fix doctests

Author: Xavier Caruso

src/sage/modules/ore_module.py

@@ -1812,6 +1812,10 @@ def __classcall_private__(cls, ambient, gens, saturate, names):
         - ``gens`` -- a list of generators (formatted as coordinates
           vectors) of this submodule
 
+        - ``saturate`` -- a boolean; if ``True``, return the saturation
+          of this submodule in the ambient space (see :meth:`saturate`
+          for more details)
+
         - ``names`` -- the name of the vectors of the basis of
           the submodule, or ``None``
 
@@ -1856,7 +1860,9 @@ def __init__(self, ambient, submodule, names) -> None:
         - ``ambient`` -- a Ore module, the ambient module where
           this submodule sits
 
-        - ``basis`` -- the echelon basis of this submodule
+        - ``submodule`` -- an instance of the class
+          :class:`sage.modules.submodule_helper.SubmoduleHelper`
+          describing this submodule
 
         - ``names`` -- the name of the vectors of the basis of
           the submodule, or ``None``
@@ -2024,6 +2030,15 @@ def saturate(self, names=None, coerce=False):
         of `M` consisting of vectors `x` such that `a x \in N` for a
         nonzero scalar `a` in the base ring.
 
+        INPUT:
+
+        - ``names`` -- a string or a list of strings, the names
+          of the vectors in a basis of the saturation
+
+        - ``coerce`` (default: ``False``) -- a boolean; if
+          ``True``, a coercion map from this Ore module to
+          its saturation is set
+
         EXAMPLES::
 
             sage: A.<t> = GF(3)[]
@@ -2304,6 +2319,9 @@ def __classcall_private__(cls, cover, gens, remove_torsion, names):
         - ``gens`` -- a list of generators (formatted as coordinates
           vectors) of the submodule by which we quotient out
 
+        - ``remove_torsion`` -- a boolean; if ``True``, quotient
+          out in addition by the torsion
+
         - ``names`` -- the name of the vectors of the basis of
           the quotient, or ``None``
 
@@ -2350,8 +2368,9 @@ def __init__(self, cover, submodule, names) -> None:
         - ``cover`` -- a Ore module, the cover module of this
           quotient
 
-        - ``basis`` -- the echelon basis of the submodule
-          defining the quotient
+        - ``submodule`` -- an instance of the class
+          :class:`sage.modules.submodule_helper.SubmoduleHelper`
+          describing this submodule
 
         - ``names`` -- the name of the vectors of the basis of
           the submodule, or ``None``

src/sage/modules/ore_module_morphism.py

@@ -733,7 +733,12 @@ def inverse(self):
 
     def kernel(self, names=None):
         r"""
-        Return ``True`` if this morphism is injective.
+        Return the kernel of this morphism.
+
+        INPUT:
+
+        - ``names`` (default: ``None``) -- the name of the vectors in a
+          basis of the kernel
 
         EXAMPLES::
 
@@ -766,7 +771,16 @@ def kernel(self, names=None):
 
     def image(self, saturate=False, names=None):
         r"""
-        Return ``True`` if this morphism is injective.
+        Return the image of this morphism.
+
+        INPUT:
+
+        - ``saturate`` (default: ``False``) -- a boolean; if ``True``,
+          return the saturation (in the codomain) of the image (see
+          :meth:`saturate` for more details)
+
+        - ``names`` (default: ``None``) -- the name of the vectors in a
+          basis of the image
 
         EXAMPLES::
 
@@ -793,7 +807,16 @@ def image(self, saturate=False, names=None):
 
     def cokernel(self, remove_torsion=False, names=None):
         r"""
-        Return ``True`` if this morphism is injective.
+        Return the cokernel of this morphism.
+
+        INPUT:
+
+        - ``remove_torsion`` (default: ``False``) -- a boolean;
+          if ``True``, return the cokernel quotiented out by its
+          torsion part
+
+        - ``names`` (default: ``None``) -- the name of the vectors in a
+          basis of the cokernel
 
         EXAMPLES::
 
@@ -818,7 +841,12 @@ def cokernel(self, remove_torsion=False, names=None):
 
     def coimage(self, names=None):
         r"""
-        Return ``True`` if this morphism is injective.
+        Return the coimage of this morphism.
+
+        INPUT:
+
+        - ``names`` (default: ``None``) -- the name of the vectors in a
+          basis of the coimage
 
         EXAMPLES::
 

src/sage/modules/submodule_helper.py

@@ -130,8 +130,16 @@ def __eq__(self, other):
             sage: SH2 = SubmoduleHelper(matrix(Fq, [[2, 6]]))
             sage: SH1 == SH2
             True
+
+        ::
+
+            sage: SHZ = SubmoduleHelper(matrix(ZZ, [[1, 3]]))
+            sage: SHZ == SH1
+            False
         """
-        return self.basis == other.basis
+        sb = self.basis
+        ob = other.basis
+        return sb.parent() is ob.parent() and sb == ob
 
 
 class SubmoduleHelper_field(SubmoduleHelper):