switch to nauty for generating posets

Author: fchapoton

src/sage/combinat/posets/posets.py

@@ -8884,11 +8884,11 @@ class FinitePosets_n(UniqueRepresentation, Parent):
         sage: P.cardinality()
         5
         sage: for p in P: print(p.cover_relations())
-        []
-        [[1, 2]]
+        [[1, 2], [0, 2]]
         [[0, 1], [0, 2]]
+        [[0, 2]]
         [[0, 1], [1, 2]]
-        [[1, 2], [0, 2]]
+        []
     """
 
     def __init__(self, n) -> None:
@@ -8945,8 +8945,8 @@ def __iter__(self):
             sage: list(P)
             [Finite poset containing 2 elements, Finite poset containing 2 elements]
         """
-        from sage.graphs.digraph_generators import DiGraphGenerators
-        for dig in DiGraphGenerators()(self._n, is_poset):
+        from sage.graphs.digraph_generators import DiGraphGenerators as DG
+        for dig in DG().nauty_posetg(f"{self._n} o"):
             # We need to relabel the digraph since range(self._n) must be a linear
             # extension. Too bad we need to compute this again. TODO: Fix this.
             label_dict = dict(zip(dig.topological_sort(), range(dig.order())))

src/sage/combinat/tutorial.py

@@ -844,15 +844,15 @@
 
 Partial orders on a set of `8` elements, up to isomorphism::
 
-    sage: C = Posets(8); C
-    Posets containing 8 elements
+    sage: C = Posets(7); C
+    Posets containing 7 elements
     sage: C.cardinality()
-    16999
+    2045
 
 ::
 
     sage: C.unrank(20).plot()
-    Graphics object consisting of 20 graphics primitives
+    Graphics object consisting of ... graphics primitives
 
 .. image:: ../../media/a_poset.png
 

src/sage/databases/findstat.py

@@ -4002,16 +4002,17 @@ def _finite_lattices(n):
     TESTS::
 
         sage: from sage.databases.findstat import _finite_lattices
-        sage: [L.cover_relations() for L in _finite_lattices(4)]
-        [[['bottom', 0], ['bottom', 1], [0, 'top'], [1, 'top']],
-         [['bottom', 0], [0, 1], [1, 'top']]]
+        sage: sorted((L.cover_relations() for L in _finite_lattices(4)),
+        ....:        key=len)
+        [[['bottom', 0], [0, 1], [1, 'top']],
+         [['bottom', 0], ['bottom', 1], [0, 'top'], [1, 'top']]]         
     """
     if n <= 2:
         for P in Posets(n):
             if P.is_lattice():
                 yield LatticePoset(P)
     else:
-        for P in Posets(n-2):
+        for P in Posets(n - 2):
             Q = P.with_bounds()
             if Q.is_lattice():
                 yield LatticePoset(Q)