sagemathgh-39342: simplify some .extend in combinat

    
by avoiding lists inside if possible

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: sagemath#39342
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert, Frédéric Chapoton

src/sage/combinat/designs/bibd.py

@@ -613,7 +613,7 @@ def BIBD_from_TD(v, k, existence=False):
 
         BIBD = TDkv._blocks
         for i in range(k):
-            BIBD.extend([[x+i*v for x in B] for B in BIBDvk])
+            BIBD.extend([x+i*v for x in B] for B in BIBDvk)
 
     # Second construction
     elif ((v-1) % k == 0 and
@@ -630,7 +630,7 @@ def BIBD_from_TD(v, k, existence=False):
         inf = v*k
         BIBD = TDkv
         for i in range(k):
-            BIBD.extend([[inf if x == v else x+i*v for x in B] for B in BIBDv1k])
+            BIBD.extend([inf if x == v else x+i*v for x in B] for B in BIBDv1k)
 
     # Third construction
     elif ((v-k) % k == 0 and
@@ -650,7 +650,8 @@ def BIBD_from_TD(v, k, existence=False):
         BIBDvpkk = [B for B in BIBDvpkk if min(B) < v]
 
         for i in range(k):
-            BIBD.extend([[(x-v)+inf if x >= v else x+i*v for x in B] for B in BIBDvpkk])
+            BIBD.extend([(x-v)+inf if x >= v else x+i*v for x in B]
+                        for B in BIBDvpkk)
 
         BIBD.append(list(range(k * v, v * k + k)))
 

src/sage/combinat/designs/database.py

@@ -1058,8 +1058,8 @@ def OA_11_185():
     assert all(len(B) in (11,13) or set(B) == set(special_set) for B in PBD)
 
     OA = OA_from_PBD(11,185,[B for B in PBD if len(B) < 17],check=False)[:-185]
-    OA.extend([[i]*11 for i in range(185) if i not in special_set])
-    OA.extend([[special_set[x] for x in B] for B in orthogonal_array(11,17)])
+    OA.extend([i]*11 for i in range(185) if i not in special_set)
+    OA.extend([special_set[x] for x in B] for B in orthogonal_array(11,17))
     return OA
 
 
@@ -1126,21 +1126,21 @@ def OA_10_205():
     GDD = [[relabel[xx] for xx in B if xx in relabel] for B in pplane if p not in B]
 
     # We turn the GDD into a PBD by extending the groups with a new point 204.
-    GDD.extend([[relabel[xx] for xx in G]+[204] for G in groups])
+    GDD.extend([relabel[xx] for xx in G]+[204] for G in groups)
 
     # We build the OA, knowing that the blocks of size 9 are disjoint
     blocks_of_size_9 = [B for B in GDD if len(B) == 9]
     blocks_of_size_9_union = sum(blocks_of_size_9,[])
 
     OA = OA_from_PBD(10,205,[B for B in GDD if len(B) != 9],check=False)[:-205]
 
-    OA.extend([[B[xx] for xx in R]
-               for R in orthogonal_array(10,9)
-               for B in blocks_of_size_9])
+    OA.extend([B[xx] for xx in R]
+              for R in orthogonal_array(10,9)
+              for B in blocks_of_size_9)
 
     # The missing [i,i,...] blocks
-    OA.extend([[i]*10
-               for i in set(range(205)).difference(blocks_of_size_9_union)])
+    OA.extend([i]*10
+              for i in set(range(205)).difference(blocks_of_size_9_union))
 
     return OA
 
@@ -1627,7 +1627,8 @@ def OA_10_796():
     OA = OA_relabel(OA,17,47,blocks=[OA[0]]) # making sure [46]*17 is a block
     PBD = [[i*47+x for i,x in enumerate(B) if (x < 46 or i < 13)] for B in OA]
     extra_point = 10000
-    PBD.extend([list(range(i*47,(i+1)*47-int(i >= 13)))+[extra_point] for i in range(17)]) # Adding the columns
+    PBD.extend(list(range(i*47,(i+1)*47-int(i >= 13)))+[extra_point]
+               for i in range(17))  # Adding the columns
 
     rel = {v:i for i,v in enumerate(set(range(17*47)).difference([(i+1)*47-1 for i in range(13,17)]))}
     rel[extra_point] = len(rel)
@@ -1645,7 +1646,7 @@ def OA_10_796():
     for B in PBD:
         if len(B) >= 47:
             B.sort(key=lambda x:int(x == extra_point))
-            OA.extend([[B[i] for i in BB] for BB in iOA[len(B)]])
+            OA.extend([B[i] for i in BB] for BB in iOA[len(B)])
             span.update(B[:-1])
         else:
             others.append(B)

src/sage/combinat/designs/orthogonal_arrays_build_recursive.py

@@ -256,7 +256,7 @@ def construction_3_5(k, n, m, r, s, t, explain_construction=False):
     group_k_3 = [B[-1] for B in master_design if B[-3] not in group_k_1 and B[-2] not in group_k_2]
     group_k_3 = list(set(group_k_3))
     assert len(group_k_3) <= t
-    group_k_3.extend([x for x in range(q) if x not in group_k_3])
+    group_k_3.extend(x for x in range(q) if x not in group_k_3)
     group_k_3 = group_k_3[:t]
 
     # Relabelling the OA
@@ -545,7 +545,7 @@ def construction_q_x(k, q, x, check=True, explain_construction=False):
     # delete points.
     #
     # TD.extend([range(i*q,(i+1)*q) for i in range(x)])
-    TD.extend([list(range(i*q,(i+1)*q))+[p2] for i in range(x,q)])
+    TD.extend(list(range(i*q,(i+1)*q))+[p2] for i in range(x,q))
 
     points_to_delete = set([i*q+j for i in range(x) for j in range(1,q)]+[i*q for i in range(x,q)])
     points_to_keep = set(range(q**2+2))-points_to_delete
@@ -1567,7 +1567,8 @@ def brouwer_separable_design(k, t, q, x, check=False, verbose=False, explain_con
         blocks_of_size_q_plus_t = _reorder_matrix(blocks_of_size_q_plus_t)
 
         for i,classs in enumerate(OA_tq1_classes):
-            OA.extend([R[xx] if xx < t+q else N-i-1 for xx in B] for R in blocks_of_size_q_plus_t for B in classs)
+            OA.extend([R[xx] if xx < t+q else N-i-1 for xx in B]
+                      for R in blocks_of_size_q_plus_t for B in classs)
 
         # The set of size x
         OA.extend([N-1-xx for xx in R] for R in orthogonal_array(k,x))

src/sage/combinat/interval_posets.py

@@ -592,8 +592,8 @@ def _mul_(self, other: TIP) -> TIP:
         n = self._size
         m = other.size()
         relations = self._poset.cover_relations()
-        relations.extend([(i + n, j + n)
-                          for i, j in other._poset.cover_relations_iterator()])
+        relations.extend((i + n, j + n)
+                         for i, j in other._poset.cover_relations_iterator())
         P = FinitePoset(DiGraph([list(range(1, n + m + 1)), relations],
                                 format='vertices_and_edges'))  # type:ignore
         return TamariIntervalPoset(P, check=False)  # type:ignore
@@ -1980,9 +1980,9 @@ def subposet(self, start, end) -> TIP:
         relations = [(i - start + 1, j - start + 1)
                      for (i, j) in self.increasing_cover_relations()
                      if i >= start and j < end]
-        relations.extend([(j - start + 1, i - start + 1)
-                          for (j, i) in self.decreasing_cover_relations()
-                          if i >= start and j < end])
+        relations.extend((j - start + 1, i - start + 1)
+                         for (j, i) in self.decreasing_cover_relations()
+                         if i >= start and j < end)
         return TamariIntervalPoset(end - start, relations, check=False)
 
     sub_poset = subposet
@@ -3110,7 +3110,7 @@ def get_relations(bt, start=1):
             rroots, rrelations, rindex = get_relations(bt[1], start=index + 1)
             roots.append(index)
             relations.extend(rrelations)
-            relations.extend([(j, index) for j in rroots])
+            relations.extend((j, index) for j in rroots)
             return roots, relations, rindex
 
         _, relations, index = get_relations(binary_tree)
@@ -3224,7 +3224,7 @@ def get_relations(bt, start=1):
             roots, relations, rindex = get_relations(bt[1], start=index + 1)
             roots.append(index)
             relations.extend(lrelations)
-            relations.extend([(j, index) for j in lroots])
+            relations.extend((j, index) for j in lroots)
             return roots, relations, rindex
 
         _, relations, index = get_relations(binary_tree)

src/sage/combinat/partition.py

@@ -2720,7 +2720,7 @@ def suter_diagonal_slide(self, n, exp=1):
                     exp += 1
                     continue
                 res = [n - leng - 1]
-                res.extend([i - 1 for i in ret._list if i > 1])
+                res.extend(i - 1 for i in ret._list if i > 1)
                 ret = Partition(res)
                 exp += 1
         return ret
@@ -3066,7 +3066,7 @@ def young_subgroup(self):
         gens = []
         m = 0
         for row in self:
-            gens.extend([(c, c+1) for c in range(m+1, m+row)])
+            gens.extend((c, c + 1) for c in range(m + 1, m + row))
             m += row
         gens.append(list(range(1, self.size() + 1)))  # to ensure we get a subgroup of Sym_n
         return PermutationGroup(gens)

src/sage/combinat/partition_tuple.py

@@ -1485,7 +1485,7 @@ def young_subgroup(self):
         m = 0
         for comp in self:
             for row in comp:
-                gens.extend([(c, c+1) for c in range(m+1, m+row)])
+                gens.extend((c, c + 1) for c in range(m + 1, m + row))
                 m += row
         gens.append(list(range(1, self.size()+1)))  # to ensure we get a subgroup of Sym_n
         return PermutationGroup(gens)
@@ -1504,7 +1504,7 @@ def young_subgroup_generators(self):
         m = 0
         for comp in self:
             for row in comp:
-                gens.extend(list(range(m + 1, m + row)))
+                gens.extend(range(m + 1, m + row))
                 m += row
         return gens
 

src/sage/combinat/posets/poset_examples.py

@@ -1590,7 +1590,7 @@ def DoubleTailedDiamond(n):
 
         edges = [(i, i + 1) for i in range(1, n)]
         edges.extend([(n, n + 1), (n, n + 2), (n + 1, n + 3), (n + 2, n + 3)])
-        edges.extend([(i, i + 1) for i in range(n + 3, 2 * n + 2)])
+        edges.extend((i, i + 1) for i in range(n + 3, 2 * n + 2))
         p = DiGraph([list(range(1, 2 * n + 3)), edges])
         return DCompletePoset(p)
 

src/sage/combinat/posets/posets.py

@@ -2584,10 +2584,10 @@ def intervals_poset(self):
 
         covers = []
         for a, b in ints:
-            covers.extend([[(a, b), (a, bb)] for bb in self.upper_covers(b)])
+            covers.extend([(a, b), (a, bb)] for bb in self.upper_covers(b))
             if a != b:
-                covers.extend([[(a, b), (aa, b)] for aa in self.upper_covers(a)
-                               if self.le(aa, b)])
+                covers.extend([(a, b), (aa, b)] for aa in self.upper_covers(a)
+                              if self.le(aa, b))
 
         dg = DiGraph([ints, covers], format='vertices_and_edges')
         return constructor(dg, cover_relations=True)

src/sage/combinat/rigged_configurations/kr_tableaux.py

@@ -800,17 +800,17 @@ def _fill(self, shape):
             shape_list.append(0)
 
         lst = []
-        for col in range(1, self._s+1):
+        for col in range(1, self._s + 1):
             if (self._s - col) % 2 == 0:
-                lst.extend( [self.letters(self._r - x) for x in range(self._r)] )
+                lst.extend(self.letters(self._r - x) for x in range(self._r))
             else:
                 m = self._r
                 for j, val in enumerate(shape_list):
                     if col >= val:
                         m = j
                         break
-                lst.extend([self.letters(-x) for x in range(m+1, self._r+1)])
-                lst.extend([self.letters(m - x) for x in range(m)])
+                lst.extend(self.letters(-x) for x in range(m + 1, self._r + 1))
+                lst.extend(self.letters(m - x) for x in range(m))
 
         return self.element_class(self, lst)
 

src/sage/combinat/root_system/branching_rules.py

@@ -1774,7 +1774,8 @@ def rule(x):
             if all(t[0] == 'A' for t in stypes):
                 def rule(x):
                     ret = [sum(x[i*ns[1]:(i+1)*ns[1]]) for i in range(ns[0])]
-                    ret.extend([sum(x[ns[1]*j+i] for j in range(ns[0])) for i in range(ns[1])])
+                    ret.extend(sum(x[ns[1]*j+i] for j in range(ns[0]))
+                               for i in range(ns[1]))
                     return ret
                 return BranchingRule(Rtype, Stype, rule, "tensor")
             else:

src/sage/combinat/root_system/reflection_group_real.py

@@ -140,24 +140,24 @@ def ReflectionGroup(*args, **kwds):
             X = arg
 
         # precheck for valid input data
-        if not (isinstance(X, (CartanType_abstract,tuple)) or (X in ZZ and 4 <= X <= 37)):
+        if not (isinstance(X, (CartanType_abstract, tuple)) or (X in ZZ and 4 <= X <= 37)):
             raise ValueError(error_msg % X)
 
         # transforming two reducible types and an irreducible type
         if isinstance(X, CartanType_abstract):
             if not X.is_finite():
                 raise ValueError(error_msg % X)
-            if hasattr(X,"cartan_type"):
+            if hasattr(X, "cartan_type"):
                 X = X.cartan_type()
             if X.is_irreducible():
                 W_types.extend([(X.letter, X.n)])
             else:
-                W_types.extend([(x.letter, x.n) for x in X.component_types()])
+                W_types.extend((x.letter, x.n) for x in X.component_types())
 
-        elif X == (2,2,2) or X == ('I',2):
-            W_types.extend([('A',1), ('A',1)])
+        elif X == (2, 2, 2) or X == ('I', 2):
+            W_types.extend([('A', 1), ('A', 1)])
 
-        elif X == (2,2,3):
+        elif X == (2, 2, 3):
             W_types.extend([('A', 3)])
 
         else:

src/sage/combinat/root_system/type_C.py

@@ -83,10 +83,10 @@ def positive_roots(self):
              (0, 0, 2)]
         """
         res = []
-        for p in [0,1]:
+        for p in [0, 1]:
             for j in range(self.n):
-                res.extend([self.root(i,j,0,p) for i in range(j)])
-        res.extend([self.root(i,i,0,0) for i in range(self.n)])
+                res.extend(self.root(i, j, 0, p) for i in range(j))
+        res.extend(self.root(i, i, 0, 0) for i in range(self.n))
         return res
 
     def negative_roots(self):
@@ -105,10 +105,10 @@ def negative_roots(self):
              (0, 0, -2)]
         """
         res = []
-        for p in [0,1]:
+        for p in [0, 1]:
             for j in range(self.n):
-                res.extend( [self.root(i,j,1,p) for i in range(j) ] )
-        res.extend( [ self.root(i,i,1,1) for i in range(self.n) ] )
+                res.extend(self.root(i, j, 1, p) for i in range(j))
+        res.extend(self.root(i, i, 1, 1) for i in range(self.n))
         return res
 
     def fundamental_weight(self, i):

src/sage/combinat/root_system/type_D.py

@@ -72,7 +72,7 @@ def positive_roots(self):
         res = []
         for p in [0, 1]:
             for j in range(self.n):
-                res.extend([self.root(i, j, 0, p) for i in range(j)])
+                res.extend(self.root(i, j, 0, p) for i in range(j))
         return res
 
     def negative_roots(self):
@@ -96,7 +96,7 @@ def negative_roots(self):
         res = []
         for p in [0, 1]:
             for j in range(self.n):
-                res.extend([self.root(i, j, 1, p) for i in range(j)])
+                res.extend(self.root(i, j, 1, p) for i in range(j))
         return res
 
     def fundamental_weight(self, i):

src/sage/combinat/skew_partition.py

@@ -1009,12 +1009,9 @@ def frobenius_rank(self):
         """
         N = len(self[0])
         mu_betas = [x - j for j, x in enumerate(self[1])]
-        mu_betas.extend([- j for j in range(len(self[1]), N)])
-        res = 0
-        for i, x in enumerate(self[0]):
-            if (x - i) not in mu_betas:
-                res += 1
-        return res
+        mu_betas.extend(- j for j in range(len(self[1]), N))
+        return sum(1 for i, x in enumerate(self[0])
+                   if (x - i) not in mu_betas)
 
     def cells(self):
         """