Trac #32708: sage.tensor.modules: remove dependency on sage.manifolds

In view of Sage modularization, this ticket removes the only import from
`sage.manifolds` in the module `sage.tensor.modules`.
This was an import of `Chart` in `FreeModuleTensor._preparse_display`.
This is avoided by reimplementing `_preparse_display` in
`TensorFieldParal`.

URL: https://trac.sagemath.org/32708
Reported by: egourgoulhon
Ticket author(s): Eric Gourgoulhon
Reviewer(s): Matthias Koeppe

src/sage/manifolds/differentiable/tensorfield_paral.py

@@ -304,6 +304,7 @@
 # *****************************************************************************
 
 from sage.tensor.modules.free_module_tensor import FreeModuleTensor
+from sage.manifolds.chart import Chart
 from sage.manifolds.differentiable.tensorfield import TensorField
 from sage.parallel.decorate import parallel
 from sage.parallel.parallelism import Parallelism
@@ -727,6 +728,37 @@ def _del_derived(self, del_restrictions=True):
         if del_restrictions:
             self._del_restrictions()
 
+    def _preparse_display(self, basis=None, format_spec=None):
+        r"""
+        Helper function, to be used by FreeModuleTensor.display.
+
+        TESTS::
+
+            sage: M = Manifold(2, 'M')
+            sage: X.<x,y> = M.chart()
+            sage: t = M.tensor_field(1, 1)
+            sage: t._preparse_display()
+            (Coordinate frame (M, (∂/∂x,∂/∂y)), None)
+            sage: t._preparse_display(X.frame())
+            (Coordinate frame (M, (∂/∂x,∂/∂y)), None)
+            sage: t._preparse_display(X.frame(), X)
+            (Coordinate frame (M, (∂/∂x,∂/∂y)), Chart (M, (x, y)))
+            sage: t._preparse_display(X)  # passing a chart instead of a frame
+            (Coordinate frame (M, (∂/∂x,∂/∂y)), Chart (M, (x, y)))
+
+        """
+        if basis is None:
+            basis = self._fmodule._def_basis
+        elif isinstance(basis, Chart):
+             # a coordinate chart has been passed instead of a vector frame;
+             # the frame is then assumed to be the coordinate frame
+             # associated to the chart:
+            if format_spec is None:
+                format_spec = basis
+            basis = basis.frame()
+        return (basis, format_spec)
+
+
     def _set_comp_unsafe(self, basis=None):
         r"""
         Return the components of the tensor field in a given vector frame

src/sage/tensor/modules/free_module_tensor.py

@@ -200,10 +200,6 @@ class being:
 from sage.tensor.modules.tensor_with_indices import TensorWithIndices
 from sage.parallel.decorate import parallel
 from sage.parallel.parallelism import Parallelism
-from sage.manifolds.chart import Chart
-
-# TODO: remove the import of Chart after _preparse_display has been redefined
-# in tensor fields
 
 class FreeModuleTensor(ModuleElementWithMutability):
     r"""
@@ -583,13 +579,6 @@ def _preparse_display(self, basis=None, format_spec=None):
         """
         if basis is None:
             basis = self._fmodule._def_basis
-        elif isinstance(basis, Chart):
-             # a coordinate chart has been passed instead of a basis;
-             # the basis is then assumed to be the coordinate frame
-             # associated to the chart:
-            if format_spec is None:
-                format_spec = basis
-            basis = basis.frame()
         return (basis, format_spec)
 
     def display(self, basis=None, format_spec=None):