gh-36280: fix E228 and E225 in combinat/*/*.py
    
fix pycodestyle warning E228 and E225 in` combinat/*/*.py`

done using autopep8

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36280
Reported by: Frédéric Chapoton
Reviewer(s): Kwankyu Lee

Author: Release Manager

src/sage/combinat/cluster_algebra_quiver/cluster_seed.py

@@ -4508,13 +4508,13 @@ def get_upper_cluster_algebra_element(self,a):
             sage: C.get_upper_cluster_algebra_element([1,1,1])
             x0^4*x1^2*x2^3 + x0^2*x1^3*x2^4
         """
-        B=self.b_matrix()
+        B = self.b_matrix()
         # Checks if the length of the
         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())
-        c=self._compute_compatible_vectors(v)
+        v = _vector_decomposition(a,B.nrows())
+        c = self._compute_compatible_vectors(v)
         return self._produce_upper_cluster_algebra_element(v,c)
 
     def LLM_gen_set(self, size_limit=-1):

src/sage/combinat/cluster_algebra_quiver/mutation_type.py

@@ -311,7 +311,7 @@ def _check_special_BC_cases(dg, n, check_letter_list, check_twist_list,
                 if conn_vert_list:
                     conn_verts = list(set(dg).difference(conn_verts))
             if mut_type._letter == hope_letter and not mut_type._twist and conn_vert.issubset(conn_verts):
-                if len(check_letter)>1:
+                if len(check_letter) > 1:
                     check_twist = 1
                 if check_twist:
                     n -= 1

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -366,7 +366,7 @@ def __init__(self, data, frozen=None, user_labels=None):
             elif n+m == 1:
                 self._description = 'Quiver on 1 vertex'
             else:
-                self._description = 'Quiver on %d vertices' %(n+m)
+                self._description = 'Quiver on %d vertices' % (n+m)
 
         # constructs a quiver from a digraph
         elif isinstance(data, DiGraph):
@@ -1512,7 +1512,7 @@ def mutation_sequence(self, sequence, show_sequence=False, fig_size=1.2 ):
             raise ValueError('The quiver can only be mutated at a vertex or at a sequence of vertices')
         if any(v not in V for v in sequence):
             v = next(v for v in sequence if v not in V)
-            raise ValueError('The quiver can only be mutated at the vertex %s'%v )
+            raise ValueError('The quiver can only be mutated at the vertex %s' % v )
 
         quiver = copy( self )
         quiver_sequence = []

src/sage/combinat/crystals/affine_factorization.py

@@ -250,12 +250,12 @@ def e(self, i):
             k = self.parent().k
             n = self.parent().n
             a = min(b[0])
-            left = [j for j in (self.value[n-i-1]).reduced_word() if j != (a+x)%(k+1)]
-            right = [(j-x)%(k+1) for j in (self.value[n-i]).reduced_word()]
-            m = max([j for j in range(a) if (j+x)%(k+1) not in left])
+            left = [j for j in (self.value[n-i-1]).reduced_word() if j != (a+x) % (k+1)]
+            right = [(j-x) % (k+1) for j in (self.value[n-i]).reduced_word()]
+            m = max([j for j in range(a) if (j+x) % (k+1) not in left])
             right += [m+1]
             right.sort(reverse=True)
-            right = [(j+x)%(k+1) for j in right]
+            right = [(j+x) % (k+1) for j in right]
             t = [self.value[j] for j in range(n-i-1)] + [W.from_reduced_word(left)] + [W.from_reduced_word(right)] + [self.value[j] for j in range(n-i+1,n)]
             return self.parent()(tuple(t))
 
@@ -284,12 +284,12 @@ def f(self, i):
             k = self.parent().k
             n = self.parent().n
             a = max(b[1])
-            right = [j for j in (self.value[n-i]).reduced_word() if j != (a+x)%(k+1)]
-            left = [(j-x)%(k+1) for j in (self.value[n-i-1]).reduced_word()]
-            m = min([j for j in range(a+1,k+2) if (j+x)%(k+1) not in right])
+            right = [j for j in (self.value[n-i]).reduced_word() if j != (a+x) % (k+1)]
+            left = [(j-x) % (k+1) for j in (self.value[n-i-1]).reduced_word()]
+            m = min([j for j in range(a+1,k+2) if (j+x) % (k+1) not in right])
             left += [m-1]
             left.sort(reverse=True)
-            left = [(j+x)%(k+1) for j in left]
+            left = [(j+x) % (k+1) for j in left]
             t = [self.value[j] for j in range(n-i-1)] + [W.from_reduced_word(left)] + [W.from_reduced_word(right)] + [self.value[j] for j in range(n-i+1,n)]
             return self.parent()(tuple(t))
 
@@ -311,13 +311,13 @@ def bracketing(self, i):
             k = self.parent().k
             right = (self.value[n-i]).reduced_word()
             left = (self.value[n-i-1]).reduced_word()
-            right_n = [(j-x)%(k+1) for j in right]
-            left_n = [(j-x)%(k+1) for j in left]
+            right_n = [(j-x) % (k+1) for j in right]
+            left_n = [(j-x) % (k+1) for j in left]
             left_unbracketed = []
             while left_n:
                 m = max(left_n)
                 left_n.remove(m)
-                l = [j for j in right_n if j>m]
+                l = [j for j in right_n if j > m]
                 if l:
                     right_n.remove(min(l))
                 else:
@@ -428,7 +428,7 @@ def affine_factorizations(w, l, weight=None):
        [[1, 1, 1, s1, s2*s1, s3*s2*s1]]
     """
     if weight is None:
-        if l==0:
+        if l == 0:
             if w.is_one():
                 return [[]]
             else:
@@ -438,7 +438,7 @@ def affine_factorizations(w, l, weight=None):
     else:
         if l != len(weight):
             return []
-        if l==0:
+        if l == 0:
             if w.is_one():
                 return [[]]
             else:

src/sage/combinat/crystals/alcove_path.py

@@ -418,13 +418,13 @@ def vertices(self):
         # you to the word, it needs to be refreshed
 
         #initialization
-        lst=[]
+        lst = []
         for i in range(len_lambda_chain):
             associated_reflection = lambda_chain[i].root.associated_reflection()
             if len(associated_reflection) == 1:
                 lst.append( (prod([ s[j] for j in associated_reflection ]), [i]) )
 
-        l=copy(lst)
+        l = copy(lst)
 
         while True:
             lst2 = []
@@ -603,7 +603,7 @@ def phi(self, i):
         highest_weight_crystal = self.parent()._highest_weight_crystal
         positions, gi = self._gi(i)
 
-        m=max(gi)
+        m = max(gi)
 
         if not highest_weight_crystal and i == 0:
             raise NotImplementedError
@@ -629,7 +629,7 @@ def epsilon(self, i):
         temp = self
         temp = temp.e(i)
         while temp is not None:
-            j+=1
+            j += 1
             temp = temp.e(i)
 
         return j
@@ -899,7 +899,7 @@ def e(self, i):
         else:
             M = Integer(m)/2 - Integer(1)/2
 
-        KR_test = finite_cartan_type and i==0 and m_index < len(gi) - 1
+        KR_test = finite_cartan_type and i == 0 and m_index < len(gi) - 1
         KR_test = KR_test and M >= 1
 
         ######################################################################
@@ -909,7 +909,7 @@ def e(self, i):
         # If m_index == 0 then M >=1 guarantees this
         ######################################################################
 
-        if ( (not finite_cartan_type or i!=0) and m_index < len(gi)-1  # alpha_i is a simple root
+        if ( (not finite_cartan_type or i != 0) and m_index < len(gi)-1  # alpha_i is a simple root
             ) or KR_test:
 
             J.remove(positions[m_index])
@@ -1014,7 +1014,7 @@ def f(self, i):
         positions, gi = self._gi(i)
 
         m = max(gi)
-        m_index=gi.index(m)
+        m_index = gi.index(m)
 
         if finite_cartan_type and i == 0:
 
@@ -1037,7 +1037,7 @@ def f(self, i):
         #
         # otherwise if m_index - 1 > 0 then (C2) is enough
 
-        if ( (not finite_cartan_type or i!=0) and M > 0  # alpha_i is a simple root
+        if ( (not finite_cartan_type or i != 0) and M > 0  # alpha_i is a simple root
            ) or KR_test :# KR case
 
             J.append(positions[m_index-1])
@@ -1573,7 +1573,7 @@ def lambda_chain(self):
         if not self._root_lattice.cartan_type().is_finite():
             raise ValueError("Cartan type {0} is not finite".format(self._root_lattice.cartan_type()))
 
-        l=[]
+        l = []
         for i in self._root_lattice.positive_roots():
             for j in range(self._max_height(i)):
                 l.append(self(i,j))
@@ -1654,7 +1654,7 @@ def __init__(self, parent, root, height):
         # roots
 
         if not 0 <= height < max_height:
-            raise ValueError("%d out of allowed range [%d,%d)"%(height, 0, max_height))
+            raise ValueError("%d out of allowed range [%d,%d)" % (height, 0, max_height))
 
         v = [height/max_height]
         v.extend( [ x/max_height for x in root.associated_coroot().to_vector() ] )

src/sage/combinat/crystals/fast_crystals.py

@@ -168,14 +168,14 @@ def __init__(self, ct, shape, format):
 
             self._rootoperators.append([e1,f1,e2,f2])
 
-        if int(2*l1)%2 == 0:
-            l1_str = "%d"%l1
-            l2_str = "%d"%l2
+        if int(2*l1) % 2 == 0:
+            l1_str = "%d" % l1
+            l2_str = "%d" % l2
         else:
-            assert self._cartan_type[0] == 'B' and int(2*l2)%2 == 1
-            l1_str = "%d/2"%int(2*l1)
-            l2_str = "%d/2"%int(2*l2)
-        self.rename("The fast crystal for %s2 with shape [%s,%s]"%(ct[0],l1_str,l2_str))
+            assert self._cartan_type[0] == 'B' and int(2*l2) % 2 == 1
+            l1_str = "%d/2" % int(2*l1)
+            l2_str = "%d/2" % int(2*l2)
+        self.rename("The fast crystal for %s2 with shape [%s,%s]" % (ct[0],l1_str,l2_str))
         self.module_generators = [self(0)]
         # self._digraph = ClassicalCrystal.digraph(self)
         self._digraph = super().digraph()

src/sage/combinat/crystals/fully_commutative_stable_grothendieck.py

@@ -358,7 +358,7 @@ def __classcall_private__(cls, w, factors, excess):
         if isinstance(w.parent(), SymmetricGroup):
             H = HeckeMonoid(w.parent())
             w = H.from_reduced_word(w.reduced_word())
-        if (not w.reduced_word()) and excess!=0:
+        if (not w.reduced_word()) and excess != 0:
             raise ValueError("excess must be 0 for the empty word")
         return super().__classcall__(cls, w, factors, excess)
 
@@ -504,7 +504,7 @@ def __classcall_private__(cls, w, factors, excess, shape=False):
         if shape:
             from sage.combinat.partition import _Partitions
             from sage.combinat.skew_partition import SkewPartition
-            cond1 = isinstance(w, (tuple, list)) and len(w)==2 and w[0] in _Partitions and w[1] in _Partitions
+            cond1 = isinstance(w, (tuple, list)) and len(w) == 2 and w[0] in _Partitions and w[1] in _Partitions
             cond2 = isinstance(w, SkewPartition)
             if cond1 or cond2:
                 sh = SkewPartition([w[0], w[1]])
@@ -520,7 +520,7 @@ def __classcall_private__(cls, w, factors, excess, shape=False):
             if isinstance(w.parent(), SymmetricGroup):
                 H = HeckeMonoid(w.parent())
                 w = H.from_reduced_word(w.reduced_word())
-        if (not w.reduced_word()) and excess!=0:
+        if (not w.reduced_word()) and excess != 0:
             raise ValueError("excess must be 0 for the empty word")
         return super().__classcall__(cls, w, factors, excess)
 
@@ -733,7 +733,7 @@ def bracketing(self, i):
             while left_n:
                 m = max(left_n)
                 left_n.remove(m)
-                l = [j for j in right_n if j>=m]
+                l = [j for j in right_n if j >= m]
                 if l:
                     right_n.remove(min(l))
                 else:
@@ -882,7 +882,7 @@ def _generate_decreasing_hecke_factorizations(w, factors, ex, weight=None, paren
     for word in L:
         F = _list_all_decreasing_runs(word, factors)
         for f in F:
-            t = [[word[j] for j in range(len(word)) if f[j]==i] for i in range(factors, 0, -1)]
+            t = [[word[j] for j in range(len(word)) if f[j] == i] for i in range(factors, 0, -1)]
             if weight is None or weight == wt(t):
                 Factors.append(parent.element_class(parent, t))
     return sorted(Factors, reverse=True)
@@ -1020,7 +1020,7 @@ def _jumps(w):
         sage: _jumps(w)
         [2, 4, 8, 10]
     """
-    return [i+1 for i in range(len(w)-1) if w[i]<=w[i+1]]
+    return [i+1 for i in range(len(w)-1) if w[i] <= w[i+1]]
 
 
 def _is_valid_column_word(w, m=None):

src/sage/combinat/crystals/generalized_young_walls.py

@@ -392,9 +392,9 @@ def number_of_parts(self):
             r = new[i]
             if r == [] or r in new[i+1:]:
                 new.pop(i)
-            elif r[0] == n and len(r)%(n+1) == 0:
+            elif r[0] == n and len(r) % (n+1) == 0:
                 for j in range(n+1):
-                    temp = [k%(n+1) for k in range(j+len(r)/(n+1)-1,j-1,-1)]
+                    temp = [k % (n+1) for k in range(j+len(r)/(n+1)-1,j-1,-1)]
                     if temp not in new:
                         new.insert(i+1, temp)
                 new.pop(i)
@@ -425,7 +425,7 @@ def sum_of_weighted_row_lengths(self):
             15
         """
         n = self.parent().cartan_type().rank() - 1
-        m = lambda i: len([1 for r in self.data if r and r[0] == (i-1)%(n+1)])
+        m = lambda i: len([1 for r in self.data if r and r[0] == (i-1) % (n+1)])
         for r in self.data:
             if r and r[0] == n:
                 raise ValueError('Statistic only valid for generalized Young walls in Y_0')