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 set`, ``False`` if not.
"""
if not obj.is_set:
# If known to not be a set, it's also not an absolute set. No further checking or caching.
return False
# From this point on, `obj` is known to be a set.
if obj.cached_absolute == _mo.CacheStatus.UNKNOWN:
import algebraixlib.algebras.clans as _clans
import algebraixlib.algebras.relations as _relations
# In order to find out whether this is an absolute set, we need to know whether `obj` is a
# relation or a clan (both sets). If it is one of these, it is not an absolute set -- but
# we also don't know whether it is an absolute relation or clan. So we return `False` but
# don't cache anything. (But we have now cached that it is a relation or a clan.)
if _relations.is_member(obj) or _clans.is_member(obj):
return False
is_absolute_set = all(elem.is_atom for elem in obj)
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_set))
# In order to determine whether this is an absolute set, we need to also examine whether this
# is a relation or a clan (both are sets). Absolute relations and absolute clans are not
# absolute sets.
return obj.cached_is_absolute and not obj.cached_is_relation and not obj.cached_is_clan
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.
:type obj: _mo.MathObject|_mo.Multiset
:return: ``True`` if ``obj`` is an :term:`absolute multiset`, ``False`` if not.
"""
import algebraixlib.algebras.multiclans as _multiclans
if not obj.is_multiset:
# If known to not be a multiset, it's also not an absolute multiset. No further checking or
# caching.
return False
# From this point on, `obj` is known to be a multiset.
if obj.cached_absolute == _mo.CacheStatus.UNKNOWN:
# In order to find out whether this is an absolute multiset, we need to know whether `obj`
# is a multiclan (also a multiset). If it is one, it is not an absolute multiset -- but
# we also don't know whether it is an absolute multiclan. So we return `False` but don't
# cache anything. (But we have now cached that it is a multiclan.)
if _multiclans.is_member(obj):
return False
is_absolute_multiset = all(elem.is_atom for elem in obj.data)
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_multiset))
# In order to determine whether this is an absolute multiset, we need to also examine whether
# this is a multiclan (also a multisets). Absolute multiclans are not absolute multisets.
return obj.cached_is_absolute and not obj.cached_is_multiclan
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 set`, ``False`` if not.
"""
if not obj.is_set:
# If known to not be a set, it's also not an absolute set. No further checking or caching.
return False
# From this point on, `obj` is known to be a set.
if obj.cached_absolute == _mo.CacheStatus.UNKNOWN:
import algebraixlib.algebras.clans as _clans
import algebraixlib.algebras.relations as _relations
# In order to find out whether this is an absolute set, we need to know whether `obj` is a
# relation or a clan (both sets). If it is one of these, it is not an absolute set -- but
# we also don't know whether it is an absolute relation or clan. So we return `False` but
# don't cache anything. (But we have now cached that it is a relation or a clan.)
if _relations.is_member(obj) or _clans.is_member(obj):
return False
is_absolute_set = all(elem.is_atom for elem in obj)
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_set))
# In order to determine whether this is an absolute set, we need to also examine whether this
# is a relation or a clan (both are sets). Absolute relations and absolute clans are not
# absolute sets.
return obj.cached_is_absolute and not obj.cached_is_relation and not obj.cached_is_clan
def is_absolute_member(obj: _mo.MathObject) -> bool:
"""Return whether ``obj`` is a member of the :term:`absolute ground set` of this algebra.
:type obj: _mo.MathObject|_mo.Multiset
:return: ``True`` if ``obj`` is an :term:`absolute multiset`, ``False`` if not.
"""
import algebraixlib.algebras.multiclans as _multiclans
if not obj.is_multiset:
# If known to not be a multiset, it's also not an absolute multiset. No further checking or
# caching.
return False
# From this point on, `obj` is known to be a multiset.
if obj.cached_absolute == CacheStatus.UNKNOWN:
# In order to find out whether this is an absolute multiset, we need to know whether `obj`
# is a multiclan (also a multiset). If it is one, it is not an absolute multiset -- but
# we also don't know whether it is an absolute multiclan. So we return `False` but don't
# cache anything. (But we have now cached that it is a multiclan.)
if _multiclans.is_member(obj):
return False
is_absolute_multiset = all(elem.is_atom for elem in obj.data)
obj.cache_absolute(CacheStatus.from_bool(is_absolute_multiset))
# In order to determine whether this is an absolute multiset, we need to also examine whether
# this is a multiclan (also a multisets). Absolute multiclans are not absolute multisets.
return obj.cached_is_absolute and not obj.cached_is_multiclan
def is_absolute_member(obj: _mo.MathObject) -> bool:
"""Return whether ``obj`` is a member of the :term:`absolute ground set` of this algebra.
:type obj: _mo.MathObject|_mo.Couplet
:return: ``True`` if ``obj`` is an :term:`absolute couplet`, ``False`` if not.
"""
if not obj.is_couplet:
# If known to not be a couplet, it's also not an absolute couplet. No further caching.
return False
# From this point on, `obj` is known to be a couplet.
if obj.cached_absolute == _mo.CacheStatus.UNKNOWN:
is_absolute_couplet = obj.left.is_atom and obj.right.is_atom
obj.cache_absolute(_mo.CacheStatus.from_bool(is_absolute_couplet))
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.
:type obj: _mo.MathObject|_mo.Couplet
:return: ``True`` if ``obj`` is an :term:`absolute couplet`, ``False`` if not.
"""
if not obj.is_couplet:
# If known to not be a couplet, it's also not an absolute couplet. No further caching.
return False
# From this point on, `obj` is known to be a couplet.
if obj.cached_absolute == CacheStatus.UNKNOWN:
is_absolute_couplet = obj.left.is_atom and obj.right.is_atom
obj.cache_absolute(CacheStatus.from_bool(is_absolute_couplet))
return obj.cached_is_absolute
