def get_rights_for_left(mclan: 'P(P(M x M) x N)', left: '( M )', _checked=True) -> 'P(M x N)':
"""Return the multiset of the right components of all couplets in the multiclan ``mclan``
associated with the left component ``left``.
:return: The :term:`right multiset` of the :term:`multiclan` ``mclan`` associated with the
:term:`left component` ``left`` or `Undef()` if ``mclan`` is not a multiclan.
"""
if _checked:
if not is_member(mclan):
return _undef.make_or_raise_undef2(mclan)
if left is _undef.Undef():
return _mo.Set()
left = _mo.auto_convert(left)
else:
assert is_member_or_undef(mclan)
assert _mo.is_mathobject_or_undef(left)
if mclan is _undef.Undef():
return _undef.make_or_raise_undef(2)
if left is _undef.Undef():
return _mo.Set()
clan_itr = iter(mclan)
rights = _sets.multify(_relations.get_rights_for_left(next(clan_itr), left, _checked=False))
for rel in clan_itr:
rights = _multisets.add(
_sets.multify(_relations.get_rights_for_left(rel, left, _checked=False)),
rights, _checked=False)
if not rights.is_empty:
if mclan.cached_is_absolute:
rights.cache_absolute(_mo.CacheStatus.IS)
return rights
def get_left(rel: 'P(M x M)', right: '( M )', _checked=True) -> '( M )':
r"""Return the left component of the couplet that has a right component of ``right``.
In general, use with :term:`right-functional` :term:`relation`\s; that is, relations
where all :term:`right component`\s appear at most once.
:return: The :term:`left component` of the :term:`couplet` that has a :term:`right component`
of ``right``, or `Undef()` if there is not exactly one couplet with the right component
``right`` in ``rel`` or ``rel`` is not a :term:`relation`.
"""
if _checked:
if not is_member(rel):
return _undef.make_or_raise_undef2(rel)
if right is _undef.Undef():
return _undef.make_or_raise_undef(2)
right = _mo.auto_convert(right)
else:
assert is_member_or_undef(rel)
assert _mo.is_mathobject_or_undef(right)
if right is _undef.Undef() or rel is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = None
for elem in rel:
assert elem.is_couplet
if elem.right == right:
if result is not None:
return _undef.make_or_raise_undef() # Early Undef() exit if more than one found.
result = elem.left
if result is None:
return _undef.make_or_raise_undef() # Undef() exit if none found.
return result
def get_rights_for_left(rel: 'P(M x M)', left: '( M )', _checked=True) -> 'P( M )':
"""Return the set of the right components of all couplets in the relation ``rel`` associated
with the :term:`left component` ``left``.
:return: The :term:`right set` of the :term:`relation` ``rel`` associated with the :term:`left
component` or `Undef()` if ``rel`` is not a :term:`relation`.
"""
if _checked:
if not is_member(rel):
return _undef.make_or_raise_undef2(rel)
if left is _undef.Undef():
return _mo.Set()
left = _mo.auto_convert(left)
else:
assert is_member_or_undef(rel)
assert _mo.is_mathobject_or_undef(left)
if rel is _undef.Undef():
return _undef.make_or_raise_undef(2)
if left is _undef.Undef():
return _mo.Set()
result = _mo.Set((elem.right for elem in rel if elem.left == left), direct_load=True)
if not result.is_empty:
if rel.cached_is_absolute:
result.cache_absolute(_mo.CacheStatus.IS)
return result
def get_rights_for_left(mclan: 'P(P(M x M) x N)',
left: '( M )',
_checked=True) -> 'P(M x N)':
"""Return the multiset of the right components of all couplets in the multiclan ``mclan``
associated with the left component ``left``.
:return: The :term:`right multiset` of the :term:`multiclan` ``mclan`` associated with the
:term:`left component` ``left`` or `Undef()` if ``mclan`` is not a multiclan.
"""
if _checked:
if not is_member(mclan):
return _undef.make_or_raise_undef2(mclan)
if left is _undef.Undef():
return _mo.Set()
left = _mo.auto_convert(left)
else:
assert is_member_or_undef(mclan)
assert _mo.is_mathobject_or_undef(left)
if mclan is _undef.Undef():
return _undef.make_or_raise_undef(2)
if left is _undef.Undef():
return _mo.Set()
clan_itr = iter(mclan)
rights = _sets.multify(
_relations.get_rights_for_left(next(clan_itr), left, _checked=False))
for rel in clan_itr:
rights = _multisets.add(_sets.multify(
_relations.get_rights_for_left(rel, left, _checked=False)),
rights,
_checked=False)
if not rights.is_empty:
if mclan.cached_is_absolute:
rights.cache_absolute(_mo.CacheStatus.IS)
return rights
def get_left(rel: 'P(M x M)', right: '( M )', _checked=True) -> '( M )':
r"""Return the left component of the couplet that has a right component of ``right``.
In general, use with :term:`right-functional` :term:`relation`\s; that is, relations
where all :term:`right component`\s appear at most once.
:return: The :term:`left component` of the :term:`couplet` that has a :term:`right component`
of ``right``, or `Undef()` if there is not exactly one couplet with the right component
``right`` in ``rel`` or ``rel`` is not a :term:`relation`.
"""
if _checked:
if not is_member(rel):
return _undef.make_or_raise_undef2(rel)
if right is _undef.Undef():
return _undef.make_or_raise_undef(2)
right = _mo.auto_convert(right)
else:
assert is_member_or_undef(rel)
assert _mo.is_mathobject_or_undef(right)
if right is _undef.Undef() or rel is _undef.Undef():
return _undef.make_or_raise_undef(2)
result = None
for elem in rel:
assert elem.is_couplet
if elem.right == right:
if result is not None:
return _undef.make_or_raise_undef(
) # Early Undef() exit if more than one found.
result = elem.left
if result is None:
return _undef.make_or_raise_undef() # Undef() exit if none found.
return result
def get_rights_for_left(rel: 'P(M x M)',
left: '( M )',
_checked=True) -> 'P( M )':
"""Return the set of the right components of all couplets in the relation ``rel`` associated
with the :term:`left component` ``left``.
:return: The :term:`right set` of the :term:`relation` ``rel`` associated with the :term:`left
component` or `Undef()` if ``rel`` is not a :term:`relation`.
"""
if _checked:
if not is_member(rel):
return _undef.make_or_raise_undef2(rel)
if left is _undef.Undef():
return _mo.Set()
left = _mo.auto_convert(left)
else:
assert is_member_or_undef(rel)
assert _mo.is_mathobject_or_undef(left)
if rel is _undef.Undef():
return _undef.make_or_raise_undef(2)
if left is _undef.Undef():
return _mo.Set()
result = _mo.Set((elem.right for elem in rel if elem.left == left),
direct_load=True)
if not result.is_empty:
if rel.cached_is_absolute:
result.cache_absolute(_mo.CacheStatus.IS)
return result