def transpose(multiclan: 'P(P(M x M) x N)', _checked=True) -> 'P(P(M x M) x N)':
"""Return a multiclan where all relations have their left and right components swapped.
:return: The :term:`unary multi-extension` of :term:`transposition` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``multiclan``, or `Undef()` if ``multiclan`` is not a :term:`multiclan`.
"""
if _checked:
if not is_member(multiclan):
return _undef.make_or_raise_undef2(multiclan)
else:
assert is_member_or_undef(multiclan)
if multiclan is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.unary_multi_extend(multiclan, _functools.partial(
_relations.transpose, _checked=False), _checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
result.cache_absolute(multiclan.cached_absolute)
result.cache_functional(multiclan.cached_right_functional)
result.cache_right_functional(multiclan.cached_functional)
result.cache_reflexive(multiclan.cached_reflexive)
result.cache_symmetric(multiclan.cached_symmetric)
result.cache_transitive(multiclan.cached_transitive)
result.cache_regular(multiclan.cached_right_regular)
result.cache_right_regular(multiclan.cached_regular)
return result
def transpose(multiclan: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
"""Return a multiclan where all relations have their left and right components swapped.
:return: The :term:`unary multi-extension` of :term:`transposition` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``multiclan``, or `Undef()` if ``multiclan`` is not a :term:`multiclan`.
"""
if _checked:
if not is_member(multiclan):
return _undef.make_or_raise_undef2(multiclan)
else:
assert is_member_or_undef(multiclan)
if multiclan is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.unary_multi_extend(multiclan,
_functools.partial(
_relations.transpose,
_checked=False),
_checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
result.cache_absolute(multiclan.cached_absolute)
result.cache_functional(multiclan.cached_right_functional)
result.cache_right_functional(multiclan.cached_functional)
result.cache_reflexive(multiclan.cached_reflexive)
result.cache_symmetric(multiclan.cached_symmetric)
result.cache_transitive(multiclan.cached_transitive)
result.cache_regular(multiclan.cached_right_regular)
result.cache_right_regular(multiclan.cached_regular)
return result
def defined_at(mclan: 'P(P(M x M) x N)', left: '( M )', _checked=True):
r"""Return the :term:`relation`\s of ``mclan`` that are defined for ``left``."""
if not is_member(mclan):
return _undef.make_or_raise_undef(2)
if left is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.unary_multi_extend(mclan,
_functools.partial(
_relations.defined_at,
left=left,
_checked=_checked),
_checked=_checked)
if result is _undef.Undef() or not result:
return _undef.make_or_raise_undef2(result)
result.cache_multiclan(_mo.CacheStatus.IS)
if not result.is_empty:
if mclan.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if mclan.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
if mclan.cached_is_regular:
result.cache_regular(_mo.CacheStatus.IS)
if mclan.cached_is_right_regular:
result.cache_right_regular(_mo.CacheStatus.IS)
return result
def transpose(multiclan: 'P(P(M x M) x N)', _checked=True) -> 'P(P(M x M) x N)':
"""Return the :term:`transposition` of the :term:`multiclan` ``multiclan``.
:return: The :term:`unary extension` of :term:`transposition` from the :term:`algebra of
relations` to the :term:`algebra of multiclans`, applied to ``multiclan``, or `Undef()`
if ``multiclan`` is not a :term:`multiclan`.
"""
if _checked:
if not is_member(multiclan):
return _make_or_raise_undef()
else:
assert is_member(multiclan)
return _extension.unary_multi_extend(multiclan, partial(
_relations.transpose, _checked=False), _checked=False)
def defined_at(mclan: 'P(P(M x M) x N)', left: '( M )', _checked=True):
r"""Return the :term:`relation`\s of ``mclan`` that are defined for ``left``."""
if not is_member(mclan):
return _undef.make_or_raise_undef(2)
if left is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.unary_multi_extend(
mclan, _functools.partial(_relations.defined_at, left=left, _checked=_checked),
_checked=_checked)
if result is _undef.Undef() or not result:
return _undef.make_or_raise_undef2(result)
result.cache_multiclan(_mo.CacheStatus.IS)
if not result.is_empty:
if mclan.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if mclan.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
if mclan.cached_is_regular:
result.cache_regular(_mo.CacheStatus.IS)
if mclan.cached_is_right_regular:
result.cache_right_regular(_mo.CacheStatus.IS)
return result