gh-40255: some care for ruff RET in algebras/
    
This is about simplifying code, following `ruff check --select=RET
src/sage/algebras`

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40255
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert, Frédéric Chapoton

Author: Release Manager

src/sage/algebras/cluster_algebra.py

@@ -1988,8 +1988,7 @@ def F_polynomial(self, g_vector):
                 msg += "you can compute it by mutating from the initial seed along the sequence "
                 msg += str(self._path_dict[g_vector])
                 raise KeyError(msg)
-            else:
-                raise KeyError("the g-vector %s has not been found yet" % str(g_vector))
+            raise KeyError("the g-vector {} has not been found yet".format(g_vector))
 
     def find_g_vector(self, g_vector, depth=infinity):
         r"""

src/sage/algebras/commutative_dga.py

@@ -1286,8 +1286,7 @@ def _element_constructor_(self, x, coerce=True):
 
         if isinstance(x, sage.interfaces.abc.SingularElement):
             # self._singular_().set_ring()
-            x = self.element_class(self, x.sage_poly(self.cover_ring()))
-            return x
+            return self.element_class(self, x.sage_poly(self.cover_ring()))
 
         return self.element_class(self, x)
 

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py

@@ -749,8 +749,7 @@ def one(self):
         """
         if not self.is_unitary():
             raise TypeError("algebra is not unitary")
-        else:
-            return self(self._one)
+        return self(self._one)
 
     def random_element(self, *args, **kwargs):
         """

src/sage/algebras/finite_gca.py

@@ -160,8 +160,7 @@ def __classcall_private__(cls, base, names=None, degrees=None,
         if names is None:
             if degrees is None:
                 raise ValueError("you must specify names or degrees")
-            else:
-                n = len(degrees)
+            n = len(degrees)
             names = tuple(f'x{i}' for i in range(n))
         elif isinstance(names, str):
             names = tuple(names.split(','))
@@ -397,13 +396,13 @@ def _repr_term(self, w) -> str:
             return '1'
         # Non-trivial case:
         terms = []
-        for i in range(len(w)):
-            if w[i] == 0:
+        for i, wi in enumerate(w):
+            if wi == 0:
                 continue
-            elif w[i] == 1:
+            if wi == 1:
                 terms.append(self._names[i])
             else:
-                terms.append(self._names[i] + f'^{w[i]}')
+                terms.append(self._names[i] + f'^{wi}')
         return self._mul_symbol.join(terms)
 
     def _latex_term(self, w) -> str:
@@ -432,13 +431,13 @@ def _latex_term(self, w) -> str:
             return '1'
         # Non-trivial case:
         terms = []
-        for i in range(len(w)):
-            if w[i] == 0:
+        for i, wi in enumerate(w):
+            if wi == 0:
                 continue
-            elif w[i] == 1:
+            if wi == 1:
                 terms.append(self._names[i])
             else:
-                terms.append(self._names[i] + '^{' + str(w[i]) + '}')
+                terms.append(self._names[i] + '^{' + str(wi) + '}')
         latex_mul = self._mul_latex_symbol + ' '  # add whitespace
         return latex_mul.join(terms)
 

src/sage/algebras/free_algebra_element.py

@@ -82,7 +82,7 @@ def __init__(self, A, x):
 
         IndexedFreeModuleElement.__init__(self, A, x)
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return string representation of ``self``.
 
@@ -104,10 +104,9 @@ def _repr_(self):
         M = P.monoid()
         from sage.structure.parent_gens import localvars
         with localvars(M, P.variable_names(), normalize=False):
-            x = repr_lincomb(v, strip_one=True)
-        return x
+            return repr_lincomb(v, strip_one=True)
 
-    def _latex_(self):
+    def _latex_(self) -> str:
         r"""
         Return latex representation of ``self``.
 

src/sage/algebras/fusion_rings/f_matrix.py

@@ -1379,12 +1379,9 @@ def _map_triv_reduce(self, mapper, input_iter, worker_pool=None, chunksize=None,
         else:
             mapped = worker_pool.imap_unordered(executor, input_iter, chunksize=chunksize)
         # Reduce phase
-        results = set()
-        for child_eqns in mapped:
-            if child_eqns is not None:
-                results.update(child_eqns)
-        results = list(results)
-        return results
+        results = {eqn for child_eqns in mapped for eqn in child_eqns
+                   if child_eqns is not None}
+        return list(results)
 
     ########################
     #   Equations set up   #
@@ -1770,8 +1767,7 @@ def _par_graph_gb(self, eqns=None, term_order='degrevlex', largest_comp=45, verb
                 small_comps.append(comp_eqns)
         input_iter = zip_longest(small_comps, [], fillvalue=term_order)
         small_comp_gb = self._map_triv_reduce('compute_gb', input_iter, worker_pool=self.pool, chunksize=1, mp_thresh=50)
-        ret = small_comp_gb + temp_eqns
-        return ret
+        return small_comp_gb + temp_eqns
 
     def _get_component_variety(self, var, eqns):
         r"""
@@ -2324,7 +2320,7 @@ def find_cyclotomic_solution(self, equations=None, algorithm='', verbose=True, o
             []
         """
         if self._poly_ring.ngens() == 0:
-            return
+            return None
         self._reset_solver_state()
         self._var_to_sextuple = {self._poly_ring.gen(i): s for i, s in self._idx_to_sextuple.items()}
 

src/sage/algebras/fusion_rings/fusion_double.py

@@ -328,9 +328,9 @@ def s_matrix(self, unitary=False, base_coercion=True):
             [ 1/3  1/3 -1/3    0    0 -1/3  2/3 -1/3]
         """
         b = self.basis()
-        S = matrix([[self.s_ij(b[x], b[y], unitary=unitary, base_coercion=base_coercion)
-                     for x in self.get_order()] for y in self.get_order()])
-        return S
+        return matrix([[self.s_ij(b[x], b[y], unitary=unitary,
+                                  base_coercion=base_coercion)
+                        for x in self.get_order()] for y in self.get_order()])
 
     @cached_method
     def N_ijk(self, i, j, k):

src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py

@@ -1552,8 +1552,6 @@ def product_on_basis(self, g1, g2):
         g1 = self.monomial(g1)
         g2 = self.monomial(g2)
 
-        result = None
-
         g1_Tietze = g1.Tietze()
         g2_Tietze = g2.Tietze()
 
@@ -1563,9 +1561,8 @@ def product_on_basis(self, g1, g2):
         # The product is calculated from the corresponding product of the braids
         # ----------------------------------------------------------------------
         braid_group = self.braid_group()
-        braid_product = braid_group(g1_Tietze+g2_Tietze)
-        result = self._braid_image(braid_product)
-        return result
+        braid_product = braid_group(g1_Tietze + g2_Tietze)
+        return self._braid_image(braid_product)
 
     ############################################################################
     # --------------------------------------------------------------------------
@@ -2043,8 +2040,7 @@ def _braid_image_from_reduced_powers(self, braid_tietze):
                 return self.one()
             k = braid_tietze[0]*len_braid
             result_vect = self._reduce_gen_power(k)
-            result = self.from_vector(result_vect)
-            return result
+            return self.from_vector(result_vect)
 
         # ----------------------------------------------------------------------
         # Try to use former calculations (from dynamic library) to obtain the
@@ -2094,8 +2090,7 @@ def _braid_image_from_reduced_powers(self, braid_tietze):
                 braid_preimage = tuple(word_result)
             result_vect = self._mult_by_regular_rep(vect, tuple(word_right), RepresentationType.RegularRight, braid_preimage)
 
-        result = self.from_vector(result_vect)
-        return result
+        return self.from_vector(result_vect)
 
     # --------------------------------------------------------------------------
     # _braid_image_from_former_calculations
@@ -2649,7 +2644,6 @@ def _extend_braid_automorphism(self, element, braid_automorphism):
             sage: CHA2.mirror_isomorphism(br)   # indirect doctest
             c^-1
         """
-
         result = self.zero()
         for braid in element.support():
             autom_braid = braid_automorphism(braid)

src/sage/algebras/hecke_algebras/cubic_hecke_base_ring.py

@@ -273,7 +273,7 @@ def construction(self):
             sage: ER = chbr.CubicHeckeExtensionRing('a, b, c')
             sage: ER._test_category()   # indirect doctest
         """
-        return None
+        return
 
     def __reduce__(self):
         r"""

src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py

@@ -708,7 +708,7 @@ def construction(self):
             sage: MS = c1.matrix().parent()
             sage: MS._test_category()   # indirect doctest
         """
-        return None
+        return
 
     def __reduce__(self):
         r"""
@@ -894,8 +894,8 @@ def invert_gen(matr):
             matri += cf2 * matr
             matri += cf3 * matr**2
             d1, d2 = matr.dimensions()
-            matrI = matrix(original_base_ring, d1, d2, lambda i, j: original_base_ring(matri[i, j]))
-            return matrI
+            return matrix(original_base_ring, d1, d2,
+                          lambda i, j: original_base_ring(matri[i, j]))
 
         if n == 2:
             if representation_type.is_split():