Trac #28579: Wedge Product with Scalar Fields

The wedge product of differential forms was not compatible with scalar
fields:

{{{
sage: M = Manifold(2, 'M')
sage: c_cart.<x,y> = M.chart()
sage: a = M.diff_form(1, [x, y], name='a')
sage: f = M.scalar_field(x^2, name='f')
sage: a.wedge(f)
AttributeError                            Traceback (most recent call
last)
<ipython-input-1-039619b3382c> in <module>()
      3 a = M.diff_form(Integer(1), [x, y], name='a')
      4 f = M.scalar_field(x**Integer(2), name='f')
----> 5 a.wedge(f)
...
AttributeError: 'DiffScalarFieldAlgebra_with_category.element_class'
object has no attribute '_ambient_domain'
}}}

In this ticket, this gets fixed.

This ticket is part of the metaticket #28519.

URL: https://trac.sagemath.org/28579
Reported by: gh-DeRhamSource
Ticket author(s): Michael Jung
Reviewer(s): Eric Gourgoulhon

Author: Release Manager

src/sage/manifolds/differentiable/diff_form.py

@@ -505,7 +505,17 @@ def wedge(self, other):
             sage: c1.display(e_xy)
             c = (-x^3 - (x - 1)*y^2) dx/\dy
 
+        Wedging with scalar fields yields the multiplication from right::
+
+            sage: f = M.scalar_field(x, name='f')
+            sage: f.add_expr_by_continuation(c_uv, W)
+            sage: t = a.wedge(f)
+            sage: t.display()
+            x*y dx + x^2 dy
+
         """
+        if other._tensor_rank == 0:
+            return self * other
         from sage.tensor.modules.format_utilities import is_atomic
         if self._domain.is_subset(other._domain):
             if not self._ambient_domain.is_subset(other._ambient_domain):
@@ -1415,7 +1425,16 @@ def wedge(self, other):
             sage: s[1,2,3] == a[1]*b[2,3] + a[2]*b[3,1] + a[3]*b[1,2]
             True
 
+        Wedging with scalar fields yields the multiplication from right::
+
+            sage: f = M.scalar_field(x, name='f')
+            sage: t = a.wedge(f)
+            sage: t.display()
+            2*x dx + (x^2 + x) dy + x*y*z dz
+
         """
+        if other._tensor_rank == 0:
+            return self * other
         if self._domain.is_subset(other._domain):
             if not self._ambient_domain.is_subset(other._ambient_domain):
                 raise ValueError("incompatible ambient domains for exterior " +

src/sage/manifolds/differentiable/scalarfield.py

@@ -631,6 +631,7 @@ def __init__(self, parent, coord_expression=None, chart=None, name=None,
         ScalarField.__init__(self, parent, coord_expression=coord_expression,
                              chart=chart, name=name, latex_name=latex_name)
         self._tensor_type = (0,0)
+        self._tensor_rank = 0
 
     ####### Required methods for an algebra element (beside arithmetic) #######
 
@@ -1053,7 +1054,7 @@ def degree(self):
             0
 
         """
-        return 0
+        return self._tensor_rank
 
     def gradient(self, metric=None):
         r"""