def test_membership(self):
self.assertTrue(is_member(Multiset()))
self.assertTrue(is_member(Multiset(3)))
self.assertFalse(is_member(Atom(3)))
self.assertTrue(is_absolute_member(Multiset(3)))
self.assertFalse(is_absolute_member(Multiset(Couplet(3, 4))))
self.assertRaises(TypeError, lambda: is_member(3))
def test_membership(self):
self.assertTrue(is_member(Multiset()))
self.assertTrue(is_member(Multiset(3)))
self.assertFalse(is_member(Atom(3)))
self.assertTrue(is_absolute_member(Multiset(3)))
self.assertFalse(is_absolute_member(Multiset(Couplet(3, 4))))
self.assertRaises(AttributeError, lambda: is_member(3))
def unary_multi_extend(set_or_mset, op, _checked=True) -> 'P( M x N )':
r"""Return the :term:`unary extension` of ``op`` from one :term:`algebra` to another algebra.
For this extension, the elements of the extended algebra must be :term:`multiset`\s of the
elements of the original algebra.
:param set_or_mset: A :term:`set` or a :term:`multiset` with elements on which ``op`` operates.
:param op: A :term:`unary operation` that operates on the elements of ``set_or_mset``.
:return: A set that consists of the defined results of ``op`` when executed on the elements of
``set_or_mset``, or `Undef()` if ``set_or_mset`` is neither a set nor a multiset.
"""
if _checked:
if not _multisets.is_member(set_or_mset) and not _sets.is_member(
set_or_mset):
return _undef.make_or_raise_undef2(set_or_mset)
else:
assert _multisets.is_member(set_or_mset) or _sets.is_member(set_or_mset) \
or set_or_mset is _undef.Undef()
if set_or_mset is _undef.Undef():
return _undef.make_or_raise_undef(2)
def _get_values_set(set_):
result_counter = _collections.Counter()
for elem in set_:
result = op(elem)
if result is not _undef.Undef():
result_counter[result] += 1
return result_counter
def _get_values_multiset(mset):
result_counter = _collections.Counter()
for elem, multiplicity in mset.data.items():
result = op(elem)
if result is not _undef.Undef():
result_counter[result] += multiplicity
return result_counter
get_values = _get_values_multiset if _multisets.is_member(
set_or_mset) else _get_values_set
return _mo.Multiset(get_values(set_or_mset))
def binary_multi_extend(multiset1: 'P( M x N )',
multiset2: 'P( M x N )',
op,
_checked=True) -> 'P( M x N )':
r"""Return the :term:`binary extension` of ``op`` from one :term:`algebra` to another algebra.
For this extension, the elements of the extended algebra must be :term:`multiset`\s of the
elements of the original algebra.
:param multiset1: A :term:`multiset` with elements on which ``op`` operates.
:param multiset2: A multiset with elements on which ``op`` operates.
:param op: A :term:`binary operation` that operates on the elements of ``multiset1`` and
``multiset2``.
:return: A multiset that consists of the defined results of ``op`` when executed on all
combinations of the elements of ``multiset1`` and ``multiset2``, or `Undef()` if either
set is not a :class:`~.Multiset`.
"""
if _checked:
if not _multisets.is_member(multiset1):
return _undef.make_or_raise_undef2(multiset1)
if not _multisets.is_member(multiset2):
return _undef.make_or_raise_undef2(multiset2)
else:
assert _multisets.is_member_or_undef(multiset1)
assert _multisets.is_member_or_undef(multiset2)
if multiset1 is _undef.Undef() or multiset2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
def _get_values(_set1, _set2):
return_count = _collections.Counter()
for elem1, multi1 in _set1.data.items():
for elem2, multi2 in _set2.data.items():
result = op(elem1, elem2)
if result is not _undef.Undef():
return_count[result] += multi1 * multi2
return return_count
return _mo.Multiset(_get_values(multiset1, multiset2), direct_load=True)
def unary_multi_extend(set_or_mset, op, _checked=True) -> 'P( M x N )':
r"""Return the :term:`unary extension` of ``op`` from one :term:`algebra` to another algebra.
For this extension, the elements of the extended algebra must be :term:`multiset`\s of the
elements of the original algebra.
:param set_or_mset: A :term:`set` or a :term:`multiset` with elements on which ``op`` operates.
:param op: A :term:`unary operation` that operates on the elements of ``set_or_mset``.
:return: A set that consists of the defined results of ``op`` when executed on the elements of
``set_or_mset``, or `Undef()` if ``set_or_mset`` is neither a set nor a multiset.
"""
if _checked:
if not _multisets.is_member(set_or_mset) and not _sets.is_member(set_or_mset):
return _undef.make_or_raise_undef2(set_or_mset)
else:
assert _multisets.is_member(set_or_mset) or _sets.is_member(set_or_mset) \
or set_or_mset is _undef.Undef()
if set_or_mset is _undef.Undef():
return _undef.make_or_raise_undef(2)
def _get_values_set(set_):
result_counter = _collections.Counter()
for elem in set_:
result = op(elem)
if result is not _undef.Undef():
result_counter[result] += 1
return result_counter
def _get_values_multiset(mset):
result_counter = _collections.Counter()
for elem, multiplicity in mset.data.items():
result = op(elem)
if result is not _undef.Undef():
result_counter[result] += multiplicity
return result_counter
get_values = _get_values_multiset if _multisets.is_member(set_or_mset) else _get_values_set
return _mo.Multiset(get_values(set_or_mset))
def binary_multi_extend(multiset1: 'P( M x N )', multiset2: 'P( M x N )', op,
_checked=True) -> 'P( M x N )':
r"""Return the :term:`binary extension` of ``op`` from one :term:`algebra` to another algebra.
For this extension, the elements of the extended algebra must be :term:`multiset`\s of the
elements of the original algebra.
:param multiset1: A :term:`multiset` with elements on which ``op`` operates.
:param multiset2: A multiset with elements on which ``op`` operates.
:param op: A :term:`binary operation` that operates on the elements of ``multiset1`` and
``multiset2``.
:return: A multiset that consists of the defined results of ``op`` when executed on all
combinations of the elements of ``multiset1`` and ``multiset2``, or `Undef()` if either
set is not a :class:`~.Multiset`.
"""
if _checked:
if not _multisets.is_member(multiset1):
return _undef.make_or_raise_undef2(multiset1)
if not _multisets.is_member(multiset2):
return _undef.make_or_raise_undef2(multiset2)
else:
assert _multisets.is_member_or_undef(multiset1)
assert _multisets.is_member_or_undef(multiset2)
if multiset1 is _undef.Undef() or multiset2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
def _get_values(_set1, _set2):
return_count = _collections.Counter()
for elem1, multi1 in _set1.data.items():
for elem2, multi2 in _set2.data.items():
result = op(elem1, elem2)
if result is not _undef.Undef():
return_count[result] += multi1 * multi2
return return_count
return _mo.Multiset(_get_values(multiset1, multiset2), direct_load=True)