gh-40400: faster Hochschild lattices
    
by being smarter about telling the covering relations

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40400
Reported by: Frédéric Chapoton
Reviewer(s):

Author: Release Manager

src/sage/combinat/posets/hochschild_lattice.py

@@ -19,6 +19,7 @@
 from typing import Iterator
 
 from sage.combinat.posets.lattices import LatticePoset
+from sage.graphs.digraph import DiGraph
 from sage.topology.simplicial_complex import SimplicialComplex
 
 
@@ -84,12 +85,23 @@ def sommets(n) -> Iterator[tuple[int, ...]]:
         for w in iterator_False(n - 1):
             yield (1,) + w
 
-    verts = list(sommets(n))
-
-    def compare(a, b) -> bool:
-        return all(ai <= bi for ai, bi in zip(a, b))
-
-    return LatticePoset([verts, compare])
+    verts = frozenset(sommets(n))
+
+    def cover_relations(a):
+        for i, ai in enumerate(a):
+            if not ai:
+                continue
+            b = list(a)
+            for k in range(ai - 1, -1, -1):
+                b[i] = k
+                tb = tuple(b)
+                if tb in verts:
+                    yield tb
+                    break
+
+    dg = DiGraph({a: list(cover_relations(a)) for a in verts},
+                 format="dict_of_lists")
+    return LatticePoset(dg.reverse(), cover_relations=True, check=False)
 
 
 def hochschild_fan(n):