From 8d753dcaf07b85d423661f0128bd6d1fff7b71ee Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Mon, 26 Sep 2022 19:59:04 -0700
Subject: [PATCH] src/sage/manifolds/differentiable/vectorfield_module.py
 (VectorFieldModule_abstract): New

---
 .../differentiable/diff_form_module.py        |  8 ++-----
 .../differentiable/tensorfield_module.py      |  8 ++-----
 .../differentiable/vectorfield_module.py      | 23 ++++++++++++++-----
 3 files changed, 21 insertions(+), 18 deletions(-)

diff --git a/src/sage/manifolds/differentiable/diff_form_module.py b/src/sage/manifolds/differentiable/diff_form_module.py
index 4b9a7cae78c..5a337b6c72c 100644
--- a/src/sage/manifolds/differentiable/diff_form_module.py
+++ b/src/sage/manifolds/differentiable/diff_form_module.py
@@ -47,10 +47,10 @@
 from sage.manifolds.differentiable.diff_form import DiffForm, DiffFormParal
 from sage.manifolds.differentiable.tensorfield import TensorField
 from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
-from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule
+from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule_abstract
 
 
-class DiffFormModule(UniqueRepresentation, Parent):
+class DiffFormModule(VectorFieldModule_abstract):
     r"""
     Module of differential forms of a given degree `p` (`p`-forms) along a
     differentiable manifold `U` with values on a differentiable manifold `M`.
@@ -558,10 +558,6 @@ def tensor_type(self):
             return (0, 1)
         raise NotImplementedError
 
-    tensor_power = VectorFieldModule.tensor_power
-
-    tensor = tensor_product = VectorFieldModule.tensor_product
-
     def degree(self):
         r"""
         Return the degree of the differential forms in ``self``.
diff --git a/src/sage/manifolds/differentiable/tensorfield_module.py b/src/sage/manifolds/differentiable/tensorfield_module.py
index d845ae03766..0479792a82e 100644
--- a/src/sage/manifolds/differentiable/tensorfield_module.py
+++ b/src/sage/manifolds/differentiable/tensorfield_module.py
@@ -50,10 +50,10 @@
                                                             MultivectorFieldParal)
 from sage.manifolds.differentiable.automorphismfield import (AutomorphismField,
                                                              AutomorphismFieldParal)
-from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule
+from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule_abstract
 
 
-class TensorFieldModule(UniqueRepresentation, Parent):
+class TensorFieldModule(VectorFieldModule_abstract):
     r"""
     Module of tensor fields of a given type `(k,l)` along a differentiable
     manifold `U` with values on a differentiable manifold `M`, via a
@@ -563,10 +563,6 @@ def tensor_type(self):
         """
         return self._tensor_type
 
-    tensor_power = VectorFieldModule.tensor_power
-
-    tensor = tensor_product = VectorFieldModule.tensor_product
-
     @cached_method
     def zero(self):
         """
diff --git a/src/sage/manifolds/differentiable/vectorfield_module.py b/src/sage/manifolds/differentiable/vectorfield_module.py
index 8c023117eab..1d850014fab 100644
--- a/src/sage/manifolds/differentiable/vectorfield_module.py
+++ b/src/sage/manifolds/differentiable/vectorfield_module.py
@@ -53,14 +53,29 @@
 from sage.rings.integer import Integer
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.tensor.modules.finite_rank_free_module import FiniteRankFreeModule
+from sage.tensor.modules.finite_rank_free_module import (
+    FiniteRankFreeModule_abstract,
+    FiniteRankFreeModule,
+)
 
 if TYPE_CHECKING:
     from sage.manifolds.differentiable.diff_map import DiffMap
     from sage.manifolds.differentiable.manifold import DifferentiableManifold
 
 
-class VectorFieldModule(UniqueRepresentation, Parent):
+class VectorFieldModule_abstract(UniqueRepresentation, Parent):
+    r"""
+    Abstract base class for modules of vector fields.
+    """
+
+    tensor_power = FiniteRankFreeModule_abstract.tensor_power
+
+    tensor_product = FiniteRankFreeModule_abstract.tensor_product
+
+    tensor = FiniteRankFreeModule_abstract.tensor
+
+
+class VectorFieldModule(VectorFieldModule_abstract):
     r"""
     Module of vector fields along a differentiable manifold `U`
     with values on a differentiable manifold `M`, via a differentiable
@@ -848,10 +863,6 @@ def _tensor(self, tensor_type, name=None, latex_name=None, sym=None,
             self, tensor_type, name=name, latex_name=latex_name,
             sym=sym, antisym=antisym)
 
-    tensor_power = FiniteRankFreeModule.tensor_power
-
-    tensor_product = FiniteRankFreeModule.tensor_product
-
     def tensor(self, *args, **kwds):
         r"""
         Construct a tensor field on the domain of ``self`` or a tensor product of ``self`` with other modules.