



"""simple docstring"""







def   lowerCAmelCase__			(     lowerCamelCase__			) ->							list[list]:
							A         =					current_set.copy()
							for row_index, row in enumerate(lowerCamelCase__			):
														A         =					row[0]
														for column_index, column in enumerate(lowerCamelCase__			):
																					if magnitude == 0:
																												A         =					column
																												continue
																					A         =					column / magnitude
    # Subtract to cancel term
							A         =					current_set[0]
							A         =					[first_row]
							A         =					current_set[1::]
							for row in current_set:
														A         =					[]
														# 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:
														A         =					final_set[0]
														A         =					[]
														A         =					[]
														for row in final_set[1::]:
																					current_first_column.append(row[0]			)
																					next_iteration.append(row[1::]			)
														A         =					simplify(lowerCamelCase__			)
														for i in range(len(lowerCamelCase__			)			):
																					resultant[i].insert(0				,      current_first_column[i]			)
														resultant.insert(0				,      lowerCamelCase__			)
														A         =					resultant
							return final_set

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							list:
							if len(lowerCamelCase__			) == 0:
														raise IndexError('solve_simultaneous() requires n lists of length n+1'			)
							A         =					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]]
							A         =					equations.copy()
							if any(0 in row for row in data_set			):
														A         =					data_set.copy()
														A         =					[]
														for row_index, row in enumerate(lowerCamelCase__			):
																					if 0 not in row:
																												A         =					data_set.pop(lowerCamelCase__			)
																												break
														if not full_row:
																					raise ValueError('solve_simultaneous() requires at least 1 full equation'			)
														data_set.insert(0				,      lowerCamelCase__			)
							A         =					data_set.copy()
							A         =					simplify(lowerCamelCase__			)
							A         =					simplified[::-1]
							A         =					[]
							for row in simplified:
														A         =					row[-1]
														if not solutions:
																					if row[-2] == 0:
																												solutions.append(0			)
																												continue
																					solutions.append(current_solution / row[-2]			)
																					continue
														A         =					row.copy()[: len(lowerCamelCase__			) - 1 :]
														while temp_row[0] == 0:
																					temp_row.pop(0			)
														if len(lowerCamelCase__			) == 0:
																					solutions.append(0			)
																					continue
														A         =					temp_row[1::]
														A         =					temp_row[::-1]
														for column_index, column in enumerate(lowerCamelCase__			):
																					current_solution -= column * solutions[column_index]
														solutions.append(lowerCamelCase__			)
							A         =					[]
							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]]))








"""simple docstring"""







def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							float:

							def get_matched_characters(lowerCamelCase__				,      lowerCamelCase__			) -> str:
														A         =					[]
														A         =					min(len(_stra			)				,      len(_stra			)			) // 2
														for i, l in enumerate(_stra			):
																					A         =					int(max(0				,      i - limit			)			)
																					A         =					int(min(i + limit + 1				,      len(_stra			)			)			)
																					if l in _stra[left:right]:
																												matched.append(lowerCamelCase__			)
																												A         =					f"""{_stra[0:_stra.index(lowerCamelCase__			)]} {_stra[_stra.index(lowerCamelCase__			) + 1:]}"""

														return "".join(lowerCamelCase__			)

							# matching characters
							A         =					get_matched_characters(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					get_matched_characters(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					len(lowerCamelCase__			)

							# transposition
							A         =					(
							    len([(ca, ca) for ca, ca in zip(lowerCamelCase__				,      lowerCamelCase__			) if ca != ca]			) // 2
							)

							if not match_count:
														A         =					0.0
							else:
														A         =					(
														    1
														    / 3
														    * (
														        match_count / len(lowerCamelCase__			)
														        + match_count / len(lowerCamelCase__			)
														        + (match_count - transpositions) / match_count
														    )
														)

							# common prefix up to 4 characters
							A         =					0
							for ca, ca in zip(stra[:4]				,      stra[:4]			):
														if ca == ca:
																					prefix_len += 1
														else:
																					break

							return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(jaro_winkler('hello', 'world'))



