From bc8a4040467f4e2dbc1fc46cb41fc8b5034d5c01 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Mon, 22 Jan 2024 16:09:49 +0100
Subject: [PATCH 1/4] some changes in posets (ruff UP and PERF)

---
 src/sage/combinat/posets/cartesian_product.py |  2 +-
 src/sage/combinat/posets/hasse_diagram.py     | 25 ++++----
 src/sage/combinat/posets/lattices.py          | 17 +++---
 src/sage/combinat/posets/linear_extensions.py |  4 +-
 src/sage/combinat/posets/moebius_algebra.py   |  6 +-
 src/sage/combinat/posets/poset_examples.py    | 57 +++++++++----------
 src/sage/combinat/posets/posets.py            | 50 ++++++++--------
 7 files changed, 80 insertions(+), 81 deletions(-)

diff --git a/src/sage/combinat/posets/cartesian_product.py b/src/sage/combinat/posets/cartesian_product.py
index abf2ec94b4d..42c23732df9 100644
--- a/src/sage/combinat/posets/cartesian_product.py
+++ b/src/sage/combinat/posets/cartesian_product.py
@@ -102,7 +102,7 @@ def __init__(self, sets, category, order=None, **kwargs):
             try:
                 self._le_ = getattr(self, 'le_' + order)
             except AttributeError:
-                raise ValueError("no order '%s' known" % (order,))
+                raise ValueError(f"no order '{order}' known")
         else:
             self._le_ = order
 
diff --git a/src/sage/combinat/posets/hasse_diagram.py b/src/sage/combinat/posets/hasse_diagram.py
index 1c61cee4760..f91bd993d6f 100644
--- a/src/sage/combinat/posets/hasse_diagram.py
+++ b/src/sage/combinat/posets/hasse_diagram.py
@@ -67,7 +67,7 @@ def __str__(self):
             sage: error.__str__()
             'no meet for 15 and 18'
         """
-        return "no {} for {} and {}".format(self.fail, self.x, self.y)
+        return f"no {self.fail} for {self.x} and {self.y}"
 
 
 class HasseDiagram(DiGraph):
@@ -792,8 +792,8 @@ def _rank(self):
         while not_found:
             y = not_found.pop()
             rank[y] = 0  # We set some vertex to have rank 0
-            component = set([y])
-            queue = set([y])
+            component = {y}
+            queue = {y}
             while queue:
                 # look at the neighbors of y and set the ranks;
                 # then look at the neighbors of the neighbors ...
@@ -1286,7 +1286,7 @@ def _leq_storage(self):
             [{0, 1, 2, 3, 4, 5, 6}, {1, 6}, {2, 6}, {3, 6}, {4, 6}, {5, 6}, {6}]
         """
         n = self.order()
-        greater_than = [set([i]) for i in range(n)]
+        greater_than = [{i} for i in range(n)]
         for i in range(n - 1, -1, -1):
             gt = greater_than[i]
             for j in self.neighbor_out_iterator(i):
@@ -2481,7 +2481,7 @@ def is_linear_interval(self, t_min, t_max) -> bool:
             return True
         return False
 
-    def diamonds(self):
+    def diamonds(self) -> tuple:
         r"""
         Return the list of diamonds of ``self``.
 
@@ -2525,8 +2525,7 @@ def diamonds(self):
                     zs = self.common_upper_covers([x, y])
                     if len(zs) != 1:
                         all_diamonds_completed = False
-                    for z in zs:
-                        diamonds.append((w, x, y, z))
+                    diamonds.extend((w, x, y, z) for z in zs)
         return (diamonds, all_diamonds_completed)
 
     def common_upper_covers(self, vertices):
@@ -2651,7 +2650,7 @@ def sublattices_iterator(self, elms, min_e):
             if e in elms:
                 continue
             current_set = set(elms)
-            gens = set([e])
+            gens = {e}
             while gens:
                 g = gens.pop()
                 if g < e and g not in elms:
@@ -2684,7 +2683,7 @@ def sublattice(elms, e):
             Helper function to get sublattice generated by list
             of elements.
             """
-            gens_remaining = set([e])
+            gens_remaining = {e}
             current_set = set(elms)
 
             while gens_remaining:
@@ -2700,7 +2699,7 @@ def sublattice(elms, e):
 
         N = self.cardinality()
         elms = [0]
-        sublats = [set([0])]
+        sublats = [{0}]
         result = []
         skip = -1
 
@@ -2981,7 +2980,7 @@ def neutral_elements(self):
             return set(range(n))
 
         todo = set(range(1, n - 1))
-        neutrals = set([0, n - 1])
+        neutrals = {0, n - 1}
         notneutrals = set()
         all_elements = set(range(n))
 
@@ -3242,7 +3241,7 @@ def fill_to_interval(S):
                 for v in fill_to_interval(c):
                     cong.union(r, v)
 
-        todo = set(cong.find(e) for part in parts for e in part)
+        todo = {cong.find(e) for part in parts for e in part}
 
         while todo:
 
@@ -3307,7 +3306,7 @@ def fill_to_interval(S):
                         d = jn[d, m]
 
             # This removes duplicates from todo.
-            todo = set(cong.find(x) for x in todo)
+            todo = {cong.find(x) for x in todo}
 
         return cong
 
diff --git a/src/sage/combinat/posets/lattices.py b/src/sage/combinat/posets/lattices.py
index 6af274fd18a..75a3af11e3b 100644
--- a/src/sage/combinat/posets/lattices.py
+++ b/src/sage/combinat/posets/lattices.py
@@ -3089,11 +3089,10 @@ def vertical_decomposition(self, elements_only=False):
                 self._hasse_diagram.vertical_decomposition(return_list=True) +
                 [self.cardinality() - 1])
         n = len(elms)
-        result = []
-        for i in range(n - 1):
-            result.append(LatticePoset(
-                self.subposet([self[e] for e in range(elms[i], elms[i + 1] + 1)])))
-        return result
+        return [LatticePoset(self.subposet([self[e]
+                                            for e in range(elms[i],
+                                                           elms[i + 1] + 1)]))
+                for i in range(n - 1)]
 
     def is_vertically_decomposable(self, certificate=False):
         r"""
@@ -3461,8 +3460,8 @@ def frattini_sublattice(self):
             sage: sorted(L.frattini_sublattice().list())
             [1, 2, 4, 10, 19, 22, 33]
         """
-        return LatticePoset(self.subposet([self[x] for x in
-                self._hasse_diagram.frattini_sublattice()]))
+        return LatticePoset(self.subposet([self[x]
+                for x in self._hasse_diagram.frattini_sublattice()]))
 
     def moebius_algebra(self, R):
         """
@@ -3634,9 +3633,9 @@ def adjunct(self, other, a, b):
         if not isinstance(other, FiniteLatticePoset):
             raise ValueError("other is not a finite lattice")
         if not self.is_greater_than(b, a):
-            raise ValueError("element %s is not greater than %s in the lattice" % (b, a))
+            raise ValueError(f"element {b} is not greater than {a} in the lattice")
         if self.covers(a, b):
-            raise ValueError("element %s covers element %s in the lattice" % (b, a))
+            raise ValueError(f"element {b} covers element {a} in the lattice")
 
         if other.cardinality() == 0:
             return self.relabel(lambda e: (0, e))
diff --git a/src/sage/combinat/posets/linear_extensions.py b/src/sage/combinat/posets/linear_extensions.py
index cca9b098d4a..736562802f5 100644
--- a/src/sage/combinat/posets/linear_extensions.py
+++ b/src/sage/combinat/posets/linear_extensions.py
@@ -141,7 +141,7 @@ def check(self):
         """
         P = self.parent().poset()
         if not P.is_linear_extension(self):
-            raise ValueError("%s is not a linear extension of %s" % (self, P))
+            raise ValueError(f"{self} is not a linear extension of {P}")
 
     def poset(self):
         r"""
@@ -625,7 +625,7 @@ def cardinality(self):
             while K[j]:
                 K.append([b for a in K[j] for b in Jup[a]])
                 j += 1
-            K = sorted(set(item for sublist in K for item in sublist))
+            K = sorted({item for sublist in K for item in sublist})
             for j in range(len(K)):
                 i = m + j + 1
                 Jup[i] = [m + K.index(a) + 1 for a in Jup[K[j]]]
diff --git a/src/sage/combinat/posets/moebius_algebra.py b/src/sage/combinat/posets/moebius_algebra.py
index 00691051587..5a4380e643f 100644
--- a/src/sage/combinat/posets/moebius_algebra.py
+++ b/src/sage/combinat/posets/moebius_algebra.py
@@ -123,7 +123,7 @@ def _repr_(self):
             sage: L.moebius_algebra(QQ)
             Moebius algebra of Finite lattice containing 16 elements over Rational Field
         """
-        return "Moebius algebra of {} over {}".format(self._lattice, self.base_ring())
+        return f"Moebius algebra of {self._lattice} over {self.base_ring()}"
 
     def a_realization(self):
         r"""
@@ -705,7 +705,7 @@ def _repr_(self):
             Category of bases of Moebius algebra of Finite lattice
              containing 16 elements over Rational Field
         """
-        return "Category of bases of {}".format(self.base())
+        return f"Category of bases of {self.base()}"
 
     def super_categories(self):
         r"""
@@ -738,7 +738,7 @@ def _repr_(self):
                 Moebius algebra of Finite lattice containing 16 elements
                  over Rational Field in the idempotent basis
             """
-            return "{} in the {} basis".format(self.realization_of(), self._basis_name)
+            return f"{self.realization_of()} in the {self._basis_name} basis"
 
         def product_on_basis(self, x, y):
             """
diff --git a/src/sage/combinat/posets/poset_examples.py b/src/sage/combinat/posets/poset_examples.py
index e166e87b141..0b4a949c27b 100644
--- a/src/sage/combinat/posets/poset_examples.py
+++ b/src/sage/combinat/posets/poset_examples.py
@@ -426,7 +426,7 @@ def DiamondPoset(n, facade=None):
         """
         n = check_int(n, 3)
         c = [[n - 1] for x in range(n)]
-        c[0] = [x for x in range(1, n - 1)]
+        c[0] = list(range(1, n - 1))
         c[n - 1] = []
         D = DiGraph({v: c[v] for v in range(n)}, format='dict_of_lists')
         return FiniteLatticePoset(hasse_diagram=D,
@@ -719,9 +719,9 @@ def ProductOfChains(chain_lengths, facade=None):
         try:
             l = [Integer(x) for x in chain_lengths]
         except TypeError:
-            raise TypeError("parameter chain_lengths must be a list of integers, not {0}".format(chain_lengths))
+            raise TypeError("parameter chain_lengths must be a list of integers, not {}".format(chain_lengths))
         if any(x < 0 for x in l):
-            raise TypeError("parameter chain_lengths must be a list of nonnegative integers, not {0}".format(l))
+            raise TypeError("parameter chain_lengths must be a list of nonnegative integers, not {}".format(l))
 
         # given the empty list, we expect the empty poset.
         if not chain_lengths:
@@ -781,9 +781,9 @@ def RandomPoset(n, p):
         try:
             p = float(p)
         except (TypeError, ValueError):
-            raise TypeError("probability must be a real number, not {0}".format(p))
+            raise TypeError(f"probability must be a real number, not {p}")
         if p < 0 or p > 1:
-            raise ValueError("probability must be between 0 and 1, not {0}".format(p))
+            raise ValueError(f"probability must be between 0 and 1, not {p}")
 
         D = DiGraph(loops=False, multiedges=False)
         D.add_vertices(range(n))
@@ -867,9 +867,9 @@ def RandomLattice(n, p, properties=None):
         try:
             p = float(p)
         except Exception:
-            raise TypeError("probability must be a real number, not {0}".format(p))
+            raise TypeError(f"probability must be a real number, not {p}")
         if p < 0 or p >= 1:
-            raise ValueError("probability must be a positive real number and below 1, not {0}".format(p))
+            raise ValueError("probability must be a positive real number and below 1, not {}".format(p))
 
         if properties is None:
             # Basic case, no special properties for lattice asked.
@@ -882,11 +882,11 @@ def RandomLattice(n, p, properties=None):
             return LatticePoset(D, cover_relations=True)
 
         if isinstance(properties, str):
-            properties = set([properties])
+            properties = {properties}
         else:
             properties = set(properties)
 
-        known_properties = set(['planar', 'dismantlable', 'distributive', 'stone'])
+        known_properties = {'planar', 'dismantlable', 'distributive', 'stone'}
         errors = properties.difference(known_properties)
         if errors:
             raise ValueError("unknown value %s for 'properties'" % errors.pop())
@@ -907,22 +907,22 @@ def RandomLattice(n, p, properties=None):
         if 'stone' in properties and len(properties) > 1:
             raise NotImplementedError("combining 'stone' with other properties is not implemented")
 
-        if properties == set(['planar']):
+        if properties == {'planar'}:
             D = _random_planar_lattice(n)
             D.relabel([i - 1 for i in Permutations(n).random_element()])
             return LatticePoset(D)
 
-        if properties == set(['dismantlable']):
+        if properties == {'dismantlable'}:
             D = _random_dismantlable_lattice(n)
             D.relabel([i - 1 for i in Permutations(n).random_element()])
             return LatticePoset(D)
 
-        if properties == set(['stone']):
+        if properties == {'stone'}:
             D = _random_stone_lattice(n)
             D.relabel([i - 1 for i in Permutations(n).random_element()])
             return LatticePoset(D)
 
-        if properties == set(['distributive']):
+        if properties == {'distributive'}:
             tmp = Poset(_random_distributive_lattice(n)).order_ideals_lattice(as_ideals=False)
             D = copy(tmp._hasse_diagram)
             D.relabel([i - 1 for i in Permutations(n).random_element()])
@@ -1106,18 +1106,17 @@ def SymmetricGroupBruhatIntervalPoset(start, end):
         start = Permutation(start)
         end = Permutation(end)
         if len(start) != len(end):
-            raise TypeError("start (%s) and end (%s) must have same length" % (start, end))
+            raise TypeError(f"start ({start}) and end ({end}) must have same length")
         if not start.bruhat_lequal(end):
-            raise TypeError("must have start (%s) <= end (%s) in Bruhat order" % (start, end))
+            raise TypeError(f"must have start ({start}) <= end ({end}) in Bruhat order")
         unseen = [start]
         nodes = {}
         while unseen:
             perm = unseen.pop(0)
             nodes[perm] = [succ_perm for succ_perm in perm.bruhat_succ()
                            if succ_perm.bruhat_lequal(end)]
-            for succ_perm in nodes[perm]:
-                if succ_perm not in nodes:
-                    unseen.append(succ_perm)
+            unseen.extend(succ_perm for succ_perm in nodes[perm]
+                          if succ_perm not in nodes)
         return Poset(nodes)
 
     @staticmethod
@@ -1393,9 +1392,9 @@ def UpDownPoset(n, m=1):
         try:
             m = Integer(m)
         except TypeError:
-            raise TypeError("parameter m must be an integer, not {0}".format(m))
+            raise TypeError(f"parameter m must be an integer, not {m}")
         if m < 1:
-            raise ValueError("parameter m must be positive, not {0}".format(m))
+            raise ValueError(f"parameter m must be positive, not {m}")
 
         covers = [[i, i + 1] if (i + 1) % (m + 1) else [i + 1, i]
                   for i in range(n - 1)]
@@ -1681,7 +1680,7 @@ def PermutationPatternInterval(bottom, top):
         top = P(top)
         bottom = P(bottom)
         if not top.has_pattern(bottom):
-            raise ValueError("{} doesn't contain {} as a pattern".format(top, bottom))
+            raise ValueError(f"{top} doesn't contain {bottom} as a pattern")
         # Make a list of lists of elements in the interval divided by rank.
         # List will be flattened at the end
         elem = [[top]]
@@ -1833,19 +1832,17 @@ def MobilePoset(ribbon, hangers, anchor=None):
         elements.extend(ribbon._elements)
 
         if anchor:
-            for cr in anchor[2].cover_relations():
-                cover_relations.append(((anchor[0], cr[0]), (anchor[0], cr[1])))
+            cover_relations.extend(((anchor[0], cr[0]), (anchor[0], cr[1]))
+                                   for cr in anchor[2].cover_relations())
             cover_relations.append((anchor[0], (anchor[0], anchor[1])))
 
-            for elmt in anchor[2]._elements:
-                elements.append((anchor[0], elmt))
+            elements.extend((anchor[0], elmt) for elmt in anchor[2]._elements)
 
         for r, hangs in hangers.items():
             for i, h in enumerate(hangs):
-                for v in h._elements:
-                    elements.append((r, i, v))
-                for cr in h.cover_relations():
-                    cover_relations.append(((r, i, cr[0]), (r, i, cr[1])))
+                elements.extend((r, i, v) for v in h._elements)
+                cover_relations.extend(((r, i, cr[0]), (r, i, cr[1]))
+                                       for cr in h.cover_relations())
                 cover_relations.append(((r, i, h.top()), r))
 
         return Mobile(DiGraph([elements, cover_relations]))
@@ -1896,7 +1893,7 @@ def _random_lattice(n, p):
     n = n - 1
     meets = [[None] * n for _ in range(n)]
     meets[0][0] = 0
-    maxs = set([0])
+    maxs = {0}
     lc_all = [[]]  # No lower covers for the bottom element.
 
     for i in range(1, n):
diff --git a/src/sage/combinat/posets/posets.py b/src/sage/combinat/posets/posets.py
index 0a8352274ee..3a8252983e3 100644
--- a/src/sage/combinat/posets/posets.py
+++ b/src/sage/combinat/posets/posets.py
@@ -677,6 +677,13 @@ def Poset(data=None, element_labels=None, cover_relations=False, linear_extensio
         ...
         ValueError: the provided list of elements is not a linear extension
         for the poset as it contains duplicate elements
+
+    TESTS::
+
+        sage: Poset([("a","b","c"),(["a","b","c"])])
+        Traceback (most recent call last):
+        ...
+        TypeError: not a list of relations
     """
     # Avoiding some errors from the user when data should be a pair
     if not (element_labels is None or isinstance(element_labels, (dict, list))):
@@ -716,17 +723,14 @@ def Poset(data=None, element_labels=None, cover_relations=False, linear_extensio
             else:  # type 1
                 elements, relations = data
                 # check that relations are relations
-                for r in relations:
-                    try:
-                        u, v = r
-                    except ValueError:
-                        raise TypeError("not a list of relations")
+                if not all(len(r) == 2 for r in relations):
+                    raise TypeError("not a list of relations")
             D = DiGraph()
             D.add_vertices(elements)
             D.add_edges(relations, loops=False)
         elif len(data) > 2:
             # type 3, list/tuple of upper covers
-            vertices = sorted(set(x for item in data for x in item))
+            vertices = sorted({x for item in data for x in item})
             if len(vertices) != len(data):
                 # by default, assuming vertices are the range 0..n
                 vertices = range(len(data))
@@ -987,10 +991,10 @@ def __classcall__(cls, hasse_diagram, elements=None, category=None, facade=None,
             if facade is None:
                 facade = poset in Sets().Facade()
             if elements is None:
-                relabel = {i: x for i, x in enumerate(poset._elements)}
+                relabel = dict(enumerate(poset._elements))
             else:
                 elements = tuple(elements)
-                relabel = {i: x for i, x in enumerate(elements)}
+                relabel = dict(enumerate(elements))
             hasse_diagram = poset._hasse_diagram.relabel(relabel, inplace=False)
             hasse_diagram = hasse_diagram.copy(immutable=True)
         else:
@@ -2179,7 +2183,7 @@ def cover_relations(self):
             sage: P.cover_relations()
             [[1, 2], [0, 2], [2, 3], [3, 4]]
         """
-        return [c for c in self.cover_relations_iterator()]
+        return list(self.cover_relations_iterator())
 
     @combinatorial_map(name="cover_relations_graph")
     def cover_relations_graph(self):
@@ -4124,7 +4128,7 @@ def upper_covers(self, x):
 
         .. SEEALSO:: :meth:`lower_covers`
         """
-        return [e for e in self.upper_covers_iterator(x)]
+        return list(self.upper_covers_iterator(x))
 
     def lower_covers_iterator(self, x):
         """
@@ -4159,7 +4163,7 @@ def lower_covers(self, x):
 
         .. SEEALSO:: :meth:`upper_covers`
         """
-        return [e for e in self.lower_covers_iterator(x)]
+        return list(self.lower_covers_iterator(x))
 
     def cardinality(self):
         """
@@ -4708,7 +4712,7 @@ def isomorphic_subposets(self, other):
         L = self._hasse_diagram.transitive_closure().subgraph_search_iterator(other._hasse_diagram.transitive_closure(), induced=True, return_graphs=False)
         # Since subgraph_search_iterator returns labelled copies, we
         # remove duplicates.
-        return [self.subposet([self._list[i] for i in x]) for x in sorted(set(frozenset(y) for y in L))]
+        return [self.subposet([self._list[i] for i in x]) for x in sorted({frozenset(y) for y in L})]
 
     # Caveat: list is overridden by the method list above!!!
     def antichains(self, element_constructor=type([])):
@@ -5842,7 +5846,7 @@ def dual(self):
             elements = reversed(self._elements)
         else:
             elements = None
-        H = self._hasse_diagram.relabel({i: x for i, x in enumerate(self._elements)},
+        H = self._hasse_diagram.relabel(dict(enumerate(self._elements)),
                                         inplace=False)
         return self._dual_class(H.reverse(),
                                 elements=elements,
@@ -6388,7 +6392,7 @@ def subposet(self, elements):
             TypeError: 'sage.rings.integer.Integer' object is not iterable
         """
         H = self._hasse_diagram
-        elms = sorted(set(self._element_to_vertex(e) for e in elements))
+        elms = sorted({self._element_to_vertex(e) for e in elements})
 
         if not elms:
             return Poset()
@@ -6401,7 +6405,7 @@ def subposet(self, elements):
                 lt[i].update(lt[low])
             if i in elms:
                 relations += [(x, i) for x in lt[i]]
-                lt[i] = set([i])
+                lt[i] = {i}
 
         g = DiGraph([elms, relations], format='vertices_and_edges')
         if self._is_facade:
@@ -6425,20 +6429,20 @@ def random_subposet(self, p):
 
         TESTS::
 
-            sage: P = posets.IntegerPartitions(4)                                       # needs sage.combinat
+            sage: P = posets.IntegerPartitions(3)                                       # needs sage.combinat
             sage: P.random_subposet(1) == P                                             # needs sage.combinat
             True
+            sage: P.random_subposet(1.41) == P                                          # needs sage.combinat
+            Traceback (most recent call last):
+            ...
+            ValueError: probability p must be in [0..1]
         """
         from sage.misc.randstate import current_randstate
         random = current_randstate().python_random().random
-        elements = []
         p = float(p)
         if p < 0 or p > 1:
             raise ValueError("probability p must be in [0..1]")
-        for v in self:
-            if random() <= p:
-                elements.append(v)
-        return self.subposet(elements)
+        return self.subposet([v for v in self if random() <= p])
 
     def random_order_ideal(self, direction='down'):
         """
@@ -7120,7 +7124,7 @@ def order_complex(self, on_ints=False):
         from sage.topology.simplicial_complex import SimplicialComplex
         L = self.list()
         if on_ints:
-            iso = dict([(L[i], i) for i in range(len(L))])
+            iso = {L[i]: i for i in range(len(L))}
 
         facets = []
         for f in self.maximal_chains_iterator():
@@ -7129,7 +7133,7 @@ def order_complex(self, on_ints=False):
             if on_ints:
                 facets.append([iso[a] for a in f])
             elif self._is_facade:
-                facets.append([a for a in f])
+                facets.append(list(f))
             else:
                 facets.append([a.element for a in f])
 

From b34ac5f9b0396b5de22e239b5edb5d984486c75c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Mon, 22 Jan 2024 16:10:33 +0100
Subject: [PATCH 2/4] auto-annotation by ruff

---
 src/sage/combinat/posets/cartesian_product.py  |  2 +-
 src/sage/combinat/posets/elements.py           |  2 +-
 src/sage/combinat/posets/hasse_diagram.py      |  4 ++--
 src/sage/combinat/posets/incidence_algebras.py |  4 ++--
 src/sage/combinat/posets/linear_extensions.py  |  4 ++--
 src/sage/combinat/posets/mobile.py             |  2 +-
 src/sage/combinat/posets/moebius_algebra.py    | 14 +++++++-------
 src/sage/combinat/posets/posets.py             |  8 ++++----
 8 files changed, 20 insertions(+), 20 deletions(-)

diff --git a/src/sage/combinat/posets/cartesian_product.py b/src/sage/combinat/posets/cartesian_product.py
index 42c23732df9..24d763d5831 100644
--- a/src/sage/combinat/posets/cartesian_product.py
+++ b/src/sage/combinat/posets/cartesian_product.py
@@ -81,7 +81,7 @@ class CartesianProductPoset(CartesianProduct):
         :class:`CartesianProduct`
     """
 
-    def __init__(self, sets, category, order=None, **kwargs):
+    def __init__(self, sets, category, order=None, **kwargs) -> None:
         r"""
         See :class:`CartesianProductPoset` for details.
 
diff --git a/src/sage/combinat/posets/elements.py b/src/sage/combinat/posets/elements.py
index 4cfb0b28ae0..a15bae281e3 100644
--- a/src/sage/combinat/posets/elements.py
+++ b/src/sage/combinat/posets/elements.py
@@ -23,7 +23,7 @@
 
 class PosetElement(Element):
 
-    def __init__(self, poset, element, vertex):
+    def __init__(self, poset, element, vertex) -> None:
         r"""
         Establish the parent-child relationship between ``poset``
         and ``element``, where ``element`` is associated to the
diff --git a/src/sage/combinat/posets/hasse_diagram.py b/src/sage/combinat/posets/hasse_diagram.py
index f91bd993d6f..7f25f19ce4f 100644
--- a/src/sage/combinat/posets/hasse_diagram.py
+++ b/src/sage/combinat/posets/hasse_diagram.py
@@ -40,7 +40,7 @@ class LatticeError(ValueError):
     a and b" instead of "No meet for 1 and 2".
     """
 
-    def __init__(self, fail, x, y):
+    def __init__(self, fail, x, y) -> None:
         """
         Initialize the exception.
 
@@ -56,7 +56,7 @@ def __init__(self, fail, x, y):
         self.x = x
         self.y = y
 
-    def __str__(self):
+    def __str__(self) -> str:
         """
         Return string representation of the exception.
 
diff --git a/src/sage/combinat/posets/incidence_algebras.py b/src/sage/combinat/posets/incidence_algebras.py
index 943fb69fde9..3fc3f2a0b76 100644
--- a/src/sage/combinat/posets/incidence_algebras.py
+++ b/src/sage/combinat/posets/incidence_algebras.py
@@ -52,7 +52,7 @@ class IncidenceAlgebra(CombinatorialFreeModule):
 
     - :wikipedia:`Incidence_algebra`
     """
-    def __init__(self, R, P, prefix='I'):
+    def __init__(self, R, P, prefix='I') -> None:
         """
         Initialize ``self``.
 
@@ -438,7 +438,7 @@ class ReducedIncidenceAlgebra(CombinatorialFreeModule):
     `[x, y]` is isomorphic to `[x', y']` as posets. Thus the delta, Möbius,
     and zeta functions are all elements of `R_P`.
     """
-    def __init__(self, I, prefix='R'):
+    def __init__(self, I, prefix='R') -> None:
         """
         Initialize ``self``.
 
diff --git a/src/sage/combinat/posets/linear_extensions.py b/src/sage/combinat/posets/linear_extensions.py
index 736562802f5..8c430e03d41 100644
--- a/src/sage/combinat/posets/linear_extensions.py
+++ b/src/sage/combinat/posets/linear_extensions.py
@@ -513,7 +513,7 @@ def __classcall_private__(cls, poset, facade=False):
         """
         return super().__classcall__(cls, poset, facade=facade)
 
-    def __init__(self, poset, facade):
+    def __init__(self, poset, facade) -> None:
         """
         TESTS::
 
@@ -671,7 +671,7 @@ def __iter__(self):
         for lin_ext in linear_extension_iterator(self._poset._hasse_diagram):
             yield self._element_constructor_([vertex_to_element(_) for _ in lin_ext])
 
-    def __contains__(self, obj):
+    def __contains__(self, obj) -> bool:
         """
         Membership testing
 
diff --git a/src/sage/combinat/posets/mobile.py b/src/sage/combinat/posets/mobile.py
index 321942a0fd7..5e18f5c4856 100644
--- a/src/sage/combinat/posets/mobile.py
+++ b/src/sage/combinat/posets/mobile.py
@@ -64,7 +64,7 @@ class MobilePoset(FinitePoset):
     _lin_ext_type = LinearExtensionsOfMobile
     _desc = 'Finite mobile poset'
 
-    def __init__(self, hasse_diagram, elements, category, facade, key, ribbon=None, check=True):
+    def __init__(self, hasse_diagram, elements, category, facade, key, ribbon=None, check=True) -> None:
         r"""
         Initialize ``self``.
 
diff --git a/src/sage/combinat/posets/moebius_algebra.py b/src/sage/combinat/posets/moebius_algebra.py
index 5a4380e643f..5a8074c3272 100644
--- a/src/sage/combinat/posets/moebius_algebra.py
+++ b/src/sage/combinat/posets/moebius_algebra.py
@@ -96,7 +96,7 @@ class MoebiusAlgebra(Parent, UniqueRepresentation):
        European Journal of Combinatorics, **19**, 1998.
        :doi:`10.1006/eujc.1998.0227`.
     """
-    def __init__(self, R, L):
+    def __init__(self, R, L) -> None:
         """
         Initialize ``self``.
 
@@ -161,7 +161,7 @@ class E(BasisAbstract):
         Let `E_x` and `E_y` be basis elements of `M_L` for some lattice `L`.
         Multiplication is given by `E_x E_y = E_{x \vee y}`.
         """
-        def __init__(self, M, prefix='E'):
+        def __init__(self, M, prefix='E') -> None:
             """
             Initialize ``self``.
 
@@ -242,7 +242,7 @@ class I(BasisAbstract):
         Multiplication is given by `I_x I_y = \delta_{xy} I_x` where
         `\delta_{xy}` is the Kronecker delta.
         """
-        def __init__(self, M, prefix='I'):
+        def __init__(self, M, prefix='I') -> None:
             """
             Initialize ``self``.
 
@@ -381,7 +381,7 @@ class QuantumMoebiusAlgebra(Parent, UniqueRepresentation):
     \operatorname{rank} L - \operatorname{rank}` a). At `q = 1`, this
     reduces to the multiplication formula originally given by Solomon.
     """
-    def __init__(self, L, q=None):
+    def __init__(self, L, q=None) -> None:
         """
         Initialize ``self``.
 
@@ -471,7 +471,7 @@ class E(BasisAbstract):
         is the corank function (i.e., `\operatorname{crk} a =
         \operatorname{rank} L - \operatorname{rank}` a).
         """
-        def __init__(self, M, prefix='E'):
+        def __init__(self, M, prefix='E') -> None:
             """
             Initialize ``self``.
 
@@ -547,7 +547,7 @@ class C(BasisAbstract):
         filter of `x` and `P(F^x; q)` is the characteristic polynomial
         of the (sub)poset `F^x`.
         """
-        def __init__(self, M, prefix='C'):
+        def __init__(self, M, prefix='C') -> None:
             """
             Initialize ``self``.
 
@@ -626,7 +626,7 @@ class KL(BasisAbstract):
             sage: KL[4] * KL[10]
             (q+3*q^2+3*q^3+q^4)*KL[14] + (1+4*q+6*q^2+4*q^3+q^4)*KL[15]
         """
-        def __init__(self, M, prefix='KL'):
+        def __init__(self, M, prefix='KL') -> None:
             """
             Initialize ``self``.
 
diff --git a/src/sage/combinat/posets/posets.py b/src/sage/combinat/posets/posets.py
index 3a8252983e3..45142e54423 100644
--- a/src/sage/combinat/posets/posets.py
+++ b/src/sage/combinat/posets/posets.py
@@ -1013,7 +1013,7 @@ def __classcall__(cls, hasse_diagram, elements=None, category=None, facade=None,
                                      category=category, facade=facade,
                                      key=key)
 
-    def __init__(self, hasse_diagram, elements, category, facade, key):
+    def __init__(self, hasse_diagram, elements, category, facade, key) -> None:
         r"""
         EXAMPLES::
 
@@ -1230,7 +1230,7 @@ def unwrap(self, element):
         else:
             return element.element
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         r"""
         Return ``True`` if ``x`` is an element of the poset.
 
@@ -8909,7 +8909,7 @@ class FinitePosets_n(UniqueRepresentation, Parent):
         [[1, 2], [0, 2]]
     """
 
-    def __init__(self, n):
+    def __init__(self, n) -> None:
         r"""
         EXAMPLES::
 
@@ -8934,7 +8934,7 @@ def _repr_(self):
         """
         return "Posets containing %s elements" % self._n
 
-    def __contains__(self, P):
+    def __contains__(self, P) -> bool:
         """
         EXAMPLES::
 

From 2266a35ad43768c1d52d82f50878155964e57488 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Mon, 22 Jan 2024 16:20:53 +0100
Subject: [PATCH 3/4] further details in posets

---
 src/sage/combinat/posets/hasse_diagram.py  | 25 ++++++++++++----------
 src/sage/combinat/posets/lattices.py       |  2 +-
 src/sage/combinat/posets/poset_examples.py |  2 +-
 src/sage/combinat/posets/posets.py         | 10 +++++++--
 4 files changed, 24 insertions(+), 15 deletions(-)

diff --git a/src/sage/combinat/posets/hasse_diagram.py b/src/sage/combinat/posets/hasse_diagram.py
index 7f25f19ce4f..9fc250802b8 100644
--- a/src/sage/combinat/posets/hasse_diagram.py
+++ b/src/sage/combinat/posets/hasse_diagram.py
@@ -1109,11 +1109,11 @@ def moebius_function_matrix(self, algorithm='cython'):
                             m[(i, k)] = -ZZ.sum(m[(j, k)]
                                                 for j in available
                                                 if k in greater_than[j])
-                M = matrix(ZZ, n, n, m, sparse=True)
+                M = matrix(ZZ, n, n, m, sparse=True)  # noqa: F821
             elif algorithm == "matrix":
                 M = self.lequal_matrix().inverse_of_unit()
             elif algorithm == "cython":
-                M = moebius_matrix_fast(self._leq_storage)
+                M = moebius_matrix_fast(self._leq_storage)  # noqa: F821
             else:
                 raise ValueError("unknown algorithm")
             self._moebius_function_matrix = M
@@ -1187,7 +1187,7 @@ def coxeter_transformation(self, algorithm='cython'):
         if algorithm == 'matrix':
             return - self.lequal_matrix() * self.moebius_function_matrix().transpose()
         elif algorithm == 'cython':
-            return coxeter_matrix_fast(self._leq_storage)
+            return coxeter_matrix_fast(self._leq_storage)  # noqa: F821
         else:
             raise ValueError("unknown algorithm")
 
@@ -1324,11 +1324,11 @@ def _leq_matrix_boolean(self):
             Finite Field of size 2
         """
         n = self.order()
-        R = GF(2)
+        R = GF(2)  # noqa: F821
         one = R.one()
         greater_than = self._leq_storage
         D = {(i, j): one for i in range(n) for j in greater_than[i]}
-        M = matrix(R, n, n, D, sparse=True)
+        M = matrix(R, n, n, D, sparse=True)  # noqa: F821
         M.set_immutable()
         return M
 
@@ -1359,7 +1359,7 @@ def _leq_matrix(self):
         n = self.order()
         greater_than = self._leq_storage
         D = {(i, j): 1 for i in range(n) for j in greater_than[i]}
-        return matrix(ZZ, n, n, D, sparse=True, immutable=True)
+        return matrix(ZZ, n, n, D, sparse=True, immutable=True)  # noqa: F821
 
     def lequal_matrix(self, boolean=False):
         r"""
@@ -1544,7 +1544,7 @@ def _meet(self):
         self._meet_semilattice_failure = ()
         n = self.cardinality()
         if n == 0:
-            return matrix(0)
+            return matrix(0)  # noqa: F821
         meet = [[-1 for x in range(n)] for x in range(n)]
         lc = [self.neighbors_in(x) for x in range(n)]  # Lc = lower covers
 
@@ -1564,7 +1564,7 @@ def _meet(self):
                 meet[y][x] = q
                 if q == -1:
                     self._meet_semilattice_failure += ((x, y),)
-        return matrix(ZZ, meet)
+        return matrix(ZZ, meet)  # noqa: F821
 
     def meet_matrix(self):
         r"""
@@ -1708,7 +1708,7 @@ def _join(self):
         self._join_semilattice_failure = ()
         n = self.cardinality()
         if n == 0:
-            return matrix(0)
+            return matrix(0)  # noqa: F821
         join = [[-1 for x in range(n)] for x in range(n)]
         uc = [self.neighbors_out(x) for x in range(n)]  # uc = upper covers
 
@@ -1729,7 +1729,7 @@ def _join(self):
                 if q == -1:
                     self._join_semilattice_failure += ((x, y),)
 
-        return matrix(ZZ, join)
+        return matrix(ZZ, join)  # noqa: F821
 
     def join_matrix(self):
         r"""
@@ -3143,7 +3143,7 @@ def atoms_of_congruence_lattice(self):
 
         return min_congruences
 
-    def congruence(self, parts, start=None, stop_pairs=[]):
+    def congruence(self, parts, start=None, stop_pairs=None):
         """
         Return the congruence ``start`` "extended" by ``parts``.
 
@@ -3207,6 +3207,9 @@ def congruence(self, parts, start=None, stop_pairs=[]):
         from sage.sets.disjoint_set import DisjointSet
         from copy import copy
 
+        if stop_pairs is None:
+            stop_pairs = []
+
         n = self.order()
         mt = self.meet_matrix()
         jn = self.join_matrix()
diff --git a/src/sage/combinat/posets/lattices.py b/src/sage/combinat/posets/lattices.py
index 75a3af11e3b..10f1746e5e1 100644
--- a/src/sage/combinat/posets/lattices.py
+++ b/src/sage/combinat/posets/lattices.py
@@ -2003,7 +2003,7 @@ def join(L):
                                 return (B, [self._vertex_to_element(e) for e in A])
                             else:
                                 return B
-        assert False, "BUG: breadth() in lattices.py have an error."
+        raise RuntimeError("BUG: breadth() in lattices.py have an error")
 
     def complements(self, element=None):
         r"""
diff --git a/src/sage/combinat/posets/poset_examples.py b/src/sage/combinat/posets/poset_examples.py
index 0b4a949c27b..6a0e57a8887 100644
--- a/src/sage/combinat/posets/poset_examples.py
+++ b/src/sage/combinat/posets/poset_examples.py
@@ -1550,7 +1550,7 @@ def YoungFibonacci(n):
 
         covers = []
         current_level = ['']
-        for i in range(1, n + 1):
+        for _ in range(1, n + 1):
             new_level = set()
             for low in current_level:
                 ind = low.find('1')
diff --git a/src/sage/combinat/posets/posets.py b/src/sage/combinat/posets/posets.py
index 45142e54423..36f4d1eee10 100644
--- a/src/sage/combinat/posets/posets.py
+++ b/src/sage/combinat/posets/posets.py
@@ -4715,7 +4715,7 @@ def isomorphic_subposets(self, other):
         return [self.subposet([self._list[i] for i in x]) for x in sorted({frozenset(y) for y in L})]
 
     # Caveat: list is overridden by the method list above!!!
-    def antichains(self, element_constructor=type([])):
+    def antichains(self, element_constructor=None):
         """
         Return the antichains of the poset.
 
@@ -4779,6 +4779,9 @@ def antichains(self, element_constructor=type([])):
         """
         vertex_to_element = self._vertex_to_element
 
+        if element_constructor is None:
+            element_constructor = list
+
         def f(antichain):
             return element_constructor(vertex_to_element(x) for x in antichain)
         result = self._hasse_diagram.antichains(element_class=f)
@@ -4921,7 +4924,7 @@ def dilworth_decomposition(self):
             chains.append(chain)
         return chains
 
-    def chains(self, element_constructor=type([]), exclude=None):
+    def chains(self, element_constructor=None, exclude=None):
         """
         Return the chains of the poset.
 
@@ -4969,6 +4972,9 @@ def chains(self, element_constructor=type([]), exclude=None):
 
         .. SEEALSO:: :meth:`maximal_chains`, :meth:`antichains`
         """
+        if element_constructor is None:
+            element_constructor = list
+
         if exclude is not None:
             exclude = [self._element_to_vertex(x) for x in exclude]
         result = self._hasse_diagram.chains(element_class=element_constructor,

From b41465df81a467dd6cb4a17f842dc18199830835 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Fri, 26 Jan 2024 10:36:41 +0100
Subject: [PATCH 4/4] a few more details in posets

---
 src/sage/combinat/posets/hasse_diagram.py | 15 +++++----------
 1 file changed, 5 insertions(+), 10 deletions(-)

diff --git a/src/sage/combinat/posets/hasse_diagram.py b/src/sage/combinat/posets/hasse_diagram.py
index 9fc250802b8..9f46877aa0e 100644
--- a/src/sage/combinat/posets/hasse_diagram.py
+++ b/src/sage/combinat/posets/hasse_diagram.py
@@ -1857,9 +1857,8 @@ def find_nonsemidistributive_elements(self, meet_or_join):
             for x in range(n):
                 u = M1[e, x]
                 for y in range(x):
-                    if u == M1[e, y]:
-                        if u != M1[e, M2[x, y]]:
-                            return (u, e, x, y)
+                    if u == M1[e, y] and u != M1[e, M2[x, y]]:
+                        return (u, e, x, y)
 
         return None
 
@@ -2151,9 +2150,8 @@ def recursive_fit(orthocomplements, unbinded):
                 # Every element might have one possible orthocomplement,
                 # but so that they don't fit together. Must check that.
                 for lc in self.lower_covers_iterator(e):
-                    if start[lc] is not None:
-                        if not self.has_edge(e_, start[lc]):
-                            return
+                    if not (start[lc] is None or self.has_edge(e_, start[lc])):
+                        return
                 if start[e_] is None:
                     start[e] = e_
                     start[e_] = e
@@ -2191,10 +2189,7 @@ def find_nonsemimodular_pair(self, upper):
             sage: H_.find_nonsemimodular_pair(upper=False) is None
             True
         """
-        if upper:
-            neighbors = self.neighbors_out
-        else:
-            neighbors = self.neighbors_in
+        neighbors = self.neighbors_out if upper else self.neighbors_in
 
         n = self.order()
         for e in range(n):