graphs: make init_short_digraph always sort neighbors but without the extra log complexity

src/sage/algebras/lie_algebras/bgg_dual_module.py

@@ -202,15 +202,12 @@ def degree_on_basis(self, m):
             sage: M = g.verma_module(La[1] + La[4] - 1/3*La[5])
             sage: Mc = M.dual()
             sage: elt = Mc.an_element(); elt
-            f[-alpha[5]]^2*f[-alpha[4]]^2*f[-alpha[3]]^3*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
-             + 2*f[-alpha[5]]*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
-             + 3*f[-alpha[4]]*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
-             + v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
+            f[-alpha[2]]^2*f[-alpha[5]]^2*f[-alpha[3]]^3*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^* + 2*f[-alpha[2]]*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^* + 3*f[-alpha[5]]*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^* + v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
             sage: [M.degree_on_basis(m) for m in elt.support()]
-            [Lambda[1] + 3*Lambda[2] - 2*Lambda[3] - 4/3*Lambda[5],
+            [3*Lambda[1] - Lambda[2] - 2*Lambda[3] + 4*Lambda[4] - 4/3*Lambda[5],
              Lambda[1] + Lambda[4] - 1/3*Lambda[5],
-             Lambda[1] + Lambda[3] + Lambda[4] - 7/3*Lambda[5],
-             Lambda[1] + Lambda[3] - Lambda[4] - 1/3*Lambda[5]]
+             2*Lambda[1] - 2*Lambda[2] + Lambda[3] + Lambda[4] - 1/3*Lambda[5],
+             Lambda[1] + Lambda[3] + Lambda[4] - 7/3*Lambda[5]]
         """
         return self._module.degree_on_basis(m)
 

src/sage/algebras/lie_algebras/poincare_birkhoff_witt.py

@@ -767,8 +767,8 @@ def _transpose_on_basis(self, m):
             sage: f1, f2, f3, f4, f5, f6 = U.f()
             sage: e1, e2, e3, e4, e5, e6 = U.e()
             sage: elt = e1 * e4^2 * f1 * f2^3
-            sage: U._transpose_on_basis(elt.support()[0])
-            PBW[alpha[2]]^3*PBW[alpha[1]]*PBW[-alpha[4]]^2*PBW[-alpha[1]]
+            sage: U._transpose_on_basis(elt.support()[0]) == e2^3*e1*f1*f4^2
+            True
         """
         I = self._indices
         basis_mapping = self._g._transpose_basis_mapping

src/sage/categories/regular_crystals.py

@@ -842,13 +842,8 @@ def dual_equivalence_class(self, index_set=None):
                  ([[1, 3], [2, 4]], [[1, 2], [3, 4]], 3)]
                 sage: T = crystals.Tableaux(['A',4], shape=[3,2])
                 sage: G = T(2,1,4,3,5).dual_equivalence_class()
-                sage: G.edges(sort=True)
-                [([[1, 3, 5], [2, 4]], [[1, 3, 4], [2, 5]], 4),
-                 ([[1, 3, 5], [2, 4]], [[1, 2, 5], [3, 4]], 2),
-                 ([[1, 3, 5], [2, 4]], [[1, 2, 5], [3, 4]], 3),
-                 ([[1, 3, 4], [2, 5]], [[1, 2, 4], [3, 5]], 2),
-                 ([[1, 2, 4], [3, 5]], [[1, 2, 3], [4, 5]], 3),
-                 ([[1, 2, 4], [3, 5]], [[1, 2, 3], [4, 5]], 4)]
+                sage: G.edges(sort=True,sort_vertices=True)
+                [([[1, 3, 4], [2, 5]], [[1, 3, 5], [2, 4]], 4), ([[1, 3, 4], [2, 5]], [[1, 2, 4], [3, 5]], 2), ([[1, 2, 5], [3, 4]], [[1, 3, 5], [2, 4]], 2), ([[1, 2, 5], [3, 4]], [[1, 3, 5], [2, 4]], 3), ([[1, 2, 3], [4, 5]], [[1, 2, 4], [3, 5]], 3), ([[1, 2, 3], [4, 5]], [[1, 2, 4], [3, 5]], 4)]
             """
             if index_set is None:
                 index_set = self.index_set()

src/sage/combinat/growth.py

@@ -1777,7 +1777,7 @@ def _check_duality(self, n):
             ...
             ValueError: D U - U D differs from 1 I for vertex [2]:
             D U = [[2]]
-            U D + 1 I = [[1, 1], [2], [2]]
+            U D + 1 I = [[2], [1, 1], [2]]
         """
         if self.has_multiple_edges:
             def check_vertex(w, P, Q):
@@ -1843,8 +1843,8 @@ def Q_graph(self, n):
             sage: Q = Domino.Q_graph(3); Q
             Finite poset containing 8 elements
 
-            sage: Q.upper_covers(Partition([1,1]))
-            [[1, 1, 1, 1], [3, 1], [2, 2]]
+            sage: sorted(Q.upper_covers(Partition([1,1])))
+            [[1, 1, 1, 1], [2, 2], [3, 1]]
         """
         if self.has_multiple_edges:
             D = DiGraph([(x, y, e) for k in range(n - 1)

src/sage/combinat/permutation.py

@@ -4790,12 +4790,12 @@ def permutation_poset(self):
         EXAMPLES::
 
             sage: # needs sage.combinat sage.graphs
-            sage: Permutation([3,1,5,4,2]).permutation_poset().cover_relations()
-            [[(2, 1), (5, 2)],
+            sage: sorted(Permutation([3,1,5,4,2]).permutation_poset().cover_relations())
+            [[(1, 3), (3, 5)],
+             [(1, 3), (4, 4)],
              [(2, 1), (3, 5)],
              [(2, 1), (4, 4)],
-             [(1, 3), (3, 5)],
-             [(1, 3), (4, 4)]]
+             [(2, 1), (5, 2)]]
             sage: Permutation([]).permutation_poset().cover_relations()
             []
             sage: Permutation([1,3,2]).permutation_poset().cover_relations()

src/sage/combinat/posets/hasse_diagram.py

@@ -1076,9 +1076,9 @@ def moebius_function_matrix(self, algorithm='cython'):
             True
             sage: H = posets.TamariLattice(3)._hasse_diagram
             sage: M = H.moebius_function_matrix('matrix'); M
-            [ 1 -1 -1  0  1]
-            [ 0  1  0  0 -1]
-            [ 0  0  1 -1  0]
+            [ 1 -1  0 -1  1]
+            [ 0  1 -1  0  0]
+            [ 0  0  1  0 -1]
             [ 0  0  0  1 -1]
             [ 0  0  0  0  1]
             sage: _ = H.__dict__.pop('_moebius_function_matrix')

src/sage/combinat/posets/lattices.py

@@ -349,8 +349,8 @@ def submeetsemilattice(self, elms):
             sage: L = posets.DivisorLattice(1000)
             sage: L_ = L.submeetsemilattice([200, 250, 125]); L_
             Finite meet-semilattice containing 5 elements
-            sage: L_.list()
-            [25, 50, 200, 125, 250]
+            sage: sorted(L_.list())
+            [25, 50, 125, 200, 250]
 
         .. SEEALSO::
 
@@ -3163,8 +3163,8 @@ def sublattice(self, elms):
         EXAMPLES::
 
             sage: L = LatticePoset(([], [[1,2],[1,17],[1,8],[2,3],[2,22],[2,5],[2,7],[17,22],[17,13],[8,7],[8,13],[3,16],[3,9],[22,16],[22,18],[22,10],[5,18],[5,14],[7,9],[7,14],[7,10],[13,10],[16,6],[16,19],[9,19],[18,6],[18,33],[14,33],[10,19],[10,33],[6,4],[19,4],[33,4]]))
-            sage: L.sublattice([14, 13, 22]).list()
-            [1, 2, 8, 7, 14, 17, 13, 22, 10, 33]
+            sage: sorted(L.sublattice([14, 13, 22]).list())
+            [1, 2, 7, 8, 10, 13, 14, 17, 22, 33]
 
             sage: L = posets.BooleanLattice(3)
             sage: L.sublattice([3,5,6,7])

src/sage/combinat/posets/poset_examples.py

@@ -1463,7 +1463,7 @@ def YoungsLattice(n):
 
             sage: P = posets.YoungsLattice(3); P
             Finite meet-semilattice containing 7 elements
-            sage: P.cover_relations()
+            sage: sorted(P.cover_relations())
             [[[], [1]],
              [[1], [1, 1]],
              [[1], [2]],

src/sage/combinat/posets/posets.py

@@ -6353,8 +6353,8 @@ def graphviz_string(self, graph_string="graph", edge_string="--"):
             sage: P = Poset({'a':['b'],'b':['d'],'c':['d'],'d':['f'],'e':['f'],'f':[]})
             sage: print(P.graphviz_string())
             graph {
-            "f";"d";"b";"a";"c";"e";
-            "f"--"e";"d"--"c";"b"--"a";"d"--"b";"f"--"d";
+            "f";"e";"d";"c";"b";"a";
+            "b"--"a";"d"--"b";"d"--"c";"f"--"d";"f"--"e";
             }
         """
         s = '%s {\n' % graph_string
@@ -6377,8 +6377,8 @@ def subposet(self, elements):
             ....:            'd': ['f'], 'e': ['f']})
             sage: Q = P.subposet(['a', 'b', 'f']); Q
             Finite poset containing 3 elements
-            sage: Q.cover_relations()
-            [['b', 'f'], ['a', 'f']]
+            sage: sorted(Q.cover_relations())
+            [['a', 'f'], ['b', 'f']]
 
         A subposet of a non-facade poset is again a non-facade poset::
 
@@ -6658,8 +6658,8 @@ def order_filter(self, elements):
         EXAMPLES::
 
             sage: P = Poset((divisors(1000), attrcall("divides")))
-            sage: P.order_filter([20, 25])
-            [20, 40, 25, 50, 100, 200, 125, 250, 500, 1000]
+            sage: sorted(P.order_filter([20, 25]))
+            [20, 25, 40, 50, 100, 125, 200, 250, 500, 1000]
 
         .. SEEALSO::
 
@@ -6690,7 +6690,7 @@ def order_ideal(self, elements):
         EXAMPLES::
 
             sage: P = Poset((divisors(1000), attrcall("divides")))
-            sage: P.order_ideal([20, 25])
+            sage: sorted(P.order_ideal([20, 25]))
             [1, 2, 4, 5, 10, 20, 25]
 
         .. SEEALSO::
@@ -6796,7 +6796,7 @@ def closed_interval(self, x, y):
         EXAMPLES::
 
             sage: P = Poset((divisors(1000), attrcall("divides")))
-            sage: P.closed_interval(2, 100)
+            sage: sorted(P.closed_interval(2, 100))
             [2, 4, 10, 20, 50, 100]
 
         .. SEEALSO::
@@ -6824,7 +6824,7 @@ def open_interval(self, x, y):
         EXAMPLES::
 
             sage: P = Poset((divisors(1000), attrcall("divides")))
-            sage: P.open_interval(2, 100)
+            sage: sorted(P.open_interval(2, 100))
             [4, 10, 20, 50]
 
         .. SEEALSO::

src/sage/combinat/skew_tableau.py

@@ -2121,8 +2121,14 @@ def __iter__(self):
             sage: [next(it) for x in range(10)]
             [[],
              [[1]],
-             [[1, 2]], [[1], [2]], [[None, 2], [1]], [[None, 1], [2]],
-             [[1, 2, 3]], [[1, 2], [3]], [[1, 3], [2]], [[None, 2, 3], [1]]]
+             [[1, 2]],
+             [[1], [2]],
+             [[None, 1], [2]],
+             [[None, 2], [1]],
+             [[1, 2, 3]],
+             [[1, 2], [3]],
+             [[1, 3], [2]],
+             [[None, 2, 3], [1]]]
         """
         n = 0
         while True:
@@ -2186,23 +2192,32 @@ def __iter__(self):
 
             sage: # needs sage.graphs sage.modules
             sage: StandardSkewTableaux(2).list()
-            [[[1, 2]], [[1], [2]], [[None, 2], [1]], [[None, 1], [2]]]
+            [[[1, 2]], [[1], [2]], [[None, 1], [2]], [[None, 2], [1]]]
             sage: StandardSkewTableaux(3).list()
             [[[1, 2, 3]],
-             [[1, 2], [3]], [[1, 3], [2]],
-             [[None, 2, 3], [1]], [[None, 1, 2], [3]], [[None, 1, 3], [2]],
-             [[None, 2], [1, 3]], [[None, 1], [2, 3]],
-             [[None, None, 2], [1, 3]], [[None, None, 3], [1, 2]],
+             [[1, 2], [3]],
+             [[1, 3], [2]],
+             [[None, 2, 3], [1]],
+             [[None, 1, 2], [3]],
+             [[None, 1, 3], [2]],
+             [[None, 1], [2, 3]],
+             [[None, 2], [1, 3]],
              [[None, None, 1], [2, 3]],
-             [[1], [2], [3]], [[None, 2], [None, 3], [1]],
-             [[None, 1], [None, 2], [3]], [[None, 1], [None, 3], [2]],
-             [[None, 2], [1], [3]], [[None, 3], [1], [2]],
-             [[None, 1], [2], [3]], [[None, None, 3], [None, 2], [1]],
-             [[None, None, 2], [None, 3], [1]],
-             [[None, None, 1], [None, 3], [2]],
+             [[None, None, 3], [1, 2]],
+             [[None, None, 2], [1, 3]],
+             [[1], [2], [3]],
+             [[None, 2], [None, 3], [1]],
+             [[None, 1], [None, 2], [3]],
+             [[None, 1], [None, 3], [2]],
+             [[None, 1], [2], [3]],
+             [[None, 3], [1], [2]],
+             [[None, 2], [1], [3]],
              [[None, None, 1], [None, 2], [3]],
-             [[None, None, 2], [None, 1], [3]],
-             [[None, None, 3], [None, 1], [2]]]
+             [[None, None, 1], [None, 3], [2]],
+             [[None, None, 2], [None, 3], [1]],
+             [[None, None, 3], [None, 2], [1]],
+             [[None, None, 3], [None, 1], [2]],
+             [[None, None, 2], [None, 1], [3]]]
         """
         for skp in SkewPartitions(self.n):
             for sst in StandardSkewTableaux_shape(skp):

src/sage/geometry/polyhedron/base4.py

@@ -315,8 +315,8 @@ def face_lattice(self):
             sage: square = polytopes.hypercube(2)
             sage: fl = square.face_lattice();fl
             Finite lattice containing 10 elements
-            sage: list(f.ambient_V_indices() for f in fl)
-            [(), (0,), (1,), (0, 1), (2,), (1, 2), (3,), (0, 3), (2, 3), (0, 1, 2, 3)]
+            sage: list(f.ambient_V_indices() for f in sorted(fl))
+            [(), (0,), (0, 1), (0, 1, 2, 3), (0, 3), (1,), (1, 2), (2,), (2, 3), (3,)]
             sage: poset_element = fl[5]
             sage: a_face = poset_element
             sage: a_face

src/sage/geometry/polyhedron/face.py

@@ -404,19 +404,18 @@
         EXAMPLES::
 
             sage: square = polytopes.hypercube(2)
-            sage: for face in square.face_lattice():                                    # needs sage.combinat
+            sage: for face in sorted(square.face_lattice()):                                    # needs sage.combinat
             ....:     print(face.ambient_Hrepresentation())
-            (An inequality (-1, 0) x + 1 >= 0, An inequality (0, -1) x + 1 >= 0,
-             An inequality (1, 0) x + 1 >= 0, An inequality (0, 1) x + 1 >= 0)
+            (An inequality (-1, 0) x + 1 >= 0, An inequality (0, -1) x + 1 >= 0, An inequality (1, 0) x + 1 >= 0, An inequality (0, 1) x + 1 >= 0)
             (An inequality (-1, 0) x + 1 >= 0, An inequality (0, 1) x + 1 >= 0)
-            (An inequality (-1, 0) x + 1 >= 0, An inequality (0, -1) x + 1 >= 0)
             (An inequality (-1, 0) x + 1 >= 0,)
-            (An inequality (0, -1) x + 1 >= 0, An inequality (1, 0) x + 1 >= 0)
-            (An inequality (0, -1) x + 1 >= 0,)
-            (An inequality (1, 0) x + 1 >= 0, An inequality (0, 1) x + 1 >= 0)
+            ()
             (An inequality (0, 1) x + 1 >= 0,)
+            (An inequality (-1, 0) x + 1 >= 0, An inequality (0, -1) x + 1 >= 0)
+            (An inequality (0, -1) x + 1 >= 0,)
+            (An inequality (0, -1) x + 1 >= 0, An inequality (1, 0) x + 1 >= 0)
             (An inequality (1, 0) x + 1 >= 0,)
-            ()
+            (An inequality (1, 0) x + 1 >= 0, An inequality (0, 1) x + 1 >= 0)
         """
         if index is None:
             return self._ambient_Hrepresentation
@@ -445,19 +444,18 @@
         EXAMPLES::
 
             sage: square = polytopes.hypercube(2)
-            sage: for fl in square.face_lattice():                                      # needs sage.combinat
+            sage: for fl in sorted(square.face_lattice()):                                      # needs sage.combinat
             ....:     print(fl.ambient_Vrepresentation())
             ()
             (A vertex at (1, -1),)
-            (A vertex at (1, 1),)
             (A vertex at (1, -1), A vertex at (1, 1))
-            (A vertex at (-1, 1),)
-            (A vertex at (1, 1), A vertex at (-1, 1))
-            (A vertex at (-1, -1),)
+            (A vertex at (1, -1), A vertex at (1, 1), A vertex at (-1, 1), A vertex at (-1, -1))
             (A vertex at (1, -1), A vertex at (-1, -1))
+            (A vertex at (1, 1),)
+            (A vertex at (1, 1), A vertex at (-1, 1))
+            (A vertex at (-1, 1),)
             (A vertex at (-1, 1), A vertex at (-1, -1))
-            (A vertex at (1, -1), A vertex at (1, 1),
-             A vertex at (-1, 1), A vertex at (-1, -1))
+            (A vertex at (-1, -1),)
         """
         if index is None:
             return self._ambient_Vrepresentation

src/sage/graphs/asteroidal_triples.pyx

@@ -147,8 +147,7 @@ def is_asteroidal_triple_free(G, certificate=False):
     # module sage.graphs.base.static_sparse_graph
     cdef list int_to_vertex = list(G)
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex,
-                       sort_neighbors=False)
+    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
 
     cdef bitset_t seen
     bitset_init(seen, n)

src/sage/graphs/base/static_sparse_backend.pyx

@@ -511,10 +511,6 @@ cdef class StaticSparseBackend(CGraphBackend):
             True
         """
         vertices = list(G)
-        try:
-            vertices.sort()
-        except TypeError:
-            pass
         cdef StaticSparseCGraph cg = <StaticSparseCGraph> StaticSparseCGraph(G, vertices)
         self._cg = cg
 

src/sage/graphs/base/static_sparse_graph.pxd

@@ -7,27 +7,19 @@ ctypedef unsigned int uint
 
 cdef extern from "stdlib.h":
     ctypedef void const_void "const void"
-    void qsort(void *base, int nmemb, int size,
-               int(*compar)(const_void *, const_void *)) nogil
-
     void *bsearch(const_void *key, const_void *base, size_t nmemb,
                   size_t size, int(*compar)(const_void *, const_void *)) nogil
 
-cdef extern from "search.h":
-    void *lfind(const_void *key, const_void *base, size_t *nmemb,
-                  size_t size, int(*compar)(const_void *, const_void *)) nogil
-
 ctypedef struct short_digraph_s:
     uint32_t * edges
     uint32_t ** neighbors
     PyObject * edge_labels
     int m
     int n
-    bint sorted_neighbors
 
 ctypedef short_digraph_s short_digraph[1]
 
-cdef int init_short_digraph(short_digraph g, G, edge_labelled=?, vertex_list=?, sort_neighbors=?) except -1
+cdef int init_short_digraph(short_digraph g, G, edge_labelled=?, vertex_list=?) except -1
 cdef void free_short_digraph(short_digraph g) noexcept
 cdef int init_reverse(short_digraph dst, short_digraph src) except -1
 cdef int out_degree(short_digraph g, int u) noexcept