From 3b36f0ddd3099d9da6b9eaaec12f2acc8877dcd7 Mon Sep 17 00:00:00 2001
From: Michael Jung <micjung@uni-potsdam.de>
Date: Sat, 25 Apr 2020 00:24:39 +0200
Subject: [PATCH] Trac #29570: alternating_form returns correct element

---
 .../differentiable/vectorfield_module.py      | 45 +++++++++++++++++++
 .../tensor/modules/finite_rank_free_module.py |  4 +-
 2 files changed, 48 insertions(+), 1 deletion(-)

diff --git a/src/sage/manifolds/differentiable/vectorfield_module.py b/src/sage/manifolds/differentiable/vectorfield_module.py
index a507ab01419..b631876de13 100644
--- a/src/sage/manifolds/differentiable/vectorfield_module.py
+++ b/src/sage/manifolds/differentiable/vectorfield_module.py
@@ -1762,6 +1762,51 @@ def exterior_power(self, p):
             self._exterior_powers[p] = MultivectorFreeModule(self, p)
         return self._exterior_powers[p]
 
+    def alternating_form(self, degree, name=None, latex_name=None):
+        r"""
+        Construct an alternating form on the free vector field module
+        ``self``.
+
+        An alternating form on ``self`` is actually a differential form
+        along the differentiable manifold `U` over which ``self`` is
+        defined.
+
+        INPUT:
+
+        - ``degree`` -- the degree of the alternating form
+          (i.e. its tensor rank)
+        - ``name`` -- (string; optional) name given to the alternating
+          form
+        - ``latex_name`` -- (string; optional) LaTeX symbol to denote
+          the alternating form; if none is provided, the LaTeX symbol is
+          set to ``name``
+
+        OUTPUT:
+
+        - instance of
+          :class:`~sage.manifolds.differentiable.diff_form.DiffFormParal`
+
+        EXAMPLES::
+
+            sage: M = Manifold(2, 'M')
+            sage: X.<x,y> = M.chart() # makes M parallelizable
+            sage: XM = M.vector_field_module()
+            sage: XM.alternating_form(2, name='a')
+            2-form a on the 2-dimensional differentiable manifold M
+            sage: XM.alternating_form(1, name='a')
+            1-form a on the 2-dimensional differentiable manifold M
+
+        .. SEEALSO::
+
+            :class:`~sage.manifolds.differentiable.diff_form.DiffFormParal`
+            for more examples and documentation.
+
+        """
+        if degree == 0:
+            return self._domain.scalar_field(name=name, latex_name=latex_name)
+        return self.dual_exterior_power(degree).element_class(self,
+                               degree, name=name, latex_name=latex_name)
+
     def dual_exterior_power(self, p):
         r"""
         Return the `p`-th exterior power of the dual of ``self``.
diff --git a/src/sage/tensor/modules/finite_rank_free_module.py b/src/sage/tensor/modules/finite_rank_free_module.py
index b8d048bd3a4..623454ce7a0 100644
--- a/src/sage/tensor/modules/finite_rank_free_module.py
+++ b/src/sage/tensor/modules/finite_rank_free_module.py
@@ -1084,7 +1084,7 @@ def dual_exterior_power(self, p):
         See
         :class:`~sage.tensor.modules.ext_pow_free_module.ExtPowerDualFreeModule`
         for more documentation.
-
+def dual_exterior_power
         """
         from sage.tensor.modules.ext_pow_free_module import ExtPowerDualFreeModule
         if p == 0:
@@ -1637,6 +1637,8 @@ def alternating_form(self, degree, name=None, latex_name=None):
         for more documentation.
 
         """
+        if degree == 0:
+            return self._ring()
         return self.dual_exterior_power(degree).element_class(self, degree,
                                               name=name, latex_name=latex_name)