add details in documentation

Author: Xavier Caruso

src/sage/modules/free_module.py

@@ -3163,6 +3163,8 @@ def pseudohom(self, f, twist, codomain=None, side="left"):
           pseudomorphism
 
         - ``twist`` -- the twisting morphism or the twisting derivation
+          (if a derivation is given, the corresponding morphism `\theta`
+          is automatically infered)
 
         - ``codomain`` -- (default: ``None``) the codomain of the pseudo
           morphisms; if ``None``, the codomain is the same than the domain

src/sage/modules/free_module_pseudohomspace.py

@@ -37,6 +37,10 @@ class FreeModulePseudoHomspace(UniqueRepresentation, HomsetWithBase):
     For free modules, the elements of a pseudomorphism correspond to matrices
     which define the mapping on elements of a basis.
 
+    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 space of pseudomorphisms.
+
     TESTS::
 
         sage: F = GF(125)
@@ -57,11 +61,12 @@ def __classcall_private__(cls, domain, codomain, twist):
 
         INPUT:
 
-        -  ``domain`` -- a free module,  the domain of this pseudomorphism
+        - ``domain`` -- a free module,  the domain of this pseudomorphism
 
-        -  ``codomain`` -- a free module, the codomain of this pseudomorphism
+        - ``codomain`` -- a free module, the codomain of this pseudomorphism
 
-        -  ``twist`` -- a twisting morphism/derivation or a Ore polynomial ring
+        - ``twist`` -- a twisting morphism/derivation or the corresponding
+          Ore polynomial ring
 
         TESTS::
 
@@ -94,11 +99,12 @@ def __init__(self, domain, codomain, ore):
 
         INPUT:
 
-        -  ``domain`` -- a free module,  the domain of this pseudomorphism
+        - ``domain`` -- a free module,  the domain of this pseudomorphism
 
-        -  ``codomain`` -- a free module, the codomain of this pseudomorphism
+        - ``codomain`` -- a free module, the codomain of this pseudomorphism
 
-        -  ``ore`` -- the underlying Ore polynomial ring
+        - ``ore`` -- the underlying Ore polynomial ring (built from the
+          twisting morphism and derivation)
 
         TESTS::
 

src/sage/modules/free_module_pseudomorphism.py

@@ -45,6 +45,15 @@ class FreeModulePseudoMorphism(Morphism):
     The map `\theta` (resp. `\delta`) is referred to as the
     twisting endomorphism (resp. the twisting derivation) of `f`.
 
+    .. NOTE::
+
+        The implementation currently requires that `M` and `M'`
+        are free modules.
+
+    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::
 
         sage: P.<x> = ZZ[]