further details in posets

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()

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"""

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')

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,