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)
def get_ground_set() -> _structure.Structure:
"""Return the :term:`ground set` of this :term:`algebra`."""
return _structure.PowerSet(
_structure.CartesianProduct(_relations.get_ground_set(), _structure.GenesisSetN()))
def get_ground_set() -> _structure.Structure:
"""Return the :term:`ground set` of this :term:`algebra`."""
return _structure.PowerSet(
_structure.CartesianProduct(_relations.get_ground_set(),
_structure.GenesisSetN()))
def get_ground_set() -> _structure.Structure:
"""Return the :term:`ground set` of this :term:`algebra`."""
return _structure.PowerSet(_relations.get_ground_set())
def get_ground_set() -> _structure.Structure:
"""Return the :term:`ground set` of this :term:`algebra`."""
return _structure.PowerSet(_relations.get_ground_set())
