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 relation`, ``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_relation:
# If known to not be a relation, it's also not an absolute relation. 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_relation == _mo.CacheStatus.UNKNOWN:
# The 'absolute' state has not yet been cached. Determine whether obj is an absolute
# relation.
is_absolute_relation = obj.get_ground_set().is_subset(get_absolute_ground_set())
if obj.cached_relation == _mo.CacheStatus.UNKNOWN:
if is_absolute_relation:
# If it is an absolute relation, it is also a relation.
obj.cache_relation(_mo.CacheStatus.IS)
else:
# If it is not an absolute relation, it may still be a relation.
is_relation = is_member(obj)
if not is_relation:
# If it is neither an absolute relation nor a relation, exit. (That it is not a
# relation has already been cached in is_member().)
return False
# At this point, cached_relation == IS. Cache whether this is an absolute relation.
assert obj.cached_is_relation
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_relation))
# At this point, cached_relation == IS. Return whether it is an absolute relation.
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 relation`, ``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_relation:
# If known to not be a relation, it's also not an absolute relation. 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_relation == _mo.CacheStatus.UNKNOWN:
# The 'absolute' state has not yet been cached. Determine whether obj is an absolute
# relation.
is_absolute_relation = obj.get_ground_set().is_subset(
get_absolute_ground_set())
if obj.cached_relation == _mo.CacheStatus.UNKNOWN:
if is_absolute_relation:
# If it is an absolute relation, it is also a relation.
obj.cache_relation(_mo.CacheStatus.IS)
else:
# If it is not an absolute relation, it may still be a relation.
is_relation = is_member(obj)
if not is_relation:
# If it is neither an absolute relation nor a relation, exit. (That it is not a
# relation has already been cached in is_member().)
return False
# At this point, cached_relation == IS. Cache whether this is an absolute relation.
assert obj.cached_is_relation
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_relation))
# At this point, cached_relation == IS. Return whether it is an absolute relation.
return obj.cached_is_absolute
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:`relation`, ``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_relation == _mo.CacheStatus.UNKNOWN:
is_relation = obj.get_ground_set().is_subset(get_ground_set())
obj.cache_relation(_mo.CacheStatus.from_bool(is_relation))
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:`relation`, ``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_relation == _mo.CacheStatus.UNKNOWN:
is_relation = obj.get_ground_set().is_subset(get_ground_set())
obj.cache_relation(_mo.CacheStatus.from_bool(is_relation))
return obj.cached_is_relation
