gh-37397: fix some ruff suggestions in cluster_algebra_quiver

    
this was scripted using `ruff` for the codes `UP` and `C4` in the
cluster folder.

Plus a few hand-made changes about pep8

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #37397
Reported by: Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

src/sage/combinat/cluster_algebra_quiver/cluster_seed.py

@@ -370,7 +370,7 @@ def __init__(self, data, frozen=None, is_principal=False, user_labels=None, user
             self._init_exch = dict(islice(self._init_vars.items(), self._n))
             self._U = PolynomialRing(QQ, [f'y{i}' for i in range(self._n)])
             self._F = {i: self._U(1) for i in self._init_exch.values()}
-            self._R = PolynomialRing(QQ, [val for val in self._init_vars.values()])
+            self._R = PolynomialRing(QQ, list(self._init_vars.values()))
             self._y = {self._U.gen(j): prod([self._R.gen(i)**self._M[i, j] for i in range(self._n, self._n + self._m)])
                        for j in range(self._n)}
             self._yhat = {self._U.gen(j): prod([self._R.gen(i)**self._M[i, j] for i in range(self._n + self._m)])
@@ -695,7 +695,7 @@ def use_fpolys(self, use=True, user_labels=None, user_labels_prefix=None):
                     self._init_exch = dict(islice(self._init_vars.items(), self._n))
                     self._U = PolynomialRing(QQ, [f'y{i}' for i in range(self._n)])
                     self._F = {i: self._U(1) for i in self._init_exch.values()}
-                    self._R = PolynomialRing(QQ, [val for val in self._init_vars.values()])
+                    self._R = PolynomialRing(QQ, list(self._init_vars.values()))
                     self._y = {self._U.gen(j): prod([self._R.gen(i)**self._M[i, j] for i in range(self._n, self._n + self._m)])
                                for j in range(self._n)}
                     self._yhat = {self._U.gen(j): prod([self._R.gen(i)**self._M[i, j] for i in range(self._n + self._m)])
@@ -3556,7 +3556,7 @@ def mutation_class_iter(self, depth=infinity, show_depth=False,
             dc += ' ' * (5 - len(dc))
             nr = str(len(clusters))
             nr += ' ' * (10 - len(nr))
-            print("Depth: %s found: %s Time: %.2f s" % (dc, nr, timer2 - timer))
+            print(f"Depth: {dc} found: {nr} Time: {timer2 - timer:.2f} s")
 
         # Each time we get bigger and we haven't hit the full depth
         while gets_bigger and depth_counter < depth:
@@ -3592,11 +3592,11 @@ def mutation_class_iter(self, depth=infinity, show_depth=False,
                             if only_sink_source:
                                 orbits = list(range(n))
                             else:
-                                orbits = [index for index in range(n) if index > i or sd2._M[index,i] != 0]
+                                orbits = [index for index in range(n) if index > i or sd2._M[index, i] != 0]
 
                             clusters[cl2] = [sd2, orbits, clusters[key][2]+[i]]
                             if return_paths:
-                                yield (sd2,clusters[cl2][2])
+                                yield (sd2, clusters[cl2][2])
                             else:
                                 yield sd2
             depth_counter += 1
@@ -3606,7 +3606,7 @@ def mutation_class_iter(self, depth=infinity, show_depth=False,
                 dc += ' ' * (5-len(dc))
                 nr = str(len(clusters))
                 nr += ' ' * (10-len(nr))
-                print("Depth: %s found: %s Time: %.2f s" % (dc,nr,timer2-timer))
+                print(f"Depth: {dc} found: {nr} Time: {timer2-timer:.2f} s")
 
     def mutation_class(self, depth=infinity, show_depth=False, return_paths=False,
                        up_to_equivalence=True, only_sink_source=False):
@@ -3773,7 +3773,7 @@ def cluster_class(self, depth=infinity, show_depth=False, up_to_equivalence=True
         if depth is infinity and not self.is_finite():
             raise ValueError('The variable class can - for infinite types - only be computed up to a given depth')
 
-        return [c for c in self.cluster_class_iter(depth=depth, show_depth=show_depth, up_to_equivalence=up_to_equivalence)]
+        return list(self.cluster_class_iter(depth=depth, show_depth=show_depth, up_to_equivalence=up_to_equivalence))
 
     def b_matrix_class_iter(self, depth=infinity, up_to_equivalence=True):
         r"""
@@ -3989,51 +3989,51 @@ def variable_class_iter(self, depth=infinity, ignore_bipartite_belt=False):
             (x0^8 + 4*x0^6 + 3*x0^4*x1^2 + 2*x0^2*x1^4 + x1^6 + 6*x0^4 + 6*x0^2*x1^2 + 3*x1^4 + 4*x0^2 + 3*x1^2 + 1)/(x0^3*x1^4)
             (x0^6 + 3*x0^4 + 2*x0^2*x1^2 + x1^4 + 3*x0^2 + 2*x1^2 + 1)/(x0^2*x1^3)
         """
-        mut_iter = self.mutation_class_iter(depth=depth,show_depth=False)
+        mut_iter = self.mutation_class_iter(depth=depth, show_depth=False)
         var_class = set()
 
         for seed in mut_iter:
             if seed is self:
                 seed = ClusterSeed(seed)
             if not ignore_bipartite_belt and seed.is_bipartite():
                 bipartition = seed.is_bipartite(return_bipartition=True)
-                bipartition = (list(bipartition[0]),list(bipartition[1]))
+                bipartition = (list(bipartition[0]), list(bipartition[1]))
                 if depth is not infinity:
                     print("Found a bipartite seed - restarting the depth counter at zero and constructing the variable class using its bipartite belt.")
                 depth_counter = 0
                 end = False
                 seed2 = ClusterSeed(seed)
                 for c in seed.cluster():
                     if c not in var_class:
-                        yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable',xdim=seed._n)
+                        yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable', xdim=seed._n)
                 var_class = var_class.union(seed.cluster())
 
                 init_cluster = set(seed.cluster())
                 while not end and depth_counter < depth:
                     depth_counter += 1
                     seed.mutate(bipartition[0])
                     seed.mutate(bipartition[1])
-                    if set(seed.cluster()) in [set(seed2.cluster()),init_cluster]:
+                    if set(seed.cluster()) in [set(seed2.cluster()), init_cluster]:
                         end = True
                     if not end:
                         for c in seed.cluster():
                             if c not in var_class:
-                                yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable',xdim=seed._n)
+                                yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable', xdim=seed._n)
                         var_class = var_class.union(seed.cluster())
                         seed2.mutate(bipartition[1])
                         seed2.mutate(bipartition[0])
-                        if set(seed2.cluster()) in [set(seed.cluster()),init_cluster]:
+                        if set(seed2.cluster()) in [set(seed.cluster()), init_cluster]:
                             end = True
                         if not end:
                             for c in seed2.cluster():
                                 if c not in var_class:
-                                    yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable',xdim=seed._n)
+                                    yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable', xdim=seed._n)
                             var_class = var_class.union(seed2.cluster())
                 return
             else:
                 for c in seed.cluster():
                     if c not in var_class:
-                        yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable',xdim=seed._n)
+                        yield ClusterVariable(FractionField(seed._R), c.numerator(), c.denominator(), mutation_type=self._mutation_type, variable_type='cluster variable', xdim=seed._n)
                 var_class = var_class.union(seed.cluster())
 
     def variable_class(self, depth=infinity, ignore_bipartite_belt=False):
@@ -4120,7 +4120,7 @@ def is_mutation_finite(self, nr_of_checks=None, return_path=False):
             sage: S.is_mutation_finite()
             False
         """
-        is_finite, path = is_mutation_finite(copy(self._M),nr_of_checks=nr_of_checks)
+        is_finite, path = is_mutation_finite(copy(self._M), nr_of_checks=nr_of_checks)
         if return_path:
             return is_finite, path
         else:
@@ -4403,8 +4403,8 @@ def find_upper_bound(self, verbose=False):
         """
         rank = self.n()
 
-        xvars = ['x{}'.format(t) for t in range(rank)]
-        xpvars = ['x{}p'.format(t) for t in range(rank)]
+        xvars = [f'x{t}' for t in range(rank)]
+        xpvars = [f'x{t}p' for t in range(rank)]
         gens = xvars + xpvars
         initial_product = '*'.join(g for g in xvars)
 
@@ -4418,8 +4418,7 @@ def find_upper_bound(self, verbose=False):
                                         for s in range(rank))
             deep_gens += [neighbor_product]
 
-        rels = ["-{}*{}+{}".format(gens[t], gens[t + rank],
-                                   lower_var[t + rank].numerator())
+        rels = [f"-{gens[t]}*{gens[t + rank]}+{lower_var[t + rank].numerator()}"
                 for t in range(rank)]
 
         while True:
@@ -4509,9 +4508,9 @@ def get_upper_cluster_algebra_element(self, a):
         if len(a) != B.ncols():
             raise ValueError('The length of the input vector must be the same as the number of columns of B.')
         # Runs helper functions.
-        v = _vector_decomposition(a,B.nrows())
+        v = _vector_decomposition(a, B.nrows())
         c = self._compute_compatible_vectors(v)
-        return self._produce_upper_cluster_algebra_element(v,c)
+        return self._produce_upper_cluster_algebra_element(v, c)
 
     def LLM_gen_set(self, size_limit=-1):
         r"""
@@ -4793,7 +4792,7 @@ def PathSubset(n, m):
         sage: PathSubset(4,4)
         {0, 1, 2, 3, 4, 5, 6, 7}
     """
-    S = set(2 * i + 1 for i in range(n))
+    S = {2 * i + 1 for i in range(n)}
     if m > 0:
         for j in range(n):
             if ((j+1)*m) // n - (j*m) // n == 1:
@@ -4831,7 +4830,7 @@ def SetToPath(T):
     return ans
 
 
-def is_LeeLiZel_allowable(T,n,m,b,c):
+def is_LeeLiZel_allowable(T, n, m, b, c):
     """
     Check if the subset `T` contributes to the computation of the greedy element `x[m,n]` in the rank two `(b,c)`-cluster algebra.
 

src/sage/combinat/cluster_algebra_quiver/mutation_class.py

@@ -102,9 +102,9 @@ def _digraph_mutate(dg, k, frozen=None):
     edge_it = dg.incoming_edge_iterator(dg, True)
     edges = {(v1, v2): label for v1, v2, label in edge_it}
     edge_it = dg.incoming_edge_iterator([k], True)
-    in_edges = [(v1, v2, label) for v1, v2, label in edge_it]
+    in_edges = list(edge_it)
     edge_it = dg.outgoing_edge_iterator([k], True)
-    out_edges = [(v1, v2, label) for v1, v2, label in edge_it]
+    out_edges = list(edge_it)
 
     in_edges_new = [(v2, v1, (-label[1], -label[0]))
                     for (v1, v2, label) in in_edges]
@@ -151,7 +151,7 @@ def _digraph_mutate(dg, k, frozen=None):
     return dg_new
 
 
-def _matrix_to_digraph( M ):
+def _matrix_to_digraph(M):
     """
     Return the digraph obtained from the matrix ``M``.
 
@@ -166,15 +166,15 @@ def _matrix_to_digraph( M ):
     n = M.ncols()
 
     dg = DiGraph(sparse=True)
-    for i,j in M.nonzero_positions():
+    for i, j in M.nonzero_positions():
         if i >= n:
             a, b = M[i, j], -M[i, j]
         else:
             a, b = M[i, j], M[j, i]
         if a > 0:
-            dg._backend.add_edge(i,j,(a,b),True)
+            dg._backend.add_edge(i, j, (a, b), True)
         elif i >= n:
-            dg._backend.add_edge(j,i,(-a,-b),True)
+            dg._backend.add_edge(j, i, (-a, -b), True)
     for i in range(M.nrows()):
         if i not in dg:
             dg.add_vertex(i)
@@ -310,7 +310,7 @@ def _mutation_class_iter( dg, n, m, depth=infinity, return_dig6=False, show_dept
     depth_counter = 0
     if up_to_equivalence:
         iso, orbits = _dg_canonical_form( dg, mlist )
-        iso_inv = dict( (iso[a],a) for a in iso )
+        iso_inv = { iso[a]: a for a in iso }
 
     dig6 = _digraph_to_dig6( dg, hashable=True )
     dig6s = {}
@@ -328,10 +328,10 @@ def _mutation_class_iter( dg, n, m, depth=infinity, return_dig6=False, show_dept
     if show_depth:
         timer2 = time.time()
         dc = str(depth_counter)
-        dc += ' ' * (5-len(dc))
+        dc += ' ' * (5 - len(dc))
         nr = str(len(dig6s))
-        nr += ' ' * (10-len(nr))
-        print("Depth: %s found: %s Time: %.2f s" % (dc, nr, timer2 - timer))
+        nr += ' ' * (10 - len(nr))
+        print(f"Depth: {dc} found: {nr} Time: {timer2 - timer:.2f} s")
 
     while gets_bigger and depth_counter < depth:
         gets_bigger = False
@@ -346,7 +346,7 @@ def _mutation_class_iter( dg, n, m, depth=infinity, return_dig6=False, show_dept
                     if up_to_equivalence:
                         iso, orbits = _dg_canonical_form( dg_new, mlist )
                         i_new = iso[i]
-                        iso_inv = dict( (iso[a],a) for a in iso )
+                        iso_inv = { iso[a]: a for a in iso }
                     else:
                         i_new = i
                     dig6_new = _digraph_to_dig6( dg_new, hashable=True )
@@ -357,7 +357,7 @@ def _mutation_class_iter( dg, n, m, depth=infinity, return_dig6=False, show_dept
                         gets_bigger = True
                         if up_to_equivalence:
                             orbits = [ orbit[0] for orbit in orbits if i_new not in orbit ]
-                            iso_history = dict( (a, dig6s[key][2][iso_inv[a]]) for a in iso )
+                            iso_history = { a: dig6s[key][2][iso_inv[a]] for a in iso }
                             i_history = iso_history[i_new]
                             history = dig6s[key][1] + [i_history]
                             dig6s[dig6_new] = [orbits,history,iso_history]
@@ -374,13 +374,13 @@ def _mutation_class_iter( dg, n, m, depth=infinity, return_dig6=False, show_dept
         if show_depth and gets_bigger:
             timer2 = time.time()
             dc = str(depth_counter)
-            dc += ' ' * (5-len(dc))
+            dc += ' ' * (5 - len(dc))
             nr = str(len(dig6s))
-            nr += ' ' * (10-len(nr))
-            print("Depth: %s found: %s Time: %.2f s" % (dc, nr, timer2 - timer))
+            nr += ' ' * (10 - len(nr))
+            print(f"Depth: {dc} found: {nr} Time: {timer2 - timer:.2f} s")
 
 
-def _digraph_to_dig6( dg, hashable=False ):
+def _digraph_to_dig6(dg, hashable=False):
     """
     Return the dig6 and edge data of the digraph dg.
 
@@ -487,8 +487,8 @@ def _dg_is_sink_source( dg, v ):
         sage: _dg_is_sink_source(dg, 2)
         False
     """
-    in_edges = [ edge for edge in dg._backend.iterator_in_edges([v],True) ]
-    out_edges = [ edge for edge in dg._backend.iterator_out_edges([v],True) ]
+    in_edges = list(dg._backend.iterator_in_edges([v],True))
+    out_edges = list(dg._backend.iterator_out_edges([v],True))
     return not ( in_edges and out_edges )
 
 
@@ -515,8 +515,8 @@ def _graph_without_edge_labels(dg, vertices):
     """
     vertices = list(vertices)
     edges = dg.edge_iterator(labels=True)
-    edge_labels = tuple(sorted(set(label for _, _, label in edges
-                            if label != (1, -1))))
+    edge_labels = tuple(sorted({label for _, _, label in edges
+                                if label != (1, -1)}))
     edge_partition = [[] for _ in edge_labels]
     i = 0
     while i in vertices:

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -228,8 +228,8 @@ def __init__(self, data, frozen=None, user_labels=None):
             user_labels = [tuple(x) if isinstance(x, list) else x for x in user_labels]
         elif isinstance(user_labels, dict):
             values = [tuple(user_labels[x]) if isinstance(user_labels[x], list) else user_labels[x] for x in user_labels]
-            user_labels = {key: val for key, val in zip(user_labels.keys(),
-                                                        values)}
+            user_labels = dict(zip(user_labels.keys(),
+                                   values))
 
         # constructs a quiver from a mutation type
         if type( data ) in [QuiverMutationType_Irreducible,QuiverMutationType_Reducible]:
@@ -635,10 +635,10 @@ def _graphs_concentric_circles(n, m):
                              'lightgreen': partition[2]}
 
         options = {
-            'graph_border' : True,
+            'graph_border': True,
             'edge_colors': color_dict,
             'vertex_colors': vertex_color_dict,
-            'edge_labels' : True,
+            'edge_labels': True,
             'vertex_labels': True,
         }
         if circular:
@@ -1854,11 +1854,11 @@ def mutation_class(self, depth=infinity, show_depth=False, return_paths=False,
         if depth is infinity and not self.is_mutation_finite():
             raise ValueError('the mutation class can - for infinite mutation'
                              ' types - only be computed up to a given depth')
-        return [Q for Q in self.mutation_class_iter(depth=depth, show_depth=show_depth,
-                                                    return_paths=return_paths,
-                                                    data_type=data_type,
-                                                    up_to_equivalence=up_to_equivalence,
-                                                    sink_source=sink_source)]
+        return list(self.mutation_class_iter(depth=depth, show_depth=show_depth,
+                                             return_paths=return_paths,
+                                             data_type=data_type,
+                                             up_to_equivalence=up_to_equivalence,
+                                             sink_source=sink_source))
 
     def is_finite(self):
         """

src/sage/combinat/cluster_algebra_quiver/quiver_mutation_type.py

@@ -1686,7 +1686,7 @@ def irreducible_components(self):
             sage: mut_type.irreducible_components()
             (['A', 3],)
         """
-        return tuple([self])
+        return (self,)
 
     @cached_method
     def class_size(self):