gh-40932: use n_vertices, n_edges and n_faces also in the codebase
    
To achieve better consistency, we replace `num_verts`, `num_edges` and
`num_faces` with `n_vertices`, `n_edges` and `n_faces` also in the
codebase.

`num_verts`, `num_edges` and `num_faces` remain aliases for backwards
compatibility.

dependencies: #40918
    
URL: #40932
Reported by: Martin Rubey
Reviewer(s): David Coudert

Author: Release Manager

src/sage/categories/crystals.py

@@ -171,7 +171,7 @@ def is_isomorphism(self) -> bool:
 
             index_set = self._cartan_type.index_set()
             G = self.domain().digraph(index_set=index_set)
-            if self.codomain().cardinality() != G.num_verts():
+            if self.codomain().cardinality() != G.n_vertices():
                 return False
             H = self.codomain().digraph(index_set=index_set)
             return G.is_isomorphic(H, edge_labels=True)

src/sage/combinat/posets/hasse_diagram.py

@@ -541,7 +541,7 @@ def is_chain(self) -> bool:
         """
         if self.cardinality() == 0:
             return True
-        return (self.num_edges() + 1 == self.num_verts() and  # tree
+        return (self.n_edges() + 1 == self.n_vertices() and  # tree
                 all(d <= 1 for d in self.out_degree()) and
                 all(d <= 1 for d in self.in_degree()))
 
@@ -589,7 +589,7 @@ def dual(self):
             False
         """
         H = self.reverse(immutable=False)
-        H.relabel(perm=list(range(H.num_verts() - 1, -1, -1)), inplace=True)
+        H.relabel(perm=list(range(H.n_vertices() - 1, -1, -1)), inplace=True)
         return HasseDiagram(H)
 
     def _precompute_intervals(self) -> None:

src/sage/combinat/posets/linear_extension_iterator.pyx

@@ -37,7 +37,7 @@ def _linear_extension_prepare(D):
     # the preprocessing routine found in Figure 7 of
     # "Generating Linear Extensions Fast" by
     # Pruesse and Ruskey
-    while dag_copy.num_verts() != 0:
+    while dag_copy.n_vertices() != 0:
         # find all the minimal elements of dag_copy
         minimal_elements = dag_copy.sources()
         if not minimal_elements:

src/sage/combinat/posets/posets.py

@@ -5379,7 +5379,7 @@ def factor(self) -> list:
         dg = self._hasse_diagram
         if not dg.is_connected() or not dg.order():
             raise NotImplementedError('the poset is empty or not connected')
-        if Integer(dg.num_verts()).is_prime():
+        if Integer(dg.n_vertices()).is_prime():
             return [self]
         if sum(e for _, e in self.degree_polynomial().factor()) == 1:
             return [self]

src/sage/combinat/root_system/cartan_matrix.py

@@ -1173,7 +1173,7 @@ def find_cartan_type_from_matrix(CM):
     relabel = []
     for S in CM.dynkin_diagram().connected_components_subgraphs():
         S = DiGraph(S) # We need a simple digraph here
-        n = S.num_verts()
+        n = S.n_vertices()
         # Build the list to test based upon rank
         if n == 1:
             relabel.append({1: S.vertices()[0]})

src/sage/combinat/root_system/coxeter_matrix.py

@@ -1114,7 +1114,7 @@ def recognize_coxeter_type_from_matrix(coxeter_matrix, index_set):
 
     types = []
     for S in G.connected_components_subgraphs():
-        r = S.num_verts()
+        r = S.n_vertices()
         # Handle the special cases first
         if r == 1:
             types.append(CoxeterType(['A', 1]).relabel({1: S.vertices(sort=True)[0]}))

src/sage/combinat/root_system/dynkin_diagram.py

@@ -459,7 +459,7 @@ def rank(self):
             sage: DynkinDiagram("A2","B2","F4").rank()
             8
         """
-        return self.num_verts()
+        return self.n_vertices()
 
     def dynkin_diagram(self):
         """

src/sage/combinat/species/species.py

@@ -801,7 +801,7 @@ def algebraic_equation_system(self):
         Qz = QQ['z'].fraction_field()
 
         # Generate the variable names and the corresponding polynomial rings
-        var_names = ["node%s" % i for i in range(d.num_verts())]
+        var_names = ["node%s" % i for i in range(d.n_vertices())]
         R = Qz[", ".join(var_names)]
         R_gens_dict = R.gens_dict()
 

src/sage/combinat/symmetric_group_representations.py

@@ -677,9 +677,9 @@ def representation_matrix_for_simple_transposition(self, i):
         digraph = copy(Y._digraph)
         digraph.delete_edges((u, v) for (u, v, (j, beta)) in digraph.edges(sort=True)
                              if j != i)
-        M = matrix(self._ring, digraph.num_verts())
+        M = matrix(self._ring, digraph.n_vertices())
         for g in digraph.connected_components_subgraphs():
-            if g.num_verts() == 1:
+            if g.n_vertices() == 1:
                 v, = g.vertices(sort=True)
                 w = self._word_dict[v]
                 trivial = None
@@ -726,7 +726,7 @@ def _representation_matrix_uncached(self, permutation):
             [-1/2  3/2]
             [ 1/2  1/2]
         """
-        m = self._yang_baxter_graph._digraph.num_verts()
+        m = self._yang_baxter_graph._digraph.n_vertices()
         M = matrix(self._ring, m, m, 1)
         for i in Permutation(permutation).reduced_word():
             M *= self.representation_matrix_for_simple_transposition(i)

src/sage/combinat/words/finite_word.py

@@ -1674,7 +1674,7 @@ def reduced_rauzy_graph(self, n):
         g = copy(self.rauzy_graph(n))
         # Otherwise it changes the rauzy_graph function.
         l = [v for v in g if g.in_degree(v) == 1 == g.out_degree(v)]
-        if g.num_verts() != 0 and len(l) == g.num_verts():
+        if len(l) == g.n_vertices() != 0:
             # In this case, the Rauzy graph is simply a cycle.
             g = DiGraph()
             g.allow_loops(True)