

'''simple docstring'''
def 	_lowerCAmelCase (						_UpperCamelCase						:					list[int]							,			_UpperCamelCase						:					list[int]    )				->      tuple[float, float]:
     """simple docstring"""




     if not len(_UpperCamelCase    ) == len(_UpperCamelCase    ) == 3:
          raise ValueError('Please enter a valid equation.'    )
     if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
          raise ValueError('Both a & b of two equations can\'t be zero.'    )

     # Extract the coefficients
     _SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE							   =equationa
     _SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE							   =equationa

     # Calculate the determinants of the matrices
     _SCREAMING_SNAKE_CASE							   =aa * ba - aa * ba
     _SCREAMING_SNAKE_CASE							   =ca * ba - ca * ba
     _SCREAMING_SNAKE_CASE							   =aa * ca - aa * ca

     # Check if the system of linear equations has a solution (using Cramer's rule)
     if determinant == 0:
          if determinant_x == determinant_y == 0:
               raise ValueError('Infinite solutions. (Consistent system)'    )
          else:
               raise ValueError('No solution. (Inconsistent system)'    )
     else:
          if determinant_x == determinant_y == 0:
               # Trivial solution (Inconsistent system)
               return (0.0, 0.0)
          else:
               _SCREAMING_SNAKE_CASE							   =determinant_x / determinant
               _SCREAMING_SNAKE_CASE							   =determinant_y / determinant
               # Non-Trivial Solution (Consistent system)
               return (x, y)



'''simple docstring'''
from datasets.utils.patching import _PatchedModuleObj, patch_submodule

from . import _test_patching


def 	_lowerCAmelCase (						)				->      int:
     """simple docstring"""




     import os as original_os
     from os import path as original_path
     from os import rename as original_rename
     from os.path import dirname as original_dirname
     from os.path import join as original_join

     assert _test_patching.os is original_os
     assert _test_patching.path is original_path
     assert _test_patching.join is original_join

     assert _test_patching.renamed_os is original_os
     assert _test_patching.renamed_path is original_path
     assert _test_patching.renamed_join is original_join

     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_mock__'
     with patch_submodule(_test_patching							,			'os.path.join'							,			_UpperCamelCase    ):
          # Every way to access os.path.join must be patched, and the rest must stay untouched

          # check os.path.join
          assert isinstance(_test_patching.os							,			_PatchedModuleObj    )
          assert isinstance(_test_patching.os.path							,			_PatchedModuleObj    )
          assert _test_patching.os.path.join is mock

          # check path.join
          assert isinstance(_test_patching.path							,			_PatchedModuleObj    )
          assert _test_patching.path.join is mock

          # check join
          assert _test_patching.join is mock

          # check that the other attributes are untouched
          assert _test_patching.os.rename is original_rename
          assert _test_patching.path.dirname is original_dirname
          assert _test_patching.os.path.dirname is original_dirname

          # Even renamed modules or objects must be patched

          # check renamed_os.path.join
          assert isinstance(_test_patching.renamed_os							,			_PatchedModuleObj    )
          assert isinstance(_test_patching.renamed_os.path							,			_PatchedModuleObj    )
          assert _test_patching.renamed_os.path.join is mock

          # check renamed_path.join
          assert isinstance(_test_patching.renamed_path							,			_PatchedModuleObj    )
          assert _test_patching.renamed_path.join is mock

          # check renamed_join
          assert _test_patching.renamed_join is mock

          # check that the other attributes are untouched
          assert _test_patching.renamed_os.rename is original_rename
          assert _test_patching.renamed_path.dirname is original_dirname
          assert _test_patching.renamed_os.path.dirname is original_dirname

     # check that everthing is back to normal when the patch is over

     assert _test_patching.os is original_os
     assert _test_patching.path is original_path
     assert _test_patching.join is original_join

     assert _test_patching.renamed_os is original_os
     assert _test_patching.renamed_path is original_path
     assert _test_patching.renamed_join is original_join


def 	_lowerCAmelCase (						)				->      Optional[Any]:
     """simple docstring"""




     assert _test_patching.open is open

     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_builtin_mock__'
     # _test_patching has "open" in its globals
     assert _test_patching.open is open
     with patch_submodule(_test_patching							,			'open'							,			_UpperCamelCase    ):
          assert _test_patching.open is mock

     # check that everthing is back to normal when the patch is over

     assert _test_patching.open is open


def 	_lowerCAmelCase (						)				->      str:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_missing_mock__'
     with patch_submodule(_test_patching							,			'pandas.read_csv'							,			_UpperCamelCase    ):
          pass


def 	_lowerCAmelCase (						)				->      Optional[Any]:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_missing_builtin_mock__'
     # _test_patching doesn't have "len" in its globals
     assert getattr(_test_patching							,			'len'							,			_UpperCamelCase    ) is None
     with patch_submodule(_test_patching							,			'len'							,			_UpperCamelCase    ):
          assert _test_patching.len is mock
     assert _test_patching.len is len


def 	_lowerCAmelCase (						)				->      str:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_start_and_stop_mock__'
     _SCREAMING_SNAKE_CASE							   =patch_submodule(_test_patching							,			'open'							,			_UpperCamelCase    )
     assert _test_patching.open is open
     patch.start()
     assert _test_patching.open is mock
     patch.stop()
     assert _test_patching.open is open


def 	_lowerCAmelCase (						)				->      Optional[Any]:
     """simple docstring"""




     from os import rename as original_rename
     from os.path import dirname as original_dirname
     from os.path import join as original_join

     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_successive_join__'
     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_successive_dirname__'
     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_successive_rename__'
     assert _test_patching.os.path.join is original_join
     assert _test_patching.os.path.dirname is original_dirname
     assert _test_patching.os.rename is original_rename

     with patch_submodule(_test_patching							,			'os.path.join'							,			_UpperCamelCase    ):
          with patch_submodule(_test_patching							,			'os.rename'							,			_UpperCamelCase    ):
               with patch_submodule(_test_patching							,			'os.path.dirname'							,			_UpperCamelCase    ):
                    assert _test_patching.os.path.join is mock_join
                    assert _test_patching.os.path.dirname is mock_dirname
                    assert _test_patching.os.rename is mock_rename

    # try another order
     with patch_submodule(_test_patching							,			'os.rename'							,			_UpperCamelCase    ):
          with patch_submodule(_test_patching							,			'os.path.join'							,			_UpperCamelCase    ):
               with patch_submodule(_test_patching							,			'os.path.dirname'							,			_UpperCamelCase    ):
                    assert _test_patching.os.path.join is mock_join
                    assert _test_patching.os.path.dirname is mock_dirname
                    assert _test_patching.os.rename is mock_rename

     assert _test_patching.os.path.join is original_join
     assert _test_patching.os.path.dirname is original_dirname
     assert _test_patching.os.rename is original_rename







def 	_lowerCAmelCase (						)				->      Optional[Any]:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   ='__test_patch_submodule_doesnt_exist_mock__'
     with patch_submodule(_test_patching							,			'__module_that_doesn_exist__.__attribute_that_doesn_exist__'							,			_UpperCamelCase    ):
          pass
     with patch_submodule(_test_patching							,			'os.__attribute_that_doesn_exist__'							,			_UpperCamelCase    ):
          pass
