def is_absolute_member(obj: _mo.MathObject) -> bool:
"""Return whether ``obj`` is a member of the :term:`absolute ground set` of this algebra.
:return: ``True`` if ``obj`` is an :term:`absolute clan`, ``False`` if not.
.. note:: This function may call :meth:`~.MathObject.get_ground_set` on ``obj``. The result
of this operation is cached.
"""
if obj.cached_is_not_multiclan:
# If known to not be a multiclan, it's also not an absolute multiclan. No further caching.
return False
# The `or` clause in this `if` statement is a safety thing. It should never hit.
if obj.cached_absolute == _mo.CacheStatus.UNKNOWN \
or obj.cached_multiclan == _mo.CacheStatus.UNKNOWN:
# The 'absolute' state has not yet been cached. Determine whether obj is an absolute
# multiclan.
is_absolute_mclan = obj.get_ground_set().is_subset(
get_absolute_ground_set())
if obj.cached_multiclan == _mo.CacheStatus.UNKNOWN:
if is_absolute_mclan:
# If it is an absolute multiclan, it is also a multiclan.
obj.cache_multiclan(_mo.CacheStatus.IS)
else:
# If it is not an absolute multiclan, it may still be a multiclan.
is_mclan = is_member(obj)
if not is_mclan:
# If it is neither an absolute multiclan nor a multiclan, exit. (That it is
# not a multiclan has already been cached in is_member().)
return False
# At this point, cached_multiclan == IS. Cache whether this is an absolute multiclan.
assert obj.cached_is_multiclan
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_mclan))
# At this point, cached_multiclan == IS. Return whether it is an absolute multiclan.
return obj.cached_is_absolute
def is_absolute_member(obj: _mo.MathObject) -> bool:
"""Return whether ``obj`` is a member of the :term:`absolute ground set` of this algebra.
:return: ``True`` if ``obj`` is an :term:`absolute clan`, ``False`` if not.
.. note:: This function may call :meth:`~.MathObject.get_ground_set` on ``obj``. The result
of this operation is cached.
"""
if obj.cached_is_not_multiclan:
# If known to not be a multiclan, it's also not an absolute multiclan. No further caching.
return False
# The `or` clause in this `if` statement is a safety thing. It should never hit.
if obj.cached_absolute == _mo.CacheStatus.UNKNOWN \
or obj.cached_multiclan == _mo.CacheStatus.UNKNOWN:
# The 'absolute' state has not yet been cached. Determine whether obj is an absolute
# multiclan.
is_absolute_mclan = obj.get_ground_set().is_subset(get_absolute_ground_set())
if obj.cached_multiclan == _mo.CacheStatus.UNKNOWN:
if is_absolute_mclan:
# If it is an absolute multiclan, it is also a multiclan.
obj.cache_multiclan(_mo.CacheStatus.IS)
else:
# If it is not an absolute multiclan, it may still be a multiclan.
is_mclan = is_member(obj)
if not is_mclan:
# If it is neither an absolute multiclan nor a multiclan, exit. (That it is
# not a multiclan has already been cached in is_member().)
return False
# At this point, cached_multiclan == IS. Cache whether this is an absolute multiclan.
assert obj.cached_is_multiclan
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_mclan))
# At this point, cached_multiclan == IS. Return whether it is an absolute multiclan.
return obj.cached_is_absolute
def is_absolute_member(obj: _mo.MathObject) -> bool:
"""Return ``True`` if ``obj`` is a member of the :term:`absolute ground set` of this algebra.
:return: ``True`` if ``obj`` is an :term:`absolute relation`.
.. note:: This function calls :meth:`~.MathObject.get_ground_set` on ``obj``."""
_mo.raise_if_not_mathobject(obj)
return obj.get_ground_set().is_subset(get_absolute_ground_set())
def is_member(obj: _mo.MathObject) -> bool:
"""Return ``True`` if ``obj`` is a member of the :term:`ground set` of this :term:`algebra`.
.. note:: This function calls :meth:`~.MathObject.get_ground_set` on ``obj``.
"""
_mo.raise_if_not_mathobject(obj)
if not obj.cached_is_clan and not obj.cached_is_not_clan:
obj.cache_is_clan(obj.get_ground_set().is_subset(get_ground_set()))
return obj.cached_is_clan
def is_member(obj: _mo.MathObject) -> bool:
"""Return ``True`` if ``obj`` is a member of the :term:`ground set` of this :term:`algebra`.
.. note:: This function may call :meth:`~.MathObject.get_ground_set` on ``obj``. The result
of this operation is cached.
"""
_mo.raise_if_not_mathobject(obj)
if not obj.cached_is_relation and not obj.cached_is_not_relation:
obj.cache_is_relation(obj.get_ground_set().is_subset(get_ground_set()))
return obj.cached_is_relation
def is_member(obj: _mo.MathObject) -> bool:
"""Return whether ``obj`` is a member of the :term:`ground set` of this :term:`algebra`.
:return: ``True`` if ``obj`` is a :term:`multiclan`, ``False`` if not.
.. note:: This function may call :meth:`~.MathObject.get_ground_set` on ``obj``. The result of
this operation is cached.
"""
if obj.cached_multiclan == _mo.CacheStatus.UNKNOWN:
is_multiclan = obj.get_ground_set().is_subset(get_ground_set())
obj.cache_multiclan(_mo.CacheStatus.from_bool(is_multiclan))
return obj.cached_is_multiclan
def is_member(obj: _mo.MathObject) -> bool:
"""Return whether ``obj`` is a member of the :term:`ground set` of this :term:`algebra`.
:return: ``True`` if ``obj`` is a :term:`multiclan`, ``False`` if not.
.. note:: This function may call :meth:`~.MathObject.get_ground_set` on ``obj``. The result of
this operation is cached.
"""
if obj.cached_multiclan == _mo.CacheStatus.UNKNOWN:
is_multiclan = obj.get_ground_set().is_subset(get_ground_set())
obj.cache_multiclan(_mo.CacheStatus.from_bool(is_multiclan))
return obj.cached_is_multiclan
def is_right_regular(mo: _mo.MathObject, _checked: bool = True) -> bool:
r"""Return whether ``mo`` is :term:`right-regular` or `Undef()` if not applicable.
Is implemented for :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 clans.
"""
# 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_right_regular == _mo.CacheStatus.IS:
return True
if mo.cached_right_regular == _mo.CacheStatus.IS_NOT:
return False
if mo.cached_right_regular == _mo.CacheStatus.N_A:
return _undef.make_or_raise_undef(2)
# Check type (right-regular is only defined on Sets and Multisets) and algebra memberships.
if not mo.is_set and not mo.is_multiset:
mo.cache_right_regular(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
if _clans.is_member(mo):
return _clans.is_right_regular(mo, _checked=False)
if _multiclans.is_member(mo):
return _multiclans.is_right_regular(mo, _checked=False)
# Check higher (not yet defined) algebras.
if mo.get_ground_set().get_powerset_level(_clans.get_ground_set()) > 0:
mo_iter = iter(mo)
elem1 = next(mo_iter)
if not is_right_regular(elem1):
mo.cache_right_regular(_mo.CacheStatus.IS_NOT)
return False
elem1_rights = elem1.get_rights()
right_regular = all(
is_right_regular(elem, _checked=False)
and elem.get_rights() == elem1_rights for elem in mo_iter)
mo.cache_right_regular(_mo.CacheStatus.from_bool(right_regular))
return mo.cached_is_right_regular
# Nothing applied: 'right-regular' is not defined.
mo.cache_right_regular(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
def is_right_regular(mo: _mo.MathObject, _checked: bool=True) -> bool:
r"""Return whether ``mo`` is :term:`right-regular` or `Undef()` if not applicable.
Is implemented for :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 clans.
"""
# 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_right_regular == _mo.CacheStatus.IS:
return True
if mo.cached_right_regular == _mo.CacheStatus.IS_NOT:
return False
if mo.cached_right_regular == _mo.CacheStatus.N_A:
return _undef.make_or_raise_undef(2)
# Check type (right-regular is only defined on Sets and Multisets) and algebra memberships.
if not mo.is_set and not mo.is_multiset:
mo.cache_right_regular(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
if _clans.is_member(mo):
return _clans.is_right_regular(mo, _checked=False)
if _multiclans.is_member(mo):
return _multiclans.is_right_regular(mo, _checked=False)
# Check higher (not yet defined) algebras.
if mo.get_ground_set().get_powerset_level(_clans.get_ground_set()) > 0:
mo_iter = iter(mo)
elem1 = next(mo_iter)
if not is_right_regular(elem1):
mo.cache_right_regular(_mo.CacheStatus.IS_NOT)
return False
elem1_rights = elem1.get_rights()
right_regular = all(
is_right_regular(elem, _checked=False) and elem.get_rights() == elem1_rights
for elem in mo_iter)
mo.cache_right_regular(_mo.CacheStatus.from_bool(right_regular))
return mo.cached_is_right_regular
# Nothing applied: 'right-regular' is not defined.
mo.cache_right_regular(_mo.CacheStatus.N_A)
return _undef.make_or_raise_undef(2)
def _is_powerset_property(mo: _mo.MathObject, ground_set, method) -> bool:
"""Return ``True`` if ``method`` returns ``True`` for all members of ``mo`` and ``mo`` is an
element of an n-th power set of ``ground_set``.
:param mo: The `MathObject` on which to operate. Must be a :term:`set`.
:param ground_set: The :term:`ground set` of which the set ``mo`` should be part of (at the
n-th :term:`power set` level).
:param method: A property function (must return ``True``, ``False`` or `Undef()`) that should
be run on all elements of ``mo``. It must be a function in this module.
:return: ``True`` if this instance is element of an n-th power set of ``ground_set``
and all set elements return ``True`` for ``method``, ``False`` if it is an element
of an n-th power set but any element returned ``False`` for ``method``, or `Undef()`
if it isn't an element of an n-th power set.
"""
if mo.get_ground_set().get_powerset_level(ground_set) > 0:
for element in mo:
result = method(element)
if result is _undef.Undef() or not result:
return result
return True
return _undef.Undef()
def _is_powerset_property(mo: _mo.MathObject, ground_set, method) -> bool:
"""Return ``True`` if ``method`` returns ``True`` for all members of ``mo`` and ``mo`` is an
element of an n-th power set of ``ground_set``.
:param mo: The `MathObject` on which to operate. Must be a :term:`set`.
:param ground_set: The :term:`ground set` of which the set ``mo`` should be part of (at the
n-th :term:`power set` level).
:param method: A property function (must return ``True``, ``False`` or `Undef()`) that should
be run on all elements of ``mo``. It must be a function in this module.
:return: ``True`` if this instance is element of an n-th power set of ``ground_set``
and all set elements return ``True`` for ``method``, ``False`` if it is an element
of an n-th power set but any element returned ``False`` for ``method``, or `Undef()`
if it isn't an element of an n-th power set.
"""
if mo.get_ground_set().get_powerset_level(ground_set) > 0:
for element in mo:
result = method(element)
if result is _undef.Undef() or not result:
return result
return True
return _undef.Undef()
