def binary_extend(set1: 'P( M )',
set2: 'P( M )',
op,
_checked=True) -> 'P( M )':
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:`set`\s of the
elements of the original algebra.
:param set1: A :term:`set` with elements on which ``op`` operates.
:param set2: A set with elements on which ``op`` operates.
:param op: A :term:`binary operation` that operates on the elements of ``set1`` and ``set2``.
:return: A set that consists of the defined results of ``op`` when executed on all combinations
of the elements of ``set1`` and ``set2``, or `Undef()` if either set is not a
:class:`~.Set`.
"""
if _checked:
if not _sets.is_member(set1):
return _undef.make_or_raise_undef2(set1)
if not _sets.is_member(set2):
return _undef.make_or_raise_undef2(set2)
else:
assert _sets.is_member_or_undef(set1)
assert _sets.is_member_or_undef(set2)
if set1 is _undef.Undef() or set2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
def _get_values(_set1, _set2):
for e1 in _set1:
for e2 in _set2:
result = op(e1, e2)
if result is not _undef.Undef():
yield result
return _mo.Set(_get_values(set1, set2), direct_load=True)
def binary_extend(set1: 'P( M )', set2: 'P( M )', op, _checked=True) -> 'P( M )':
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:`set`\s of the
elements of the original algebra.
:param set1: A :term:`set` with elements on which ``op`` operates.
:param set2: A set with elements on which ``op`` operates.
:param op: A :term:`binary operation` that operates on the elements of ``set1`` and ``set2``.
:return: A set that consists of the defined results of ``op`` when executed on all combinations
of the elements of ``set1`` and ``set2``, or `Undef()` if either set is not a
:class:`~.Set`.
"""
if _checked:
if not _sets.is_member(set1):
return _undef.make_or_raise_undef2(set1)
if not _sets.is_member(set2):
return _undef.make_or_raise_undef2(set2)
else:
assert _sets.is_member_or_undef(set1)
assert _sets.is_member_or_undef(set2)
if set1 is _undef.Undef() or set2 is _undef.Undef():
return _undef.make_or_raise_undef(2)
def _get_values(_set1, _set2):
for e1 in _set1:
for e2 in _set2:
result = op(e1, e2)
if result is not _undef.Undef():
yield result
return _mo.Set(_get_values(set1, set2), direct_load=True)
def big_intersect(set_of_multisets: 'PP( M x N )', _checked=True) -> 'P( M x N )':
"""Return the multiset intersection of all members of ``multiset``.
:return: The :term:`multiset intersection` of all members of ``set_of_multisets`` or `Undef()`
if ``set_of_multisets`` is not a :class:`~.Set` or any of its members are not instances of
:class:`~.Multiset`.
"""
if _checked:
if not isinstance(set_of_multisets, _mo.Set):
return _undef.make_or_raise_undef2(set_of_multisets)
for element in set_of_multisets:
if not is_member(element):
return _undef.make_or_raise_undef2(element)
else:
assert _sets.is_member_or_undef(set_of_multisets)
if set_of_multisets is _undef.Undef():
return _undef.make_or_raise_undef(2)
return _sets.chain_binary_operation(
set_of_multisets, _functools.partial(intersect, _checked=False), is_member)
def big_union(set_of_multisets: 'PP( M x N )', _checked=True) -> 'P( M x N )':
"""Return the set_of_multisets union of all members of ``set_of_multisets``.
:return: The :term:`multiset union` of all members of ``set_of_multisets`` or `Undef()` if
``set_of_multisets`` is not a :class:`~.Set` or any of its members are not instances of
:class:`~.Multiset`.
"""
if _checked:
if not isinstance(set_of_multisets, _mo.Set):
return _undef.make_or_raise_undef2(set_of_multisets)
for element in set_of_multisets:
if not is_member(element):
return _undef.make_or_raise_undef2(element)
else:
assert _sets.is_member_or_undef(set_of_multisets)
if set_of_multisets is _undef.Undef():
return _undef.make_or_raise_undef(2)
return _sets.chain_binary_operation(
set_of_multisets, _functools.partial(union, _checked=False), is_member)
