sagemathgh-38427: graphs: make init_short_digraph always sort neighbo…

…rs but without the extra log complexity

    
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This PR improve the `init_short_digraph` function that is used to
initialize `StaticSparseCGraph` (used for immutable `Graph` and
`DiGraph`).

Before, a boolean parameter `sort_neighbors` was used to specify if we
wanted to sort the neighbors or not. It implied an extra `log` in the
complexity (as `qsort` was called).
With this PR, the neighbors are always sorted at no extra cost. It is
done by appending to the neighbors list the vertices in the correct
order so the call to `qsort` is not needed anymore.

This PR partly reverts sagemath#38198 and mostly reverts sagemath#37662

### 📝 Checklist

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- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: sagemath#38427
Reported by: cyrilbouvier
Reviewer(s): cyrilbouvier, David Coudert

src/sage/algebras/lie_algebras/bgg_dual_module.py

@@ -202,15 +202,16 @@ 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

@@ -838,13 +838,13 @@ 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),
+                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, 4], [3, 5]], [[1, 2, 3], [4, 5]], 3),
-                 ([[1, 2, 4], [3, 5]], [[1, 2, 3], [4, 5]], 4)]
+                 ([[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

@@ -1775,7 +1775,7 @@ 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):
@@ -1841,8 +1841,8 @@ 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

@@ -4785,12 +4785,12 @@ 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

@@ -1074,9 +1074,9 @@ 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::
 
@@ -3159,8 +3159,8 @@ 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

@@ -1459,7 +1459,7 @@ 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

@@ -6335,8 +6335,8 @@ 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
@@ -6359,8 +6359,8 @@ 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::
 
@@ -6640,8 +6640,8 @@ 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::
 
@@ -6672,7 +6672,7 @@ 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::
@@ -6778,7 +6778,7 @@ 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::
@@ -6806,7 +6806,7 @@ 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

@@ -2116,8 +2116,14 @@ 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:
@@ -2181,23 +2187,32 @@ 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

@@ -389,19 +389,18 @@ def ambient_Hrepresentation(self, index=None):
         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
@@ -429,19 +428,18 @@ def ambient_Vrepresentation(self, index=None):
         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