''simple docstring'''







									if self.streaming:
															return self.builder.as_streaming_dataset(split=self.split			)
									UpperCamelCase__         = None if self._load_from_cache_file else DownloadMode.FORCE_REDOWNLOAD
									self.builder.download_and_prepare(
									    download_mode=lowercase ,      file_format=self._file_format ,      )
									return self.builder.as_dataset(split=self.split			)
