def test_union_flags(self): s1 = Set(1) s2 = Set(2) s3 = Set(1, 2) self.assertTrue(is_absolute_member(s1)) self.assertTrue(is_absolute_member(s2)) self.assertTrue(is_absolute_member(s3)) result = union(s1, s2) self.assertEqual(s3, result) self.assertEqual(result.cached_is_absolute, CacheStatus.IS) from algebraixlib.algebras import relations as _rels rel1 = Set(Couplet('a', 1)) rel2 = Set(Couplet('b', 2)) rel3 = Set(Couplet('a', 1), Couplet('b', 2)) self.assertTrue(_rels.is_absolute_member(rel1)) self.assertTrue(_rels.is_absolute_member(rel2)) result = union(rel1, rel2) self.assertEqual(rel3, result) self.assertEqual(result.cached_is_absolute, CacheStatus.IS) from algebraixlib.algebras import clans as _clans clan1 = Set(rel1) clan2 = Set(rel2) clan3 = Set(rel1, rel2) self.assertTrue(_clans.is_absolute_member(clan1)) self.assertTrue(_clans.is_absolute_member(clan2)) self.assertTrue(_clans.is_functional(clan1)) self.assertTrue(_clans.is_functional(clan2)) self.assertTrue(_clans.is_right_functional(clan1)) self.assertTrue(_clans.is_right_functional(clan2)) result = union(clan1, clan2) self.assertEqual(clan3, result) self.assertEqual(result.cached_absolute, CacheStatus.IS) self.assertEqual(result.cached_functional, CacheStatus.IS) self.assertEqual(result.cached_right_functional, CacheStatus.IS) clan4 = Set(Set(Couplet(s1, 1), Couplet(s1, 2))) clan5 = Set(rel1, Set(Couplet(s1, 1), Couplet(s1, 2))) self.assertFalse(_clans.is_absolute_member(clan4)) self.assertFalse(_clans.is_functional(clan4)) result = union(clan1, clan4) self.assertEqual(clan5, result) self.assertEqual(result.cached_absolute, CacheStatus.IS_NOT) self.assertEqual(result.cached_functional, CacheStatus.IS_NOT) rel1 = Set(Couplet('a', 1), Couplet('b', 2)).cache_relation(CacheStatus.IS) rel2 = Set(Couplet('c', 3)) self.assertEqual( union(rel1, rel2).cached_relation, CacheStatus.UNKNOWN) self.assertTrue(_rels.is_member(rel2)) self.assertEqual(union(rel1, rel2).cached_relation, CacheStatus.IS)
def test_union_flags(self): s1 = Set(1) s2 = Set(2) s3 = Set(1, 2) self.assertTrue(is_absolute_member(s1)) self.assertTrue(is_absolute_member(s2)) self.assertTrue(is_absolute_member(s3)) result = union(s1, s2) self.assertEqual(s3, result) self.assertEqual(result.cached_is_absolute, CacheStatus.IS) from algebraixlib.algebras import relations as _rels rel1 = Set(Couplet('a', 1)) rel2 = Set(Couplet('b', 2)) rel3 = Set(Couplet('a', 1), Couplet('b', 2)) self.assertTrue(_rels.is_absolute_member(rel1)) self.assertTrue(_rels.is_absolute_member(rel2)) result = union(rel1, rel2) self.assertEqual(rel3, result) self.assertEqual(result.cached_is_absolute, CacheStatus.IS) from algebraixlib.algebras import clans as _clans clan1 = Set(rel1) clan2 = Set(rel2) clan3 = Set(rel1, rel2) self.assertTrue(_clans.is_absolute_member(clan1)) self.assertTrue(_clans.is_absolute_member(clan2)) self.assertTrue(_clans.is_functional(clan1)) self.assertTrue(_clans.is_functional(clan2)) self.assertTrue(_clans.is_right_functional(clan1)) self.assertTrue(_clans.is_right_functional(clan2)) result = union(clan1, clan2) self.assertEqual(clan3, result) self.assertEqual(result.cached_absolute, CacheStatus.IS) self.assertEqual(result.cached_functional, CacheStatus.IS) self.assertEqual(result.cached_right_functional, CacheStatus.IS) clan4 = Set(Set(Couplet(s1, 1), Couplet(s1, 2))) clan5 = Set(rel1, Set(Couplet(s1, 1), Couplet(s1, 2))) self.assertFalse(_clans.is_absolute_member(clan4)) self.assertFalse(_clans.is_functional(clan4)) result = union(clan1, clan4) self.assertEqual(clan5, result) self.assertEqual(result.cached_absolute, CacheStatus.IS_NOT) self.assertEqual(result.cached_functional, CacheStatus.IS_NOT) rel1 = Set(Couplet('a', 1), Couplet('b', 2)).cache_relation(CacheStatus.IS) rel2 = Set(Couplet('c', 3)) self.assertEqual(union(rel1, rel2).cached_relation, CacheStatus.UNKNOWN) self.assertTrue(_rels.is_member(rel2)) self.assertEqual(union(rel1, rel2).cached_relation, CacheStatus.IS)
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)