gh-37144: Minor ruff fixes in posets
    
This is fixing a few of `ruff` suggestions (UP and PERF and ANN) in
posets.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #37144
Reported by: Frédéric Chapoton
Reviewer(s): Alex J Best

Author: Release Manager

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.
 
@@ -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
 

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

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.
 
@@ -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 ...
@@ -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")
 
@@ -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):
@@ -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"""
@@ -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):
@@ -2481,7 +2476,7 @@ 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 +2520,7 @@ 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 +2645,7 @@ 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 +2678,7 @@ 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 +2694,7 @@ def sublattice(elms, e):
 
         N = self.cardinality()
         elms = [0]
-        sublats = [set([0])]
+        sublats = [{0}]
         result = []
         skip = -1
 
@@ -2981,7 +2975,7 @@ 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))
 
@@ -3144,7 +3138,7 @@ 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``.
 
@@ -3208,6 +3202,9 @@ 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()
@@ -3242,7 +3239,7 @@ 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 +3304,7 @@ 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
 

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``.
 

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"""
@@ -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))

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"""
@@ -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::
 
@@ -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]]]
@@ -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
 

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``.