sagemathgh-37017: cosmetic little change in topology/ (some ruff UP a…

…nd PERF)

    
a set of small fixes there

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: sagemath#37017
Reported by: Frédéric Chapoton
Reviewer(s): Frédéric Chapoton, Tobias Diez

src/sage/topology/cell_complex.py

@@ -1195,7 +1195,7 @@ def _repr_(self):
         for dim in self.cells():
             cells += len(self.cells()[dim])
         if cells != 1:
-            cells_string = " and %s %s" % (cells, cells_name)
+            cells_string = " and {} {}".format(cells, cells_name)
         else:
             cells_string = " and 1 %s" % cell_name
         return Name + " complex " + vertex_string + cells_string

src/sage/topology/cubical_complex.py

@@ -545,13 +545,12 @@ def _triangulation_(self):
         if self.dimension() < 0:  # the empty cube
             return [Simplex(())]  # the empty simplex
         v = tuple([max(j) for j in self.tuple()])
+        Sv = Simplex((v,))
         if self.dimension() == 0:  # just v
-            return [Simplex((v,))]
-        simplices = []
-        for i in range(self.dimension()):
-            for S in self.face(i, upper=False)._triangulation_():
-                simplices.append(S.join(Simplex((v,)), rename_vertices=False))
-        return simplices
+            return [Sv]
+        return [S.join(Sv, rename_vertices=False)
+                for i in range(self.dimension())
+                for S in self.face(i, upper=False)._triangulation_()]
 
     def alexander_whitney(self, dim):
         r"""
@@ -719,7 +718,7 @@ def _repr_(self):
             sage: C1._repr_()
             '[1,1] x [2,3] x [4,5]'
         """
-        s = ("[%s,%s]" % (str(x), str(y)) for x, y in self.__tuple)
+        s = ("[{},{}]".format(str(x), str(y)) for x, y in self.__tuple)
         return " x ".join(s)
 
     def _latex_(self):
@@ -1077,8 +1076,8 @@ def cells(self, subcomplex=None):
             dimension = max([cube.dimension() for cube in self._facets])
             # initialize the lists: add each maximal cube to Cells and sub_facets
             for i in range(-1, dimension+1):
-                Cells[i] = set([])
-                sub_facets[i] = set([])
+                Cells[i] = set()
+                sub_facets[i] = set()
             for f in self._facets:
                 Cells[f.dimension()].add(f)
             if subcomplex is not None:
@@ -1229,7 +1228,7 @@ def chain_complex(self, subcomplex=None, augmented=False,
                     differentials[dim] = self._complex[(dim, subcomplex)].change_ring(base_ring)
                     mat = differentials[dim]
                 if verbose:
-                    print("    boundary matrix (cached): it's %s by %s." % (mat.nrows(), mat.ncols()))
+                    print("    boundary matrix (cached): it's {} by {}.".format(mat.nrows(), mat.ncols()))
             else:
                 # 'current' is the list of cells in dimension n
                 #
@@ -1271,7 +1270,7 @@ def chain_complex(self, subcomplex=None, augmented=False,
                 else:
                     differentials[dim] = mat.change_ring(base_ring)
                 if verbose:
-                    print("    boundary matrix computed: it's %s by %s." % (mat.nrows(), mat.ncols()))
+                    print("    boundary matrix computed: it's {} by {}.".format(mat.nrows(), mat.ncols()))
         # finally, return the chain complex
         if cochain:
             return ChainComplex(data=differentials, base_ring=base_ring,
@@ -1452,7 +1451,7 @@ def suspension(self, n=1):
 
     def product(self, other):
         r"""
-        The product of this cubical complex with another one.
+        Return the product of this cubical complex with another one.
 
         :param other: another cubical complex
 
@@ -1463,10 +1462,7 @@ def product(self, other):
             sage: RP2.product(S1).homology()[1] # long time: 5 seconds
             Z x C2
         """
-        facets = []
-        for f in self._facets:
-            for g in other._facets:
-                facets.append(f.product(g))
+        facets = [f.product(g) for f in self._facets for g in other._facets]
         return CubicalComplex(facets)
 
     def disjoint_union(self, other):
@@ -1490,11 +1486,12 @@ def disjoint_union(self, other):
         embedded_left = len(tuple(self.maximal_cells()[0]))
         embedded_right = len(tuple(other.maximal_cells()[0]))
         zero = [0] * max(embedded_left, embedded_right)
-        facets = []
-        for f in self.maximal_cells():
-            facets.append(Cube([[0, 0]]).product(f._translate(zero)))
-        for f in other.maximal_cells():
-            facets.append(Cube([[1, 1]]).product(f._translate(zero)))
+        C00 = Cube([[0, 0]])
+        facets = [C00.product(f._translate(zero))
+                  for f in self.maximal_cells()]
+        C11 = Cube([[1, 1]])
+        facets.extend(C11.product(f._translate(zero))
+                      for f in other.maximal_cells())
         return CubicalComplex(facets)
 
     def wedge(self, other):
@@ -1528,11 +1525,9 @@ def wedge(self, other):
         translate_right = [-a[0] for a in other.maximal_cells()[0]]
         point_right = Cube([[0, 0]] * embedded_left)
 
-        facets = []
-        for f in self.maximal_cells():
-            facets.append(f._translate(translate_left))
-        for f in other.maximal_cells():
-            facets.append(point_right.product(f._translate(translate_right)))
+        facets = [f._translate(translate_left) for f in self.maximal_cells()]
+        facets.extend(point_right.product(f._translate(translate_right))
+                      for f in other.maximal_cells())
         return CubicalComplex(facets)
 
     def connected_sum(self, other):
@@ -1794,7 +1789,7 @@ def _string_constants(self):
         return ('Cubical', 'cube', 'cubes')
 
 
-class CubicalComplexExamples():
+class CubicalComplexExamples:
     r"""
     Some examples of cubical complexes.
 

src/sage/topology/delta_complex.py

@@ -367,7 +367,7 @@ def store_bdry(simplex, faces):
                     for j in range(d+1):
                         if not all(faces[s[j]][i] == faces[s[i]][j-1] for i in range(j)):
                             msg = "simplicial identity d_i d_j = d_{j-1} d_i fails"
-                            msg += " for j=%s, in dimension %s" % (j, d)
+                            msg += " for j={}, in dimension {}".format(j, d)
                             raise ValueError(msg)
         # self._cells_dict: dictionary indexed by dimension d: for
         # each d, have list or tuple of simplices, and for each
@@ -453,7 +453,7 @@ def subcomplex(self, data):
             try:
                 cells_to_add = set(new_data[d-1])  # begin to populate the (d-1)-cells
             except KeyError:
-                cells_to_add = set([])
+                cells_to_add = set()
             for x in d_cells:
                 if d+1 in new_dict:
                     old = new_dict[d+1]
@@ -757,11 +757,8 @@ def n_skeleton(self, n):
         """
         if n >= self.dimension():
             return self
-        else:
-            data = []
-            for d in range(n+1):
-                data.append(self._cells_dict[d])
-            return DeltaComplex(data)
+        data = [self._cells_dict[d] for d in range(n + 1)]
+        return DeltaComplex(data)
 
     def graph(self):
         r"""
@@ -1106,16 +1103,12 @@ def wedge(self, right):
         """
         data = self.disjoint_union(right).cells()
         left_verts = len(self.n_cells(0))
-        translate = {}
-        for i in range(left_verts):
-            translate[i] = i
+        translate = {i: i for i in range(left_verts)}
         translate[left_verts] = 0
         for i in range(left_verts + 1, left_verts + len(right.n_cells(0))):
-            translate[i] = i-1
+            translate[i] = i - 1
         data[0] = data[0][:-1]
-        edges = []
-        for e in data[1]:
-            edges.append([translate[a] for a in e])
+        edges = [[translate[a] for a in e] for e in data[1]]
         data[1] = edges
         return DeltaComplex(data)
 
@@ -1444,7 +1437,7 @@ def _is_glued(self, idx=-1, dim=None):
         while not_glued and i > 0:
             # count the (i-1) cells and compare to (n+1) choose i.
             old_faces = i_faces
-            i_faces = set([])
+            i_faces = set()
             all_cells = self.n_cells(i)
             for face in old_faces:
                 i_faces.update(all_cells[face])
@@ -1472,7 +1465,7 @@ def face_poset(self):
         for n in range(dim, 0, -1):
             idx = 0
             for s in self.n_cells(n):
-                covers[(n, idx)] = list(set([(n-1, i) for i in s]))
+                covers[(n, idx)] = list({(n-1, i) for i in s})
                 idx += 1
         # deal with vertices separately: they have no covers (in the
         # dual poset).
@@ -1622,7 +1615,7 @@ def _string_constants(self):
         return ('Delta', 'simplex', 'simplices')
 
 
-class DeltaComplexExamples():
+class DeltaComplexExamples:
     r"""
     Some examples of `\Delta`-complexes.
 

src/sage/topology/moment_angle_complex.py

@@ -63,11 +63,8 @@ def _cubical_complex_union(c1, c2):
         sage: union(C1, C1) == C1
         True
     """
-    facets = []
-    for f in c1.maximal_cells():
-        facets.append(f)
-    for f in c2.maximal_cells():
-        facets.append(f)
+    facets = list(c1.maximal_cells())
+    facets.extend(c2.maximal_cells())
     return CubicalComplex(facets)
 
 

src/sage/topology/simplicial_complex.py

@@ -1343,8 +1343,8 @@ def faces(self, subcomplex=None):
             sub_facets = {}
             dimension = max([face.dimension() for face in self._facets])
             for i in range(-1, dimension + 1):
-                Faces[i] = set([])
-                sub_facets[i] = set([])
+                Faces[i] = set()
+                sub_facets[i] = set()
             for f in self._facets:
                 dim = f.dimension()
                 Faces[dim].add(f)
@@ -2085,7 +2085,7 @@ def wedge(self, right, rename_vertices=True, is_mutable=True):
     def chain_complex(self, subcomplex=None, augmented=False,
                       verbose=False, check=False, dimensions=None,
                       base_ring=ZZ, cochain=False):
-        """
+        r"""
         The chain complex associated to this simplicial complex.
 
         :param dimensions: if ``None``, compute the chain complex in all
@@ -2187,7 +2187,7 @@ def chain_complex(self, subcomplex=None, augmented=False,
                     differentials[n] = self._complex[(n, subcomplex)].change_ring(base_ring)
                     mat = differentials[n]
                 if verbose:
-                    print("    boundary matrix (cached): it's %s by %s." % (mat.nrows(), mat.ncols()))
+                    print("    boundary matrix (cached): it's {} by {}.".format(mat.nrows(), mat.ncols()))
             else:
                 # 'current' is the list of faces in dimension n
                 #
@@ -2226,7 +2226,7 @@ def chain_complex(self, subcomplex=None, augmented=False,
                     self._complex[(n, subcomplex)] = mat
                     differentials[n] = mat.change_ring(base_ring)
                 if verbose:
-                    print("    boundary matrix computed: it's %s by %s." % (mat.nrows(), mat.ncols()))
+                    print("    boundary matrix computed: it's {} by {}.".format(mat.nrows(), mat.ncols()))
         # now for the cochain complex, compute the last dimension by
         # hand, and don't cache it.
         if cochain:
@@ -2942,8 +2942,8 @@ def connected_sum(self, other, is_mutable=True):
         keep_left = self._facets[0]
         keep_right = other._facets[0]
         # construct the set of facets:
-        left = set(self._facets).difference(set([keep_left]))
-        right = set(other._facets).difference(set([keep_right]))
+        left = set(self._facets).difference({keep_left})
+        right = set(other._facets).difference({keep_right})
         facet_set = ([[rename_vertex(v, keep=list(keep_left))
                        for v in face] for face in left]
                      + [[rename_vertex(v, keep=list(keep_right), left=False)
@@ -3067,7 +3067,7 @@ def is_cohen_macaulay(self, base_ring=QQ, ncpus=0):
             from sage.parallel.ncpus import ncpus as get_ncpus
             ncpus = get_ncpus()
 
-        facs = [x for x in self.face_iterator()]
+        facs = list(self.face_iterator())
         n = len(facs)
         facs_divided = [[] for i in range(ncpus)]
         for i in range(n):
@@ -3957,7 +3957,7 @@ def _enlarge_subcomplex(self, subcomplex, verbose=False):
                 print(f"  looping through {len(faces)} facets")
             for f in faces:
                 f_set = f.set()
-                int_facets = set(a.set().intersection(f_set) for a in new_facets)
+                int_facets = {a.set().intersection(f_set) for a in new_facets}
                 intersection = SimplicialComplex(int_facets)
                 if not intersection._facets[0].is_empty():
                     if (len(intersection._facets) == 1 or
@@ -3970,7 +3970,7 @@ def _enlarge_subcomplex(self, subcomplex, verbose=False):
             for f in remove_these:
                 faces.remove(f)
         if verbose:
-            print("  now constructing a simplicial complex with %s vertices and %s facets" % (len(self.vertices()), len(new_facets)))
+            print("  now constructing a simplicial complex with {} vertices and {} facets".format(len(self.vertices()), len(new_facets)))
         L = SimplicialComplex(new_facets, maximality_check=False,
                               is_immutable=self._is_immutable)
         self.__enlarged[subcomplex] = L
@@ -4181,7 +4181,7 @@ def fundamental_group(self, base_point=None, simplify=True):
         # simplicial complex, so convert the edges to frozensets so we
         # don't have to worry about it. Convert spanning_tree to a set
         # to make lookup faster.
-        spanning_tree = set(frozenset((u, v)) for u, v, _ in G.min_spanning_tree())
+        spanning_tree = {frozenset((u, v)) for u, v, _ in G.min_spanning_tree()}
         gens = [e for e in G.edge_iterator(labels=False)
                 if frozenset(e) not in spanning_tree]
         if not gens:
@@ -4192,7 +4192,7 @@ def fundamental_group(self, base_point=None, simplify=True):
         rels = []
         for f in self._n_cells_sorted(2):
             bdry = [tuple(e) for e in f.faces()]
-            z = dict()
+            z = {}
             for i in range(3):
                 x = frozenset(bdry[i])
                 if x in spanning_tree:
@@ -5049,7 +5049,7 @@ def is_golod(self) -> bool:
             sage: Y.is_golod()
             True
         """
-        H = list(a+b for (a, b) in self.bigraded_betti_numbers())
+        H = [a+b for (a, b) in self.bigraded_betti_numbers()]
         if 0 in H:
             H.remove(0)
 

src/sage/topology/simplicial_complex_examples.py

@@ -181,7 +181,7 @@ def matching(A, B):
     """
     answer = []
     if len(A) == 0 or len(B) == 0:
-        return [set([])]
+        return [set()]
     for v in A:
         for w in B:
             for M in matching(set(A).difference([v]), set(B).difference([w])):
@@ -476,7 +476,7 @@ def SurfaceOfGenus(g, orientable=True):
 
 
 def MooreSpace(q):
-    """
+    r"""
     Triangulation of the mod `q` Moore space.
 
     INPUT:
@@ -842,7 +842,7 @@ def RealProjectiveSpace(n):
         V = set(range(0, n+2))
         S = Sphere(n).barycentric_subdivision()
         X = S.facets()
-        facets = set([])
+        facets = set()
         for f in X:
             new = []
             for v in f:
@@ -1485,7 +1485,7 @@ def ShiftedComplex(generators):
     from sage.combinat.partition import Partitions
     Facets = []
     for G in generators:
-        G = list(reversed(sorted(G)))
+        G = sorted(G, reverse=True)
         L = len(G)
         for k in range(L * (L+1) // 2, sum(G) + 1):
             for P in Partitions(k, length=L, max_slope=-1, outer=G):