diff --git a/src/sage/modules/free_module_pseudohomspace.py b/src/sage/modules/free_module_pseudohomspace.py
index fc6705f8f0b..2d1df9c99d8 100644
--- a/src/sage/modules/free_module_pseudohomspace.py
+++ b/src/sage/modules/free_module_pseudohomspace.py
@@ -106,7 +106,8 @@ def __init__(self, domain, codomain, ore):
             sage: Frob = F.frobenius_endomorphism()
             sage: M = F^2
             sage: M.pseudoHom(Frob)
-            Set of Pseudoendomorphisms (twisted by z3 |--> z3^5) of Vector space of dimension 2 over Finite Field in z3 of size 5^3
+            Set of Pseudoendomorphisms (twisted by z3 |--> z3^5) of
+            Vector space of dimension 2 over Finite Field in z3 of size 5^3
         """
         self._domain = domain
         self._codomain = codomain
@@ -168,12 +169,15 @@ def _repr_(self):
             sage: Frob = Fq.frobenius_endomorphism()
             sage: V = Fq^2
             sage: V.pseudoHom(Frob)  # indirect doctest
-            Set of Pseudoendomorphisms (twisted by z3 |--> z3^7) of Vector space of dimension 2 over Finite Field in z3 of size 7^3
+            Set of Pseudoendomorphisms (twisted by z3 |--> z3^7) of
+            Vector space of dimension 2 over Finite Field in z3 of size 7^3
 
         ::
 
             sage: V.pseudoHom(Frob, codomain=Fq^3)  # indirect doctest
-            Set of Pseudomorphism (twisted by z3 |--> z3^7) from Vector space of dimension 2 over Finite Field in z3 of size 7^3 to Vector space of dimension 3 over Finite Field in z3 of size 7^3
+            Set of Pseudomorphism (twisted by z3 |--> z3^7)
+            from Vector space of dimension 2 over Finite Field in z3 of size 7^3
+            to Vector space of dimension 3 over Finite Field in z3 of size 7^3
 
         ::
 
@@ -181,7 +185,8 @@ def _repr_(self):
             sage: d = A.derivation()
             sage: M = A^3
             sage: M.pseudoHom(d)
-            Set of Pseudoendomorphisms (twisted by d/dt) of Ambient free module of rank 3 over the principal ideal domain Univariate Polynomial Ring in t over Rational Field
+            Set of Pseudoendomorphisms (twisted by d/dt) of Ambient free module of rank 3 over
+            the principal ideal domain Univariate Polynomial Ring in t over Rational Field
         """
         twist = self._ore._repr_twist()
         if self.domain() is self.codomain():
@@ -245,15 +250,18 @@ def basis(self, side="left"):
             [1 0]
             [0 0]
             Domain: Vector space of dimension 2 over Finite Field in z3 of size 7^3
-            Codomain: Vector space of dimension 2 over Finite Field in z3 of size 7^3, Free module pseudomorphism (twisted by z3 |--> z3^7) defined by the matrix
+            Codomain: Vector space of dimension 2 over Finite Field in z3 of size 7^3,
+            Free module pseudomorphism (twisted by z3 |--> z3^7) defined by the matrix
             [0 1]
             [0 0]
             Domain: Vector space of dimension 2 over Finite Field in z3 of size 7^3
-            Codomain: Vector space of dimension 2 over Finite Field in z3 of size 7^3, Free module pseudomorphism (twisted by z3 |--> z3^7) defined by the matrix
+            Codomain: Vector space of dimension 2 over Finite Field in z3 of size 7^3,
+            Free module pseudomorphism (twisted by z3 |--> z3^7) defined by the matrix
             [0 0]
             [1 0]
             Domain: Vector space of dimension 2 over Finite Field in z3 of size 7^3
-            Codomain: Vector space of dimension 2 over Finite Field in z3 of size 7^3, Free module pseudomorphism (twisted by z3 |--> z3^7) defined by the matrix
+            Codomain: Vector space of dimension 2 over Finite Field in z3 of size 7^3,
+            Free module pseudomorphism (twisted by z3 |--> z3^7) defined by the matrix
             [0 0]
             [0 1]
             Domain: Vector space of dimension 2 over Finite Field in z3 of size 7^3
diff --git a/src/sage/modules/free_module_pseudomorphism.py b/src/sage/modules/free_module_pseudomorphism.py
index a830f422eb2..72b9f6de3b3 100644
--- a/src/sage/modules/free_module_pseudomorphism.py
+++ b/src/sage/modules/free_module_pseudomorphism.py
@@ -19,7 +19,7 @@
 #  The full text of the GPL is available at:
 #
 #                  http://www.gnu.org/licenses/
-####################################################################################
+# ****************************************************************************
 
 from sage.categories.morphism import Morphism
 from sage.structure.richcmp import rich_to_bool, richcmp
@@ -32,13 +32,13 @@ class FreeModulePseudoMorphism(Morphism):
     ring homomorphism, and `\delta: R \to R` a `\theta`-derivation,
     which is a map such that:
 
-    .. MATH:
+    .. MATH::
 
         \delta(xy) = \theta(x)\delta(y) + \delta(x)y.
 
     A pseudomorphism `f : M \to M` is an additive map such that
 
-    .. MATH:
+    .. MATH::
 
         f(\lambda x) = \theta(\lambda)f(x) + \delta(\lambda) x
 
@@ -258,7 +258,7 @@ def matrix(self):
         Return the underlying matrix of this pseudomorphism.
 
         It is defined as the matrix `M` whose lines (resp. columns if
-        ``side`` is ``right``) are the coordinates of the images of
+        ``side`` is ``"right"``) are the coordinates of the images of
         the distinguished basis of the domain.
 
         EXAMPLES::
@@ -272,6 +272,8 @@ def matrix(self):
             [    0     1   z^2]
             [z + 1     1     1]
 
+        ::
+
             sage: e1, e2, e3 = M.basis()
             sage: f(e1)
             (1, z, 3)