def is_transitive(mclan, _checked=True) -> bool:
"""Return whether ``mclan`` is transitive.
:return: ``True`` if ``mclan`` is :term:`transitive`, ``False`` if it is not, or `Undef()` if
``mclan`` is not a :term:`multiclan`.
"""
if _checked:
if not is_member(mclan):
return _undef.make_or_raise_undef()
else:
assert is_member(mclan)
if mclan.cached_transitive == _mo.CacheStatus.UNKNOWN:
transitive = all(_relations.is_transitive(rel, _checked=False) for rel in mclan.data)
mclan.cache_transitive(_mo.CacheStatus.from_bool(transitive))
return mclan.cached_transitive == _mo.CacheStatus.IS
def is_transitive(clan, _checked=True) -> bool:
"""Return whether ``clan`` is transitive.
:return: ``True`` if every :term:`relation` in ``clan`` is :term:`transitive`, ``False`` if
not, or `Undef()` if ``clan`` is not a :term:`clan`.
"""
if _checked:
if not is_member(clan):
return _undef.make_or_raise_undef()
else:
assert is_member(clan)
if clan.cached_transitive == _mo.CacheStatus.UNKNOWN:
# The empty set is already handled in Set().__init__ via flags initialization.
transitive = all(_relations.is_transitive(rel, _checked=False) for rel in clan)
clan.cache_transitive(_mo.CacheStatus.from_bool(transitive))
return clan.cached_transitive == _mo.CacheStatus.IS
def is_transitive(mclan, _checked=True) -> bool:
"""Return whether ``mclan`` is transitive.
:return: ``True`` if ``mclan`` is :term:`transitive`, ``False`` if it is not, or `Undef()` if
``mclan`` is not a :term:`multiclan`.
"""
if _checked:
if not is_member(mclan):
return _undef.make_or_raise_undef2(mclan)
else:
assert is_member_or_undef(mclan)
if mclan is _undef.Undef():
return _undef.make_or_raise_undef(2)
if mclan.cached_transitive == _mo.CacheStatus.UNKNOWN:
transitive = all(
_relations.is_transitive(rel, _checked=False)
for rel in mclan.data)
mclan.cache_transitive(_mo.CacheStatus.from_bool(transitive))
return mclan.cached_transitive == _mo.CacheStatus.IS
def is_transitive(clan, _checked=True) -> bool:
"""Return whether ``clan`` is transitive.
:return: ``True`` if every :term:`relation` in ``clan`` is :term:`transitive`, ``False`` if
not, or `Undef()` if ``clan`` is not a :term:`clan`.
"""
if _checked:
if not is_member(clan):
return _undef.make_or_raise_undef2(clan)
else:
assert is_member_or_undef(clan)
if clan is _undef.Undef():
return _undef.make_or_raise_undef(2)
if clan.cached_transitive == _mo.CacheStatus.UNKNOWN:
# The empty set is already handled in Set().__init__ via flags initialization.
transitive = all(
_relations.is_transitive(rel, _checked=False) for rel in clan)
clan.cache_transitive(_mo.CacheStatus.from_bool(transitive))
return clan.cached_transitive == _mo.CacheStatus.IS
def is_transitive(mo: _mo.MathObject, _checked: bool = True) -> bool:
r"""Return whether ``mo`` is :term:`transitive` or `Undef()` if not applicable.
Is implemented for :term:`relation`\s, :term:`clan`\s, :term:`multiclan`\s and :term:`set`\s
of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets
or :term:`multiset`\s of relations.
"""
# pylint: disable=too-many-return-statements
if _checked:
if not isinstance(mo, _mo.MathObject):
return _undef.make_or_raise_undef()
# Check cache status.
if mo.cached_transitive == _mo.CacheStatus.IS:
return True
if mo.cached_transitive == _mo.CacheStatus.IS_NOT:
return False
if mo.cached_transitive == _mo.CacheStatus.N_A:
return _undef.make_or_raise_undef(2)
# Check type (transitive is only defined on Sets and Multisets) and algebra memberships.
if not mo.is_set and not mo.is_multiset:
mo.cache_transitive(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
if _relations.is_member(mo):
return _relations.is_transitive(mo, _checked=False)
if _clans.is_member(mo):
return _clans.is_transitive(mo, _checked=False)
if _multiclans.is_member(mo):
return _multiclans.is_transitive(mo, _checked=False)
# Check higher (not yet defined) algebras.
transitive = _is_powerset_property(mo, _relations.get_ground_set(),
is_transitive)
if transitive is not _undef.Undef():
mo.cache_transitive(_mo.CacheStatus.from_bool(transitive))
return transitive
# Nothing applied: 'transitive' is not defined.
mo.cache_transitive(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
def is_transitive(mo: _mo.MathObject, _checked: bool=True) -> bool:
r"""Return whether ``mo`` is :term:`transitive` or `Undef()` if not applicable.
Is implemented for :term:`relation`\s, :term:`clan`\s, :term:`multiclan`\s and :term:`set`\s
of (sets of ...) clans. Is also defined (but not yet implemented) for any combination of sets
or :term:`multiset`\s of relations.
"""
# pylint: disable=too-many-return-statements
if _checked:
if not isinstance(mo, _mo.MathObject):
return _undef.make_or_raise_undef()
# Check cache status.
if mo.cached_transitive == _mo.CacheStatus.IS:
return True
if mo.cached_transitive == _mo.CacheStatus.IS_NOT:
return False
if mo.cached_transitive == _mo.CacheStatus.N_A:
return _undef.make_or_raise_undef(2)
# Check type (transitive is only defined on Sets and Multisets) and algebra memberships.
if not mo.is_set and not mo.is_multiset:
mo.cache_transitive(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
if _relations.is_member(mo):
return _relations.is_transitive(mo, _checked=False)
if _clans.is_member(mo):
return _clans.is_transitive(mo, _checked=False)
if _multiclans.is_member(mo):
return _multiclans.is_transitive(mo, _checked=False)
# Check higher (not yet defined) algebras.
transitive = _is_powerset_property(mo, _relations.get_ground_set(), is_transitive)
if transitive is not _undef.Undef():
mo.cache_transitive(_mo.CacheStatus.from_bool(transitive))
return transitive
# Nothing applied: 'transitive' is not defined.
mo.cache_transitive(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
