trac 22349: vertex sorting

src/doc/en/thematic_tutorials/algebraic_combinatorics/walks.rst

@@ -15,9 +15,9 @@ We begin by creating a graph with 4 vertices::
 
 This graph has no edges yet::
 
-    sage: G.vertices()
+    sage: G.vertices(sort=True)
     [0, 1, 2, 3]
-    sage: G.edges()
+    sage: G.edges(sort=True)
     []
 
 Before we can add edges, we need to tell Sage that our graph can

src/doc/en/thematic_tutorials/sandpile.rst

@@ -161,7 +161,7 @@ Laplacian.
 
 **Example.** (Continued.) ::
 
-    sage: S.vertices()  # the ordering of the vertices
+    sage: S.vertices(sort=True)  # the ordering of the vertices
     [0, 1, 2, 3]
     sage: S.laplacian()
     [ 0  0  0  0]
@@ -883,9 +883,9 @@ first presented.  This internal format is returned by ``dict()``::
 Code for checking whether a given vertex is a sink::
 
     sage: S = Sandpile({0:[], 1:[0, 3, 4], 2:[0, 3, 5], 3: [2, 5], 4: [1, 3], 5: [2, 3]},0)
-    sage: [S.distance(v,0) for v in S.vertices()] # 0 is a sink
+    sage: [S.distance(v,0) for v in S.vertices(sort=True)] # 0 is a sink
     [0, 1, 1, 2, 2, 2]
-    sage: [S.distance(v,1) for v in S.vertices()] # 1 is not a sink
+    sage: [S.distance(v,1) for v in S.vertices(sort=True)] # 1 is not a sink
     [+Infinity, 0, +Infinity, +Infinity, 1, +Infinity]
 
 Methods
@@ -4609,7 +4609,7 @@ EXAMPLES::
     sage: D = SandpileDivisor(S, [0,0,1,1])
     sage: D.support()
     [2, 3]
-    sage: S.vertices()
+    sage: S.vertices(sort=True)
     [0, 1, 2, 3]
 
 ---
@@ -4654,7 +4654,7 @@ EXAMPLES::
     {'a': 0, 'b': 1, 'c': 2}
     sage: D.values()
     [0, 1, 2]
-    sage: S.vertices()
+    sage: S.vertices(sort=True)
     ['a', 'b', 'c']
 
 
@@ -4715,9 +4715,9 @@ EXAMPLES::
 
     sage: s = sandpiles.Cycle(4)
     sage: D = SandpileDivisor(s,[2,0,0,0])
-    sage: [D.weierstrass_gap_seq(v,False) for v in s.vertices()]
+    sage: [D.weierstrass_gap_seq(v,False) for v in s.vertices(sort=True)]
     [(1, 3), (1, 2), (1, 3), (1, 2)]
-    sage: [D.weierstrass_gap_seq(v) for v in s.vertices()]
+    sage: [D.weierstrass_gap_seq(v) for v in s.vertices(sort=True)]
     [((1, 3), 1), ((1, 2), 0), ((1, 3), 1), ((1, 2), 0)]
     sage: D.weierstrass_gap_seq()  # gap sequence at sink vertex, 0
     ((1, 3), 1)
@@ -4786,7 +4786,7 @@ EXAMPLES::
 
     sage: s = sandpiles.House()
     sage: K = s.canonical_divisor()
-    sage: [K.weierstrass_rank_seq(v) for v in s.vertices()]
+    sage: [K.weierstrass_rank_seq(v) for v in s.vertices(sort=True)]
     [(1, 0, -1), (1, 0, -1), (1, 0, -1), (1, 0, -1), (1, 0, 0, -1)]
 
 ---

src/sage/categories/category.py

@@ -2639,7 +2639,7 @@ def category_graph(categories = None):
     EXAMPLES::
 
         sage: G = sage.categories.category.category_graph(categories = [Groups()])
-        sage: G.vertices()
+        sage: G.vertices(sort=True)
         ['groups', 'inverse unital magmas', 'magmas', 'monoids', 'objects',
          'semigroups', 'sets', 'sets with partial maps', 'unital magmas']
         sage: G.plot()

src/sage/categories/crystals.py

@@ -847,7 +847,7 @@ def digraph(self, subset=None, index_set=None):
                 sage: S = T.subcrystal(max_depth=3)
                 sage: G = T.digraph(subset=S); G
                 Digraph on 5 vertices
-                sage: sorted(G.vertices(), key=str)
+                sage: G.vertices(sort=True, key=str)
                 [(-Lambda[0] + 2*Lambda[1] - delta,),
                  (1/2*Lambda[0] + Lambda[1] - Lambda[2] - 1/2*delta, -1/2*Lambda[0] + Lambda[1] - 1/2*delta),
                  (1/2*Lambda[0] - Lambda[1] + Lambda[2] - 1/2*delta, -1/2*Lambda[0] + Lambda[1] - 1/2*delta),

src/sage/categories/finite_coxeter_groups.py

@@ -863,7 +863,7 @@ def coxeter_knuth_graph(self):
                 sage: W = WeylGroup(['A',4], prefix='s')
                 sage: w = W.from_reduced_word([1,2,1,3,2])
                 sage: D = w.coxeter_knuth_graph()
-                sage: D.vertices()
+                sage: D.vertices(sort=True)
                 [(1, 2, 1, 3, 2),
                 (1, 2, 3, 1, 2),
                 (2, 1, 2, 3, 2),
@@ -877,7 +877,7 @@ def coxeter_knuth_graph(self):
 
                 sage: w = W.from_reduced_word([1,3])
                 sage: D = w.coxeter_knuth_graph()
-                sage: D.vertices()
+                sage: D.vertices(sort=True)
                 [(1, 3), (3, 1)]
                 sage: D.edges()
                 []

src/sage/categories/regular_crystals.py

@@ -397,7 +397,7 @@ def dual_equivalence_graph(self, X=None, index_set=None, directed=True):
 
                 sage: T = crystals.Tableaux(['A',4], shape=[3,1])
                 sage: G = T.dual_equivalence_graph(index_set=[1,2,3])
-                sage: G.vertices()
+                sage: G.vertices(sort=True)
                 [[[1, 3, 4], [2]], [[1, 2, 4], [3]], [[1, 2, 3], [4]]]
                 sage: G.edges()
                 [([[1, 3, 4], [2]], [[1, 2, 4], [3]], 2),
@@ -410,7 +410,7 @@ def dual_equivalence_graph(self, X=None, index_set=None, directed=True):
                 sage: sorted(G.edges())
                 [([[1, 2, 4], [3]], [[1, 2, 3], [4]], 3),
                  ([[2, 4, 5], [3]], [[2, 3, 5], [4]], 3)]
-                sage: sorted(G.vertices())
+                sage: sorted(G.vertices(sort=True))
                 [[[1, 3, 4], [2]],
                  [[1, 2, 4], [3]],
                  [[2, 4, 5], [3]],

src/sage/categories/semigroups.py

@@ -203,7 +203,7 @@ def cayley_graph(self, side="right", simple=False, elements = None, generators =
                 Alternating group of order 5!/2 as a permutation group
                 sage: G = A5.cayley_graph()
                 sage: G.show3d(color_by_label=True, edge_size=0.01, edge_size2=0.02, vertex_size=0.03)
-                sage: G.show3d(vertex_size=0.03, edge_size=0.01, edge_size2=0.02, vertex_colors={(1,1,1):G.vertices()}, bgcolor=(0,0,0), color_by_label=True, xres=700, yres=700, iterations=200) # long time (less than a minute)
+                sage: G.show3d(vertex_size=0.03, edge_size=0.01, edge_size2=0.02, vertex_colors={(1,1,1):G.vertices(sort=True)}, bgcolor=(0,0,0), color_by_label=True, xres=700, yres=700, iterations=200) # long time (less than a minute)
                 sage: G.num_edges()
                 120
 
@@ -239,15 +239,15 @@ def cayley_graph(self, side="right", simple=False, elements = None, generators =
 
                 sage: S = FiniteSemigroups().example(alphabet=('a','b'))
                 sage: g = S.cayley_graph(simple=True)
-                sage: g.vertices()
+                sage: g.vertices(sort=True)
                 ['a', 'ab', 'b', 'ba']
                 sage: g.edges()
                 [('a', 'ab', None), ('b', 'ba', None)]
 
             ::
 
                 sage: g = S.cayley_graph(side="left", simple=True)
-                sage: g.vertices()
+                sage: g.vertices(sort=True)
                 ['a', 'ab', 'b', 'ba']
                 sage: g.edges()
                 [('a', 'ba', None), ('ab', 'ba', None), ('b', 'ab', None),
@@ -256,7 +256,7 @@ def cayley_graph(self, side="right", simple=False, elements = None, generators =
             ::
 
                 sage: g = S.cayley_graph(side="twosided", simple=True)
-                sage: g.vertices()
+                sage: g.vertices(sort=True)
                 ['a', 'ab', 'b', 'ba']
                 sage: g.edges()
                 [('a', 'ab', None), ('a', 'ba', None), ('ab', 'ba', None),
@@ -265,14 +265,14 @@ def cayley_graph(self, side="right", simple=False, elements = None, generators =
             ::
 
                 sage: g = S.cayley_graph(side="twosided")
-                sage: g.vertices()
+                sage: g.vertices(sort=True)
                 ['a', 'ab', 'b', 'ba']
                 sage: g.edges()
                 [('a', 'a', (0, 'left')), ('a', 'a', (0, 'right')), ('a', 'ab', (1, 'right')), ('a', 'ba', (1, 'left')), ('ab', 'ab', (0, 'left')), ('ab', 'ab', (0, 'right')), ('ab', 'ab', (1, 'right')), ('ab', 'ba', (1, 'left')), ('b', 'ab', (0, 'left')), ('b', 'b', (1, 'left')), ('b', 'b', (1, 'right')), ('b', 'ba', (0, 'right')), ('ba', 'ab', (0, 'left')), ('ba', 'ba', (0, 'right')), ('ba', 'ba', (1, 'left')), ('ba', 'ba', (1, 'right'))]
 
             ::
 
-                sage: s1 = SymmetricGroup(1); s = s1.cayley_graph(); s.vertices()
+                sage: s1 = SymmetricGroup(1); s = s1.cayley_graph(); s.vertices(sort=False)
                 [()]
 
             TESTS::

src/sage/categories/weyl_groups.py

@@ -248,7 +248,7 @@ def quantum_bruhat_graph(self, index_set=()):
                 sage: g = W.quantum_bruhat_graph((1,3))
                 sage: g
                 Parabolic Quantum Bruhat Graph of Weyl Group of type ['A', 3] (as a matrix group acting on the ambient space) for nodes (1, 3): Digraph on 6 vertices
-                sage: g.vertices()
+                sage: g.vertices(sort=True)
                 [s2*s3*s1*s2, s3*s1*s2, s1*s2, s3*s2, s2, 1]
                 sage: g.edges()
                 [(s2*s3*s1*s2, s2, alpha[2]),

src/sage/coding/linear_code.py

@@ -2066,9 +2066,9 @@ def cosetGraph(self):
             sage: M = matrix.identity(GF(3), 7)
             sage: C = LinearCode(M)
             sage: G = C.cosetGraph()
-            sage: G.vertices()
+            sage: G.vertices(sort=False)
             [0]
-            sage: G.edges()
+            sage: G.edges(sort=False)
             []
         """
         from sage.matrix.constructor import matrix

src/sage/combinat/constellation.py

@@ -1222,7 +1222,7 @@ def braid_group_orbits(self):
             sage: [x.profile() for x in O[2]]
             [([2, 1], [2, 1], [3]), ([2, 1], [3], [2, 1]), ([3], [2, 1], [2, 1])]
         """
-        return [g.vertices() for g in self.braid_group_action()]
+        return [g.vertices(sort=True) for g in self.braid_group_action()]
 
 
 class Constellations_p(UniqueRepresentation, Parent):

src/sage/combinat/crystals/alcove_path.py

@@ -1911,7 +1911,7 @@ def compare_graphs(g1, g2, node1, node2):
         sage: G1 = crystals.Tableaux(['A',3], shape=[1,1]).digraph()
         sage: C = crystals.AlcovePaths(['A',3],[0,1,0])
         sage: G2 = C.digraph()
-        sage: compare_graphs(G1, G2, C( () ), G2.vertices()[0])
+        sage: compare_graphs(G1, G2, C( () ), G2.vertices(sort=True)[0])
         True
     """
     for out_edge in g1.outgoing_edges( node1 ):
@@ -1974,7 +1974,7 @@ def _test_against_tableaux(R, N, k, clss=CrystalOfAlcovePaths):
         if cc != ct:
             print("FAIL: number of nodes differ.", cc, ct)
             return
-        print("  Compare graphs: ", compare_graphs(G, H, C(()), H.vertices()[0]))
+        print("  Compare graphs: ", compare_graphs(G, H, C(()), H.vertices(sort=True)[0]))
 
 def _test_with_lspaths_crystal(cartan_type, weight, depth=10):
     r"""

src/sage/combinat/crystals/kirillov_reshetikhin.py

@@ -1576,7 +1576,7 @@ class KR_type_A2(KirillovReshetikhinGenericCrystal):
         sage: G = K.digraph()
         sage: Gdual = Kdual.digraph()
         sage: f = {0:2, 1:1, 2:0}
-        sage: Gnew = DiGraph(); Gnew.add_vertices(Gdual.vertices()); Gnew.add_edges([(u,v,f[i]) for (u,v,i) in Gdual.edges()])
+        sage: Gnew = DiGraph(); Gnew.add_vertices(Gdual.vertices(sort=True)); Gnew.add_edges([(u,v,f[i]) for (u,v,i) in Gdual.edges()])
         sage: G.is_isomorphic(Gnew, edge_labels = True)
         True
     """

src/sage/combinat/designs/twographs.py

@@ -283,7 +283,7 @@ def twograph_descendant(G, v, name=None):
     TESTS::
 
         sage: T8 = graphs.CompleteGraph(8).line_graph()
-        sage: v = T8.vertices()[0]
+        sage: v = T8.vertices(sort=True)[0]
         sage: twograph_descendant(T8, v)==T8.twograph().descendant(v)
         True
         sage: twograph_descendant(T8, v).is_strongly_regular(parameters=True)

src/sage/combinat/diagram_algebras.py

@@ -4531,9 +4531,9 @@ def to_graph(sp):
         sage: g = da.to_graph( da.to_set_partition([[1,-2],[2,-1]])); g
         Graph on 4 vertices
 
-        sage: g.vertices()
+        sage: g.vertices(sort=True)
         [-2, -1, 1, 2]
-        sage: g.edges()
+        sage: g.edges(sort=True)
         [(-2, 1, None), (-1, 2, None)]
     """
     g = Graph()
@@ -4565,9 +4565,9 @@ def pair_to_graph(sp1, sp2):
         sage: g = da.pair_to_graph( sp1, sp2 ); g
         Graph on 8 vertices
 
-        sage: g.vertices()
+        sage: g.vertices(sort=True)
         [(-2, 1), (-2, 2), (-1, 1), (-1, 2), (1, 1), (1, 2), (2, 1), (2, 2)]
-        sage: g.edges()
+        sage: g.edges(sort=True)
         [((-2, 1), (1, 1), None), ((-2, 1), (2, 2), None),
          ((-2, 2), (1, 2), None), ((-1, 1), (1, 2), None),
          ((-1, 1), (2, 1), None), ((-1, 2), (2, 2), None)]
@@ -4579,9 +4579,9 @@ def pair_to_graph(sp1, sp2):
         sage: g = da.pair_to_graph( sp3, sp4 ); g
         Graph on 8 vertices
 
-        sage: g.vertices()
+        sage: g.vertices(sort=True)
         [(-2, 1), (-2, 2), (-1, 1), (-1, 2), (1, 1), (1, 2), (2, 1), (2, 2)]
-        sage: g.edges()
+        sage: g.edges(sort=True)
         [((-2, 1), (2, 2), None), ((-1, 1), (1, 1), None),
          ((-1, 1), (1, 2), None)]
     """

src/sage/combinat/finite_state_machine.py

@@ -8684,7 +8684,7 @@ def final_components(self):
         DG = self.digraph()
         condensation = DG.strongly_connected_components_digraph()
         return [self.induced_sub_finite_state_machine([self.state(_) for _ in component])
-                for component in condensation.vertices()
+                for component in condensation.vertices(sort=True)
                 if condensation.out_degree(component) == 0]
 
 

src/sage/combinat/partition.py

@@ -5260,10 +5260,10 @@ def dual_equivalence_graph(self, directed=False, coloring=None):
         TESTS::
 
             sage: G = Partition([1]).dual_equivalence_graph()
-            sage: G.vertices()
+            sage: G.vertices(sort=False)
             [[[1]]]
             sage: G = Partition([]).dual_equivalence_graph()
-            sage: G.vertices()
+            sage: G.vertices(sort=False)
             [[]]
 
             sage: P = Partition([3,1,1])

src/sage/combinat/partition_algebra.py

@@ -1794,9 +1794,9 @@ def to_graph(sp):
         sage: g = pa.to_graph( pa.to_set_partition([[1,-2],[2,-1]])); g
         Graph on 4 vertices
 
-        sage: g.vertices() #random
+        sage: g.vertices(sort=False) #random
         [1, 2, -2, -1]
-        sage: g.edges() #random
+        sage: g.edges(sort=False) #random
         [(1, -2, None), (2, -1, None)]
     """
     g = Graph()
@@ -1831,9 +1831,9 @@ def pair_to_graph(sp1, sp2):
 
     ::
 
-        sage: g.vertices() #random
+        sage: g.vertices(sort=False) #random
         [(1, 2), (-1, 1), (-2, 2), (-1, 2), (-2, 1), (2, 1), (2, 2), (1, 1)]
-        sage: g.edges() #random
+        sage: g.edges(sort=False) #random
         [((1, 2), (-1, 1), None),
          ((1, 2), (-2, 2), None),
          ((-1, 1), (2, 1), None),
@@ -1848,9 +1848,9 @@ def pair_to_graph(sp1, sp2):
         sage: g = pa.pair_to_graph( sp3, sp4 ); g
         Graph on 8 vertices
 
-        sage: g.vertices()
+        sage: g.vertices(sort=True)
         [(-2, 1), (-2, 2), (-1, 1), (-1, 2), (1, 1), (1, 2), (2, 1), (2, 2)]
-        sage: g.edges()
+        sage: g.edges(sort=True)
         [((-2, 1), (2, 2), None), ((-1, 1), (1, 1), None),
          ((-1, 1), (1, 2), None)]
     """

src/sage/combinat/posets/hasse_diagram.py

@@ -2225,7 +2225,8 @@ def are_incomparable(self, i, j):
             sage: H = P._hasse_diagram
             sage: H.are_incomparable(1,2)
             True
-            sage: [ (i,j) for i in H.vertices() for j in H.vertices() if H.are_incomparable(i,j)]
+            sage: V = H.vertices(sort=True)
+            sage: [ (i,j) for i in V for j in V if H.are_incomparable(i,j)]
             [(1, 2), (1, 3), (2, 1), (3, 1)]
         """
         if i == j:
@@ -2249,7 +2250,8 @@ def are_comparable(self, i, j):
             sage: H = P._hasse_diagram
             sage: H.are_comparable(1,2)
             False
-            sage: [ (i,j) for i in H.vertices() for j in H.vertices() if H.are_comparable(i,j)]
+            sage: V = H.vertices(sort=True)
+            sage: [ (i,j) for i in V for j in V if H.are_comparable(i,j)]
             [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 4), (2, 0), (2, 2), (2, 3), (2, 4), (3, 0), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]
         """
         if i == j:
@@ -2291,7 +2293,7 @@ def antichains(self, element_class=list):
             sage: TestSuite(A).run()
         """
         from sage.combinat.subsets_pairwise import PairwiseCompatibleSubsets
-        return PairwiseCompatibleSubsets(self.vertices(),
+        return PairwiseCompatibleSubsets(self.vertices(sort=True),
                                          self.are_incomparable,
                                          element_class=element_class)
 
@@ -2450,7 +2452,7 @@ def diamonds(self):
         """
         diamonds = []
         all_diamonds_completed = True
-        for w in self.vertices():
+        for w in self.vertices(sort=True):
             covers = self.neighbors_out(w)
             for i, x in enumerate(covers):
                 for y in covers[i + 1:]: