Reviewer changes.

src/sage/categories/modules_with_basis.py

@@ -729,7 +729,7 @@ def echelon_form(self, elements, row_reduced=False, order=None):
 
         def submodule(self, gens, check=True, already_echelonized=False,
                       unitriangular=False, support_order=None, category=None,
-                      parent_class=None, *args, **opts):
+                      submodule_class=None, *args, **opts):
             r"""
             The submodule spanned by a finite set of elements.
 
@@ -746,7 +746,8 @@ def submodule(self, gens, check=True, already_echelonized=False,
             - ``support_order`` -- (optional) either something that can
               be converted into a tuple or a key function
             - ``category`` -- (optional) the category of the submodule
-            - ``parent_class`` -- (optional) the class of the parent to return
+            - ``submodule_class`` -- (optional) the class of the submodule
+              to return
 
             If ``already_echelonized`` is ``False``, then the
             generators are put in reduced echelon form using
@@ -909,12 +910,12 @@ def submodule(self, gens, check=True, already_echelonized=False,
             if not already_echelonized:
                 gens = self.echelon_form(gens, unitriangular, order=support_order)
 
-            if parent_class is None:
-                from sage.modules.with_basis.subquotient import SubmoduleWithBasis as parent_class
-            return parent_class(gens, ambient=self,
-                                support_order=support_order,
-                                unitriangular=unitriangular,
-                                category=category, *args, **opts)
+            if submodule_class is None:
+                from sage.modules.with_basis.subquotient import SubmoduleWithBasis as submodule_class
+            return submodule_class(gens, ambient=self,
+                                   support_order=support_order,
+                                   unitriangular=unitriangular,
+                                   category=category, *args, **opts)
 
         def quotient_module(self, submodule, check=True, already_echelonized=False, category=None):
             r"""

src/sage/combinat/symmetric_group_representations.py

@@ -1464,11 +1464,11 @@ def _acted_upon_(self, scalar, self_on_left=True):
                 -gp1 - gp2 - gp3
                 sage: g = SGA.group().an_element(); g
                 [4, 1, 2, 3]
-                sage: g * v
+                sage: g * v  # indirect doctest
                 gp3
-                sage: x * v
+                sage: x * v  # indirect doctest
                 gp3
-                sage: 2 * v
+                sage: 2 * v  # indirect doctest
                 gp1 + gp2 + gp3
             """
             P = self.parent()

src/sage/modules/with_basis/representation.py

@@ -33,7 +33,10 @@ class Representation_abstract:
     INPUT:
 
     - ``semigroup`` -- a semigroup
-    - ``base_ring`` -- a commutative ring
+    - ``side`` -- (default: ``"left"``) whether this is a
+      ``"left"`` or ``"right"`` representation
+    - ``algebra`` -- (default: ``semigroup.algebra(self.base_ring())``)
+      the semigroup algebra
 
     .. NOTE::
 
@@ -50,7 +53,7 @@ def __init__(self, semigroup, side, algebra=None):
             sage: T = G.trivial_representation()
             sage: TestSuite(T).run()
 
-        Verify that the dynamic mixin classes works::
+        Verify that the dynamic mixin classes work::
 
             sage: SGA = SymmetricGroupAlgebra(QQ, 3)
             sage: S21 = SGA.specht_module([2,1])
@@ -652,7 +655,9 @@ def subrepresentation(self, gens, check=True, already_echelonized=False,
 
         - ``gens`` -- the generators of the submodule
         - ``check`` -- ignored
-        - ``already_echelonized`` --
+        - ``already_echelonized`` -- (default: ``False``) whether
+           the elements of ``gens`` are already in (not necessarily
+           reduced) echelon form
         - ``is_closed`` -- (keyword only; default: ``False``) whether ``gens``
           already spans the subspace closed under the semigroup action
 
@@ -780,8 +785,8 @@ def _composition_series_data(self):
                     S_basis = [self.element_class(self, linear_combination((V._basis[i]._monomial_coefficients, coeff)
                                                                            for i, coeff in b._monomial_coefficients.items()))
                                for b in S._basis]
-                # Lift the basis of W', which is W as a subrepr of ``self ``
-                # This is equivanlent to [b.lift() for b in series[cur+1].basis()]
+                # Lift the basis of W', which is W as a subrepresentation of ``self``
+                # This is equivalent to [b.lift() for b in series[cur+1].basis()]
                 Wp_basis = list(series[cur+1]._basis)
                 Wp = self.subrepresentation(S_basis + Wp_basis, is_closed=True)
                 series.insert(cur+1, Wp)