improve documentation

Author: Xavier Caruso

src/sage/modules/free_module.py

@@ -3156,16 +3156,13 @@ def pseudohom(self, f, twist, codomain=None, side="left"):
             f(\lambda x) = \theta(\lambda) f(x) + \delta(\lambda) x
 
         When `\delta` is nonzero, this requires that `M` coerces into `M'`.
-        .. WARNING::
 
-            At the moment, it is not possible to specify both a twisting
-            endomorphism and a twisting derivation. Only one of those can be
-            used, preferably using the `twist` argument.
+        .. NOTE::
 
-        We represent pseudo morphisms by matrices with coefficient in the base
-        ring `R`. See class
-        :class:`sage.modules.free_module_pseudomorphism.FreeModulePseudoMorphism`
-        for details.
+            Internally, pseudomorphisms are represented by matrices with
+            coefficient in the base ring `R`. See class
+            :class:`sage.modules.free_module_pseudomorphism.FreeModulePseudoMorphism`
+            for details.
 
         INPUT:
 

src/sage/modules/free_module_pseudohomspace.py

@@ -202,7 +202,10 @@ def _repr_(self):
 
     def ore_ring(self, var='x'):
         r"""
-        Return the underlying Ore polynomial ring.
+        Return the underlying Ore polynomial ring, that is
+        the Ore polynomial ring over the base field twisted
+        by the twisting morphism and the twisting derivation
+        attached to this homspace.
 
         INPUT:
 

src/sage/modules/free_module_pseudomorphism.py

@@ -49,21 +49,15 @@ class FreeModulePseudoMorphism(Morphism):
 
         The implementation currently requires that `M` and `M'`
         are free modules.
-    .. WARNING::
-
-        At the moment, it is not possible to specify both a twisting
-        endomorphism and a twisting derivation. Only one of those can be
-        used, preferably using the `twist` argument in the method
-        :meth:`sage.rings.module.free_module.FreeModule_generic.pseudohom`.
-
-    We represent pseudo morphisms by matrices with coefficient in the
-    base ring `R`. The matrix `\mathcal M_f` representing a pseudo
-    morphism is such that its lines (resp. columns if ``side`` is
-    ``"right"``) are the coordinates of the images of the distinguished
-    basis of the domain (see also method :meth:`matrix`). More
-    concretely, let `n` (resp. `n'`) be the dimension of `M` (resp.
-    `M'`), let `(e_1, \dots, e_n)` be a basis of `M`. For any `x =
-    \sum_{i=1}^n x_i e_i \in M`, we have
+
+    We represent pseudomorphisms by matrices with coefficient in the
+    base ring `R`. The matrix `\mathcal M_f` representing `f` is such
+    that its lines (resp. columns if ``side`` is ``"right"``) are the
+    coordinates of the images of the distinguished basis of the domain
+    (see also method :meth:`matrix`).
+    More concretely, let `n` (resp. `n'`) be the dimension of `M`
+    (resp. `M'`), let `(e_1, \dots, e_n)` be a basis of `M`.
+    For any `x = \sum_{i=1}^n x_i e_i \in M`, we have
 
     .. MATH::
 
@@ -77,23 +71,23 @@ class FreeModulePseudoMorphism(Morphism):
                \end{pmatrix}
                .
 
-    If ``side`` is ``"right"``, we have:
+    When ``side`` is ``"right"``, the formula is
 
     .. MATH::
 
         f(x) = \mathcal M_f
                \begin{pmatrix}
                  \theta(x_1) \\ \vdots \\ \theta(x_n)
                \end{pmatrix}
-               
                +
                \begin{pmatrix}
                  \delta(x_1) \\ \vdots \\ \theta(x_n)
                \end{pmatrix}
                .
 
-    This class is not supposed to be instantiated directly; the user should
-    use instead the method :meth:`sage.rings.module.free_module.FreeModule_generic.pseudohom`
+    This class is not supposed to be instantiated directly; the user
+    should use instead the method
+    :meth:`sage.rings.module.free_module.FreeModule_generic.pseudohom`
     to create a pseudomorphism.
 
     TESTS::