def test_binary_multi_extend_errors(self):
self.assertRaises(
AttributeError,
lambda: extension.binary_multi_extend(1, 2, sets.union))
self.assertRaises(
AttributeError,
lambda: extension.binary_multi_extend(Multiset(1), 2, sets.union))
self.assertRaises(
AttributeError,
lambda: extension.binary_multi_extend(1, Multiset(2), sets.union))
def cross_intersect(multiclan1: 'P(P(M x M) x N)',
multiclan2: 'PP(M x M)',
_checked=True) -> 'PP(M x M)':
r"""Return the :term:`cross-intersection` of ``multiclan1`` and ``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`intersection` from the :term:`algebra
of relations` (which inherits it from the :term:`algebra of sets`) to the :term:`algebra
of multiclans` applied to ``multiclan1`` and ``multiclan2``, or `Undef()` if
``multiclan1`` or ``multiclan2`` are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef2(multiclan1)
if not is_member(multiclan2):
return _undef.make_or_raise_undef2(multiclan2)
else:
assert is_member_or_undef(multiclan1)
assert is_member_or_undef(multiclan2)
if multiclan1 is _undef.Undef() or multiclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(multiclan1,
multiclan2,
_functools.partial(
_sets.intersect,
_checked=False),
_checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
if multiclan1.cached_is_functional or multiclan2.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_functional or multiclan2.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
return result
def cross_right_functional_union(
multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the :term:`cross-right-functional union` of ``multiclan1`` and ``multiclan2``.
:return: The :term:`binary multi-extension` of the :term:`right-functional union` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``multiclan1`` and ``multiclan2``, or `Undef()` if ``multiclan1`` or ``multiclan2`` are
not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef()
if not is_member(multiclan2):
return _undef.make_or_raise_undef()
else:
assert is_member(multiclan1)
assert is_member(multiclan2)
result = _extension.binary_multi_extend(multiclan1, multiclan2, _functools.partial(
_relations.right_functional_union, _checked=False), _checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
result.cache_right_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_not_functional or multiclan2.cached_is_not_functional:
result.cache_functional(_mo.CacheStatus.IS_NOT)
return result
def cross_intersect(multiclan1: 'P(P(M x M) x N)', multiclan2: 'PP(M x M)',
_checked=True) -> 'PP(M x M)':
r"""Return the :term:`cross-intersection` of ``multiclan1`` and ``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`intersection` from the :term:`algebra
of relations` (which inherits it from the :term:`algebra of sets`) to the :term:`algebra
of multiclans` applied to ``multiclan1`` and ``multiclan2``, or `Undef()` if
``multiclan1`` or ``multiclan2`` are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef2(multiclan1)
if not is_member(multiclan2):
return _undef.make_or_raise_undef2(multiclan2)
else:
assert is_member_or_undef(multiclan1)
assert is_member_or_undef(multiclan2)
if multiclan1 is _undef.Undef() or multiclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(multiclan1, multiclan2, _functools.partial(
_sets.intersect, _checked=False), _checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
if multiclan1.cached_is_functional or multiclan2.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_functional or multiclan2.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
return result
def compose(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the composition of ``multiclan1`` with ``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`composition` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``multiclan1`` and ``multiclan2``, or `Undef()` if ``multiclan1`` or ``multiclan2``
are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef2(multiclan1)
if not is_member(multiclan2):
return _undef.make_or_raise_undef2(multiclan2)
else:
assert is_member_or_undef(multiclan1)
assert is_member_or_undef(multiclan2)
if multiclan1 is _undef.Undef() or multiclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(multiclan1, multiclan2, _functools.partial(
_relations.compose, _checked=False), _checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
if multiclan1.cached_is_absolute and multiclan2.cached_is_absolute:
result.cache_absolute(_mo.CacheStatus.IS)
if multiclan1.cached_is_functional and multiclan2.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_functional and multiclan2.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
return result
def compose(multiclan1: 'P(P(M x M) x N)',
multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the composition of ``multiclan1`` with ``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`composition` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``multiclan1`` and ``multiclan2``, or `Undef()` if ``multiclan1`` or ``multiclan2``
are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef2(multiclan1)
if not is_member(multiclan2):
return _undef.make_or_raise_undef2(multiclan2)
else:
assert is_member_or_undef(multiclan1)
assert is_member_or_undef(multiclan2)
if multiclan1 is _undef.Undef() or multiclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(multiclan1,
multiclan2,
_functools.partial(
_relations.compose,
_checked=False),
_checked=False)
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
if multiclan1.cached_is_absolute and multiclan2.cached_is_absolute:
result.cache_absolute(_mo.CacheStatus.IS)
if multiclan1.cached_is_functional and multiclan2.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_functional and multiclan2.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
return result
def cross_functional_union(mclan1: 'P(P(M x M) x N)',
mclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the :term:`cross-functional union` of ``mclan1`` and ``mclan2``.
:return: The :term:`binary multi-extension` of the :term:`functional union` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``mclan1`` and ``mclan2``, or `Undef()` if ``mclan1`` or ``mclan2`` are
not :term:`multiclan`\s.
"""
if _checked:
if not is_member(mclan1):
return _undef.make_or_raise_undef2(mclan1)
if not is_member(mclan2):
return _undef.make_or_raise_undef2(mclan2)
else:
assert is_member_or_undef(mclan1)
assert is_member_or_undef(mclan2)
if mclan1 is _undef.Undef() or mclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(
mclan1,
mclan2,
_functools.partial(_relations.functional_union, _checked=False),
_checked=False)
if not result.is_empty:
result.cache_multiclan(CacheStatus.IS)
result.cache_functional(CacheStatus.IS)
if mclan1.cached_is_not_right_functional or mclan2.cached_is_not_right_functional:
result.cache_right_functional(CacheStatus.IS_NOT)
return result
def test_intersect(self):
self._check_wrong_argument_types_binary(intersect)
result = intersect(_set1, _set2)
self.assertEqual(result, _set1i2)
a_c_0 = Multiset([Multiset('a'), Multiset('a'), Multiset('c'), Multiset()])
ci = extension.binary_multi_extend(_ab_c, _ac_a, intersect)
self.assertEqual(ci, a_c_0)
def test_union(self):
self._check_wrong_argument_types_binary(union)
result = union(_set1, _set2)
self.assertEqual(result, _set1u2)
abc_ab_ac = Multiset([Multiset('a', 'b', 'c'), Multiset('a', 'b'), Multiset('a', 'c'),
Multiset('a', 'c')])
ab_c = _ab_c
ac_a = _ac_a
cu = extension.binary_multi_extend(ab_c, ac_a, union)
self.assertEqual(cu, abc_ab_ac)
def test_intersect(self):
self._check_wrong_argument_types_binary(intersect)
result = intersect(_set1, _set2)
self.assertEqual(result, _set1i2)
a_c_0 = Multiset(
[Multiset('a'),
Multiset('a'),
Multiset('c'),
Multiset()])
ci = extension.binary_multi_extend(_ab_c, _ac_a, intersect)
self.assertEqual(ci, a_c_0)
def test_union(self):
self._check_wrong_argument_types_binary(union)
result = union(_set1, _set2)
self.assertEqual(result, _set1u2)
abc_ab_ac = Multiset([
Multiset('a', 'b', 'c'),
Multiset('a', 'b'),
Multiset('a', 'c'),
Multiset('a', 'c')
])
ab_c = _ab_c
ac_a = _ac_a
cu = extension.binary_multi_extend(ab_c, ac_a, union)
self.assertEqual(cu, abc_ab_ac)
def superstrict(multiclan1: 'P(P(M x M) x N)',
multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the superstriction of ``multiclan1`` and ``multiclan2``.
The :term:`superstriction` of two :term:`multiclan`\s is a multiclan that contains all
:term:`relation`\s from ``multiclan1`` that are a :term:`supermultiset` of a relation from
``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`superstriction` from the
:term:`algebra of relations` (which inherits it from the :term:`algebra of sets`) to the
:term:`algebra of multiclans` applied to ``multiclan1`` and ``multiclan2``, or `Undef()`
if ``multiclan1`` or ``multiclan2`` are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef2(multiclan1)
if not is_member(multiclan2):
return _undef.make_or_raise_undef2(multiclan2)
else:
assert is_member_or_undef(multiclan1)
assert is_member_or_undef(multiclan2)
if multiclan1 is _undef.Undef() or multiclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(multiclan1,
multiclan2,
_functools.partial(
_sets.superstrict,
_checked=False),
_checked=False)
for elem, multi in result.data.items():
result.data[elem] = multiclan2.data[elem]
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
if multiclan1.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_reflexive:
result.cache_reflexive(_mo.CacheStatus.IS)
if multiclan1.cached_is_symmetric:
result.cache_symmetric(_mo.CacheStatus.IS)
if multiclan1.cached_is_transitive:
result.cache_transitive(_mo.CacheStatus.IS)
if multiclan1.cached_is_regular:
result.cache_regular(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_regular:
result.cache_right_regular(_mo.CacheStatus.IS)
return result
def superstrict(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the superstriction of ``multiclan1`` and ``multiclan2``.
The :term:`superstriction` of two :term:`multiclan`\s is a multiclan that contains all
:term:`relation`\s from ``multiclan1`` that are a :term:`supermultiset` of a relation from
``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`superstriction` from the
:term:`algebra of relations` (which inherits it from the :term:`algebra of sets`) to the
:term:`algebra of multiclans` applied to ``multiclan1`` and ``multiclan2``, or `Undef()`
if ``multiclan1`` or ``multiclan2`` are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _undef.make_or_raise_undef2(multiclan1)
if not is_member(multiclan2):
return _undef.make_or_raise_undef2(multiclan2)
else:
assert is_member_or_undef(multiclan1)
assert is_member_or_undef(multiclan2)
if multiclan1 is _undef.Undef() or multiclan2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = _extension.binary_multi_extend(multiclan1, multiclan2, _functools.partial(
_sets.superstrict, _checked=False), _checked=False)
for elem, multi in result.data.items():
result.data[elem] = multiclan2.data[elem]
if not result.is_empty:
result.cache_multiclan(_mo.CacheStatus.IS)
if multiclan1.cached_is_functional:
result.cache_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_functional:
result.cache_right_functional(_mo.CacheStatus.IS)
if multiclan1.cached_is_reflexive:
result.cache_reflexive(_mo.CacheStatus.IS)
if multiclan1.cached_is_symmetric:
result.cache_symmetric(_mo.CacheStatus.IS)
if multiclan1.cached_is_transitive:
result.cache_transitive(_mo.CacheStatus.IS)
if multiclan1.cached_is_regular:
result.cache_regular(_mo.CacheStatus.IS)
if multiclan1.cached_is_right_regular:
result.cache_right_regular(_mo.CacheStatus.IS)
return result
def cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the :term:`cross-union` of ``multiclan1`` and ``multiclan2``.
:return: The :term:`binary multi-extension` of :term:`union` from the
:term:`algebra of relations` (which inherits it from the :term:`algebra of multisets`)
to the :term:`algebra of multiclans` applied to ``multiclan1`` and ``multiclan2``,
or `Undef()` if ``multiclan1`` or ``multiclan2`` are not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _make_or_raise_undef()
if not is_member(multiclan2):
return _make_or_raise_undef()
else:
assert is_member(multiclan1)
assert is_member(multiclan2)
return _extension.binary_multi_extend(multiclan1, multiclan2, partial(
_sets.union, _checked=False), _checked=False)
def functional_cross_union(multiclan1: 'P(P(M x M) x N)', multiclan2: 'P(P(M x M) x N)',
_checked=True) -> 'P(P(M x M) x N)':
r"""Return the :term:`left-functional cross-union` of ``multiclan1`` and ``multiclan2``.
:return: The :term:`binary multi-extension` of the :term:`left-functional union` from the
:term:`algebra of relations` to the :term:`algebra of multiclans`, applied to
``multiclan1`` and ``multiclan2``, or `Undef()` if ``multiclan1`` or ``multiclan2`` are
not :term:`multiclan`\s.
"""
if _checked:
if not is_member(multiclan1):
return _make_or_raise_undef()
if not is_member(multiclan2):
return _make_or_raise_undef()
else:
assert is_member(multiclan1)
assert is_member(multiclan2)
return _extension.binary_multi_extend(multiclan1, multiclan2, partial(
_relations.functional_union, _checked=False), _checked=False)
def test_binary_multi_extend_errors(self):
self.assertRaises(AttributeError, lambda: extension.binary_multi_extend(1, 2, sets.union))
self.assertRaises(AttributeError, lambda: extension.binary_multi_extend(Multiset(1), 2, sets.union))
self.assertRaises(AttributeError, lambda: extension.binary_multi_extend(1, Multiset(2), sets.union))
def test_binary_multi_extend_errors(self):
self.assertIs(extension.binary_multi_extend(1, 2, sets.union), Undef())
self.assertIs(extension.binary_multi_extend(Multiset(1), 2, sets.union), Undef())
self.assertIs(extension.binary_multi_extend(1, Multiset(2), sets.union), Undef())
