Trac #31323: Make self-diffeomorphisms default

Currently, if you construct a diffeomorphism from a manifold to itself,
you have to specify the manifold as the codmain. With the changes in
this ticket, this is no longer necessary and we assume that the user
want's to specify a self-diffeomorphism if no codomain is given.

URL: https://trac.sagemath.org/31323
Reported by: gh-tobiasdiez
Ticket author(s): Tobias Diez
Reviewer(s): Travis Scrimshaw

src/sage/manifolds/differentiable/manifold.py

@@ -952,7 +952,7 @@ def diff_map(self, codomain, coord_functions=None, chart1=None,
             coord_functions = {(chart1, chart2): coord_functions}
         return homset(coord_functions, name=name, latex_name=latex_name)
 
-    def diffeomorphism(self, codomain, coord_functions=None, chart1=None,
+    def diffeomorphism(self, codomain=None, coord_functions=None, chart1=None,
                        chart2=None, name=None, latex_name=None):
         r"""
         Define a diffeomorphism between the current manifold and another one.
@@ -962,8 +962,8 @@ def diffeomorphism(self, codomain, coord_functions=None, chart1=None,
 
         INPUT:
 
-        - ``codomain`` -- codomain of the diffeomorphism (the arrival manifold
-          or some subset of it)
+        - ``codomain`` -- (default: ``None``) codomain of the diffeomorphism (the arrival manifold
+          or some subset of it). If ``None``, the current manifold is taken.
         - ``coord_functions`` -- (default: ``None``) if not ``None``, must be
           either
 
@@ -1030,6 +1030,9 @@ def diffeomorphism(self, codomain, coord_functions=None, chart1=None,
         examples.
 
         """
+        if codomain is None:
+            codomain = self
+
         homset = Hom(self, codomain)
         if coord_functions is None:
             coord_functions = {}