Add more typing

src/sage/manifolds/differentiable/diff_form.py

@@ -44,11 +44,14 @@
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 
+from typing import Optional, TYPE_CHECKING
 from sage.misc.cachefunc import cached_method
 from sage.tensor.modules.free_module_alt_form import FreeModuleAltForm
 from sage.manifolds.differentiable.tensorfield import TensorField
 from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
 
+if TYPE_CHECKING:
+    from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule
 
 class DiffForm(TensorField):
     r"""
@@ -372,14 +375,13 @@ def _del_derived(self):
         self.exterior_derivative.clear_cache()
 
     @cached_method
-    def exterior_derivative(self):
+    def exterior_derivative(self) -> 'DiffForm':
         r"""
         Compute the exterior derivative of ``self``.
 
         OUTPUT:
 
-        - instance of :class:`DiffForm` representing the exterior derivative
-          of the differential form
+        - the exterior derivative of the differential form
 
         EXAMPLES:
 
@@ -573,7 +575,7 @@ def wedge(self, other):
                                           other_r._restrictions[dom])
         return resu
 
-    def degree(self):
+    def degree(self) -> int:
         r"""
         Return the degree of ``self``.
 
@@ -1134,8 +1136,8 @@ class DiffFormParal(FreeModuleAltForm, TensorFieldParal):
         no symmetry;  no antisymmetry
 
     """
-    def __init__(self, vector_field_module, degree, name=None,
-                 latex_name=None):
+    def __init__(self, vector_field_module: 'VectorFieldModule', degree: int, name: Optional[str]=None,
+                 latex_name: Optional[str]=None):
         r"""
         Construct a differential form.
 
@@ -1288,14 +1290,13 @@ def __call__(self, *args):
         return TensorFieldParal.__call__(self, *args)
 
     @cached_method
-    def exterior_derivative(self):
+    def exterior_derivative(self) -> 'DiffFormParal':
         r"""
         Compute the exterior derivative of ``self``.
 
         OUTPUT:
 
-        - a :class:`DiffFormParal` representing the exterior
-          derivative of the differential form
+        - the exterior derivative of the differential form
 
         EXAMPLES:
 

src/sage/manifolds/differentiable/manifold.py

@@ -3707,7 +3707,7 @@ def affine_connection(self, name, latex_name=None):
                                                                AffineConnection
         return AffineConnection(self, name, latex_name)
 
-    def metric(self, name, signature=None, latex_name=None, dest_map=None) -> PseudoRiemannianMetric:
+    def metric(self, name=None, signature=None, latex_name=None, dest_map=None) -> PseudoRiemannianMetric:
         r"""
         Define a pseudo-Riemannian metric on the manifold.
 

src/sage/manifolds/differentiable/tensorfield.py

@@ -52,13 +52,22 @@
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 from __future__ import print_function
+from typing import Optional, Tuple, TYPE_CHECKING, Union
 
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.structure.element import ModuleElement
 from sage.tensor.modules.free_module_tensor import FreeModuleTensor
 from sage.tensor.modules.tensor_with_indices import TensorWithIndices
 
+if TYPE_CHECKING:
+    from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule
+    from sage.manifolds.differentiable.manifold import DifferentiableManifold
+    from sage.manifolds.differentiable.diff_map import DiffMap
+    from sage.tensor.modules.comp import Components
+    from sage.manifolds.differentiable.metric import PseudoRiemannianMetric
+
+TensorType = Tuple[int, int]
 class TensorField(ModuleElement):
     r"""
     Tensor field along a differentiable manifold.
@@ -115,8 +124,7 @@ class TensorField(ModuleElement):
     INPUT:
 
     - ``vector_field_module`` -- module `\mathfrak{X}(U,\Phi)` of vector
-      fields along `U` associated with the map `\Phi: U \rightarrow M` (cf.
-      :class:`~sage.manifolds.differentiable.vectorfield_module.VectorFieldModule`)
+      fields along `U` associated with the map `\Phi: U \rightarrow M`
     - ``tensor_type`` -- pair `(k,l)` with `k` being the contravariant rank
       and `l` the covariant rank
     - ``name`` -- (default: ``None``) name given to the tensor field
@@ -362,8 +370,8 @@ class TensorField(ModuleElement):
         True
 
     """
-    def __init__(self, vector_field_module, tensor_type, name=None,
-                 latex_name=None, sym=None, antisym=None, parent=None):
+    def __init__(self, vector_field_module: 'VectorFieldModule', tensor_type: TensorType, name: Optional[str] = None,
+                 latex_name: Optional[str] = None, sym=None, antisym=None, parent=None):
         r"""
         Construct a tensor field.
 
@@ -411,7 +419,7 @@ def __init__(self, vector_field_module, tensor_type, name=None,
             parent = vector_field_module.tensor_module(*tensor_type)
         ModuleElement.__init__(self, parent)
         self._vmodule = vector_field_module
-        self._tensor_type = tuple(tensor_type)
+        self._tensor_type = tensor_type
         self._tensor_rank = self._tensor_type[0] + self._tensor_type[1]
         self._is_zero = False # a priori, may be changed below or via
                               # method __bool__()
@@ -799,14 +807,13 @@ def domain(self):
         """
         return self._domain
 
-    def base_module(self):
+    def base_module(self) -> 'VectorFieldModule':
         r"""
         Return the vector field module on which ``self`` acts as a tensor.
 
         OUTPUT:
 
-        - instance of
-          :class:`~sage.manifolds.differentiable.vectorfield_module.VectorFieldModule`
+        - the underlying vector field module
 
         EXAMPLES:
 
@@ -826,7 +833,7 @@ def base_module(self):
         """
         return self._vmodule
 
-    def tensor_type(self):
+    def tensor_type(self) -> TensorType:
         r"""
         Return the tensor type of ``self``.
 
@@ -907,7 +914,7 @@ def symmetries(self):
 
     #### End of simple accessors #####
 
-    def set_restriction(self, rst):
+    def set_restriction(self, rst: 'TensorField'):
         r"""
         Define a restriction of ``self`` to some subdomain.
 
@@ -943,8 +950,6 @@ def set_restriction(self, rst):
             True
 
         """
-        if not isinstance(rst, TensorField):
-            raise TypeError("the argument must be a tensor field")
         if not rst._domain.is_subset(self._domain):
             raise ValueError("the domain of the declared restriction is not " +
                              "a subset of the field's domain")
@@ -972,17 +977,15 @@ def set_restriction(self, rst):
                                             latex_name=self._latex_name)
         self._is_zero = False  # a priori
 
-    def restrict(self, subdomain, dest_map=None):
+    def restrict(self, subdomain: 'DifferentiableManifold', dest_map: Optional['DiffMap'] = None):
         r"""
         Return the restriction of ``self`` to some subdomain.
 
         If the restriction has not been defined yet, it is constructed here.
 
         INPUT:
 
-        - ``subdomain`` --
-          :class:`~sage.manifolds.differentiable.manifold.DifferentiableManifold`;
-          open subset `U` of the tensor field domain `S`
+        - ``subdomain`` -- open subset `U` of the tensor field domain `S`
         - ``dest_map`` --
           :class:`~sage.manifolds.differentiable.diff_map.DiffMap`
           (default: ``None``); destination map `\Psi:\ U \rightarrow V`,
@@ -1320,7 +1323,7 @@ def _add_comp_unsafe(self, basis=None):
         rst = self.restrict(basis._domain, dest_map=basis._dest_map)
         return rst._add_comp_unsafe(basis)
 
-    def add_comp(self, basis=None):
+    def add_comp(self, basis=None) -> 'Components':
         r"""
         Return the components of ``self`` in a given vector frame
         for assignment.
@@ -1337,8 +1340,7 @@ def add_comp(self, basis=None):
 
         OUTPUT:
 
-        - components in the given frame, as a
-          :class:`~sage.tensor.modules.comp.Components`; if such
+        - components in the given frame; if such
           components did not exist previously, they are created
 
         EXAMPLES::
@@ -1785,6 +1787,7 @@ def display(self, frame=None, chart=None):
             except AttributeError:
                 # case of a genuine vector frame
                 pass
+
         rst = self.restrict(frame._domain, dest_map=frame._dest_map)
         return rst.display(frame, chart)
 
@@ -3101,7 +3104,7 @@ def trace(self, pos1=0, pos2=1):
             resu._restrictions[rst._domain] = rst
         return resu
 
-    def contract(self, *args):
+    def contract(self, *args) -> 'TensorField':
         r"""
         Contraction of ``self`` with another tensor field on one or
         more indices.

src/sage/manifolds/differentiable/tensorfield_paral.py

@@ -308,6 +308,9 @@
 from sage.parallel.decorate import parallel
 from sage.parallel.parallelism import Parallelism
 from sage.symbolic.ring import SR
+from typing import TYPE_CHECKING
+if TYPE_CHECKING:
+    from sage.tensor.modules.comp import Components
 
 class TensorFieldParal(FreeModuleTensor, TensorField):
     r"""
@@ -1084,7 +1087,7 @@ class :class:`~sage.tensor.modules.comp.Components`; if such
         # The add_comp operation is performed on the subdomain:
         return rst.add_comp(basis=basis)
 
-    def comp(self, basis=None, from_basis=None):
+    def comp(self, basis=None, from_basis=None) -> 'Components':
         r"""
         Return the components in a given vector frame.
 
@@ -1102,8 +1105,7 @@ def comp(self, basis=None, from_basis=None):
 
         OUTPUT:
 
-        - components in the vector frame ``basis``, as an instance of the
-          class :class:`~sage.tensor.modules.comp.Components`
+        - components in the vector frame ``basis``
 
         EXAMPLES::
 

src/sage/manifolds/differentiable/vectorfield_module.py

@@ -39,7 +39,6 @@
 #******************************************************************************
 
 from sage.manifolds.differentiable.diff_map import DiffMap
-from sage.manifolds.differentiable.manifold import DifferentiableManifold
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent
 from sage.categories.modules import Modules
@@ -48,6 +47,9 @@
 from sage.tensor.modules.finite_rank_free_module import FiniteRankFreeModule
 from sage.manifolds.differentiable.vectorfield import (VectorField,
                                                        VectorFieldParal)
+from typing import TYPE_CHECKING
+if TYPE_CHECKING:
+    from sage.manifolds.differentiable.manifold import DifferentiableManifold
 
 class VectorFieldModule(UniqueRepresentation, Parent):
     r"""
@@ -183,7 +185,7 @@ class VectorFieldModule(UniqueRepresentation, Parent):
     """
     Element = VectorField
 
-    def __init__(self, domain: DifferentiableManifold, dest_map: DiffMap=None):
+    def __init__(self, domain: 'DifferentiableManifold', dest_map: DiffMap=None):
         r"""
         Construct the module of vector fields taking values on a (a priori)
         non-parallelizable differentiable manifold.
@@ -382,7 +384,7 @@ def _latex_(self):
         else:
            return self._latex_name
 
-    def domain(self):
+    def domain(self) -> 'DifferentiableManifold':
         r"""
         Return the domain of the vector fields in this module.
 
@@ -391,10 +393,7 @@ def domain(self):
 
         OUTPUT:
 
-        - instance of
-          :class:`~sage.manifolds.differentiable.manifold.DifferentiableManifold`
-          representing the domain of the vector fields that belong to this
-          module
+        - the domain of the vector fields that belong to this module
 
         EXAMPLES::
 
@@ -411,7 +410,7 @@ def domain(self):
         """
         return self._domain
 
-    def ambient_domain(self):
+    def ambient_domain(self) -> 'DifferentiableManifold':
         r"""
         Return the manifold in which the vector fields of this module take
         their values.
@@ -421,9 +420,7 @@ def ambient_domain(self):
 
         OUTPUT:
 
-        - instance of
-          :class:`~sage.manifolds.differentiable.manifold.DifferentiableManifold`
-          representing the manifold in which the vector fields of this
+        - the manifold in which the vector fields of this
           module take their values
 
         EXAMPLES::
@@ -1541,7 +1538,7 @@ def _repr_(self):
                            " mapped into the {}".format(self._ambient_domain)
         return description
 
-    def domain(self) -> DifferentiableManifold:
+    def domain(self) -> 'DifferentiableManifold':
         r"""
         Return the domain of the vector fields in ``self``.
 
@@ -1570,7 +1567,7 @@ def domain(self) -> DifferentiableManifold:
         """
         return self._domain
 
-    def ambient_domain(self) -> DifferentiableManifold:
+    def ambient_domain(self) -> 'DifferentiableManifold':
         r"""
         Return the manifold in which the vector fields of ``self``
         take their values.

src/sage/tensor/modules/free_module_tensor.py

@@ -193,6 +193,7 @@ class being:
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 from __future__ import absolute_import
+from typing import Dict
 
 from sage.rings.integer import Integer
 from sage.structure.element import ModuleElement
@@ -202,6 +203,7 @@ class being:
 from sage.parallel.decorate import parallel
 from sage.parallel.parallelism import Parallelism
 from sage.manifolds.chart import Chart
+from sage.tensor.modules.free_module_basis import FreeModuleBasis
 
 # TODO: remove the import of Chart after _preparse_display has been redefined
 # in tensor fields
@@ -292,7 +294,7 @@ def __init__(self, fmodule, tensor_type, name=None, latex_name=None,
             self._latex_name = self._name
         else:
             self._latex_name = latex_name
-        self._components = {}  # dict. of the sets of components on various
+        self._components:Dict[FreeModuleBasis, Components] = {}  # dict. of the sets of components on various
                               # bases, with the bases as keys (initially empty)
 
         # Treatment of symmetry declarations: