DifferentiableManifold.tangent_space, TangentSpace: Accept keyword 'b…

…ase_ring'

src/sage/manifolds/differentiable/manifold.py

@@ -3403,7 +3403,7 @@ def is_manifestly_parallelizable(self):
         """
         return bool(self._covering_frames)
 
-    def tangent_space(self, point):
+    def tangent_space(self, point, base_ring=None):
         r"""
         Tangent space to ``self`` at a given point.
 
@@ -3412,6 +3412,8 @@ def tangent_space(self, point):
         - ``point`` -- :class:`~sage.manifolds.point.ManifoldPoint`;
           point `p` on the manifold
 
+        - ``base_ring`` -- (default: the symbolic ring) the base ring
+
         OUTPUT:
 
         - :class:`~sage.manifolds.differentiable.tangent_space.TangentSpace`
@@ -3445,7 +3447,7 @@ def tangent_space(self, point):
             raise TypeError("{} is not a manifold point".format(point))
         if point not in self:
             raise ValueError("{} is not a point on the {}".format(point, self))
-        return TangentSpace(point)
+        return TangentSpace(point, base_ring=base_ring)
 
     def curve(self, coord_expression, param, chart=None,
               name=None, latex_name=None):

src/sage/manifolds/differentiable/tangent_space.py

@@ -222,7 +222,7 @@ class TangentSpace(FiniteRankFreeModule):
     """
     Element = TangentVector
 
-    def __init__(self, point):
+    def __init__(self, point, base_ring=None):
         r"""
         Construct the tangent space at a given point.
 
@@ -243,7 +243,9 @@ def __init__(self, point):
         latex_name = r"T_{%s}\,%s"%(point._latex_name, manif._latex_name)
         self._point = point
         self._manif = manif
-        FiniteRankFreeModule.__init__(self, SR, manif._dim, name=name,
+        if base_ring is None:
+            base_ring = SR
+        FiniteRankFreeModule.__init__(self, base_ring, manif._dim, name=name,
                                       latex_name=latex_name,
                                       start_index=manif._sindex)
         # Initialization of bases of the tangent space from existing vector