
"""simple docstring"""

def     lowercase__						(					lowerCAmelCase				:					list[list] ) ->      list[list]:






    """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     lowercase__						(					lowerCAmelCase				:					list[list] ) ->      list:






    """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()
   SCREAMING_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]]))





"""simple docstring"""

import os
from typing import Optional

import fsspec
from fsspec.archive import AbstractArchiveFileSystem
from fsspec.utils import DEFAULT_BLOCK_SIZE
class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							str							      =	""
      __SCREAMING_SNAKE_CASE   :							str							      =	(
          None  # protocol passed in prefix to the url. ex: "gzip", for gzip://file.txt::http://foo.bar/file.txt.gz
      )
      __SCREAMING_SNAKE_CASE   :							str							      =	None  # compression type in fsspec. ex: "gzip"
      __SCREAMING_SNAKE_CASE   :							str							      =	None  # extension of the filename to strip. ex: "".gz" to get file.txt from file.txt.gz




      def __init__(							self   ,       lowercase_ = ""   ,       lowercase_ = None   ,       lowercase_ = None   ,       **lowercase_							)						->					str:
          super().__init__(self   ,       **lowercase_							)
          # always open as "rb" since fsspec can then use the TextIOWrapper to make it work for "r" mode
          UpperCAmelCase									=					fsspec.open(
              lowercase_   ,       mode='rb'   ,       protocol=lowercase_   ,       compression=self.compression   ,       client_kwargs={
                  'requote_redirect_url': False,  # see https://github.com/huggingface/datasets/pull/5459
                  'trust_env': True,  # Enable reading proxy env variables.
                  **(target_options or {}).pop('client_kwargs'   ,       {}							),  # To avoid issues if it was already passed.
              }   ,       **(target_options or {})   ,       )
          UpperCAmelCase									=					os.path.basename(self.file.path.split('::'							)[0]							)
          UpperCAmelCase									=					(
              self.compressed_name[: self.compressed_name.rindex('.'							)]
              if '.' in self.compressed_name
              else self.compressed_name
          )
          UpperCAmelCase									=					None




      @classmethod
      def     a_      (							cls   ,       lowercase_							)						->					Union[str, Any]:
          # compressed file paths are always relative to the archive root
          return super()._strip_protocol(lowercase_							).lstrip('/'							)




      def     a_      (							self							)						->					int:
          if self.dir_cache is None:
              UpperCAmelCase									=					{**self.file.fs.info(self.file.path							), 'name': self.uncompressed_name}
              UpperCAmelCase									=					{f['name']: f}




      def     a_      (							self   ,       lowercase_							)						->					Any:
          return self.file.open().read()




      def     a_      (							self   ,       lowercase_   ,       lowercase_ = "rb"   ,       lowercase_=None   ,       lowercase_=True   ,       lowercase_=None   ,       **lowercase_   ,       )						->					Optional[Any]:
          UpperCAmelCase									=					self._strip_protocol(lowercase_							)
          if mode != "rb":
              raise ValueError(F"Tried to read with mode {mode} on file {self.file.path} opened with mode 'rb'"							)
          return self.file.open()

class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							List[Any]							      =	"bz2"
      __SCREAMING_SNAKE_CASE   :							Union[str, Any]							      =	"bz2"
      __SCREAMING_SNAKE_CASE   :							Union[str, Any]							      =	".bz2"

class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							List[str]							      =	"gzip"
      __SCREAMING_SNAKE_CASE   :							Any							      =	"gzip"
      __SCREAMING_SNAKE_CASE   :							List[str]							      =	".gz"

class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							List[str]							      =	"lz4"
      __SCREAMING_SNAKE_CASE   :							List[Any]							      =	"lz4"
      __SCREAMING_SNAKE_CASE   :							Tuple							      =	".lz4"

class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							List[str]							      =	"xz"
      __SCREAMING_SNAKE_CASE   :							Union[str, Any]							      =	"xz"
      __SCREAMING_SNAKE_CASE   :							List[Any]							      =	".xz"

class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							List[str]							      =	"zstd"
      __SCREAMING_SNAKE_CASE   :							int							      =	"zstd"
      __SCREAMING_SNAKE_CASE   :							Tuple							      =	".zst"




      def __init__(							self   ,       lowercase_   ,       lowercase_ = "rb"   ,       lowercase_ = None   ,       lowercase_ = None   ,       lowercase_ = DEFAULT_BLOCK_SIZE   ,       **lowercase_   ,       )						->					str:
          super().__init__(
              fo=lowercase_   ,       mode=lowercase_   ,       target_protocol=lowercase_   ,       target_options=lowercase_   ,       block_size=lowercase_   ,       **lowercase_   ,       )
          # We need to wrap the zstd decompressor to avoid this error in fsspec==2021.7.0 and zstandard==0.15.2:
          #
          # File "/Users/user/.virtualenvs/hf-datasets/lib/python3.7/site-packages/fsspec/core.py", line 145, in open
          #     out.close = close
          # AttributeError: 'zstd.ZstdDecompressionReader' object attribute 'close' is read-only
          #
          # see https://github.com/intake/filesystem_spec/issues/725
          UpperCAmelCase									=					self.file.__enter__
          class      _UpperCAmelCase							:




                def __init__(							self   ,       lowercase_							)						->					List[Any]:
                    UpperCAmelCase									=					file_




                def __enter__(							self							)						->					List[str]:
                    self._file.__enter__()
                    return self




                def __exit__(							self   ,       *lowercase_   ,       **lowercase_							)						->					List[str]:
                    self._file.__exit__(*lowercase_   ,       **lowercase_							)




                def __iter__(							self							)						->					Optional[int]:
                    return iter(self._file							)




                def     a_      (							self							)						->					Tuple:
                    return next(self._file							)




                def __getattr__(							self   ,       lowercase_							)						->					Optional[int]:
                    return getattr(self._file   ,       lowercase_							)

          def fixed_enter(*lowercase_   ,       **lowercase_							):
              return WrappedFile(_enter(*lowercase_   ,       **lowercase_							)							)

          UpperCAmelCase									=					fixed_enter



