def is_regular(mclan, _checked=True) -> bool:
"""Return whether ``mclan`` is (left-)regular.
:return: ``True`` if ``mclan`` is :term:`regular`, ``False`` if 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_regular == _mo.CacheStatus.UNKNOWN:
# The empty set is already handled in Set().__init__ via flags initialization.
if mclan.cached_is_not_functional:
mclan.cache_regular(_mo.CacheStatus.IS_NOT)
return False
itr = iter(mclan.data)
rel = next(itr)
if not _relations.is_functional(rel):
mclan.cache_regular(_mo.CacheStatus.IS_NOT)
return False
left_set = rel.get_left_set()
regular = all(
_relations.is_functional(rel) and left_set == rel.get_left_set() for rel in itr)
mclan.cache_regular(_mo.CacheStatus.from_bool(regular))
return mclan.cached_is_regular
def is_regular(mclan, _checked=True) -> bool:
"""Return whether ``mclan`` is (left-)regular.
:return: ``True`` if ``mclan`` is :term:`regular`, ``False`` if 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_regular == _mo.CacheStatus.UNKNOWN:
# The empty set is already handled in Set().__init__ via flags initialization.
if mclan.cached_is_not_functional:
mclan.cache_regular(_mo.CacheStatus.IS_NOT)
return False
itr = iter(mclan.data)
rel = next(itr)
if not _relations.is_functional(rel):
mclan.cache_regular(_mo.CacheStatus.IS_NOT)
return False
left_set = rel.get_left_set()
regular = all(
_relations.is_functional(rel) and left_set == rel.get_left_set()
for rel in itr)
mclan.cache_regular(_mo.CacheStatus.from_bool(regular))
return mclan.cached_is_regular
def is_functional(mclan, _checked=True) -> bool:
"""Return whether ``mclan`` is functional.
:return: ``True`` if every :term:`relation` in ``mclan`` is :term:`functional` (is a
:term:`function`), ``False`` if 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_functional == _mo.CacheStatus.UNKNOWN:
# The empty set is already handled in Set().__init__ via flags initialization.
functional = all(_relations.is_functional(rel, _checked=False) for rel in mclan.data)
mclan.cache_functional(_mo.CacheStatus.from_bool(functional))
return mclan.cached_is_functional
def is_functional(clan, _checked=True) -> bool:
"""Return whether ``clan`` is functional.
:return: ``True`` if every :term:`relation` in ``clan`` is :term:`functional` (is a
:term:`function`), ``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_functional == _mo.CacheStatus.UNKNOWN:
# The empty set is already handled in Set().__init__ via flags initialization.
functional = all(
_relations.is_functional(rel, _checked=False) for rel in clan)
clan.cache_functional(_mo.CacheStatus.from_bool(functional))
return clan.cached_is_functional
def is_functional(mo: _mo.MathObject, _checked: bool = True) -> bool:
r"""Return whether ``mo`` is :term:`functional` 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_functional == _mo.CacheStatus.IS:
return True
if mo.cached_functional == _mo.CacheStatus.IS_NOT:
return False
if mo.cached_functional == _mo.CacheStatus.N_A:
return _undef.make_or_raise_undef(2)
# Check type (functional is only defined on Sets and Multisets) and algebra memberships.
if not mo.is_set and not mo.is_multiset:
mo.cache_functional(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
if _relations.is_member(mo):
return _relations.is_functional(mo, _checked=False)
if _clans.is_member(mo):
return _clans.is_functional(mo, _checked=False)
if _multiclans.is_member(mo):
return _multiclans.is_functional(mo, _checked=False)
# Check higher (not yet defined) algebras.
functional = _is_powerset_property(mo, _clans.get_ground_set(),
is_functional)
if functional is not _undef.Undef():
mo.cache_functional(_mo.CacheStatus.from_bool(functional))
return functional
# Nothing applied: 'functional' is not defined.
mo.cache_functional(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
def is_functional(mo: _mo.MathObject, _checked: bool=True) -> bool:
r"""Return whether ``mo`` is :term:`functional` 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_functional == _mo.CacheStatus.IS:
return True
if mo.cached_functional == _mo.CacheStatus.IS_NOT:
return False
if mo.cached_functional == _mo.CacheStatus.N_A:
return _undef.make_or_raise_undef(2)
# Check type (functional is only defined on Sets and Multisets) and algebra memberships.
if not mo.is_set and not mo.is_multiset:
mo.cache_functional(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
if _relations.is_member(mo):
return _relations.is_functional(mo, _checked=False)
if _clans.is_member(mo):
return _clans.is_functional(mo, _checked=False)
if _multiclans.is_member(mo):
return _multiclans.is_functional(mo, _checked=False)
# Check higher (not yet defined) algebras.
functional = _is_powerset_property(mo, _clans.get_ground_set(), is_functional)
if functional is not _undef.Undef():
mo.cache_functional(_mo.CacheStatus.from_bool(functional))
return functional
# Nothing applied: 'functional' is not defined.
mo.cache_functional(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
