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. :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