Add a bit more typing

src/sage/manifolds/differentiable/diff_form.py

@@ -1335,7 +1335,7 @@ def _init_derived(self):
         """
         TensorFieldParal._init_derived(self)
 
-    def _del_derived(self, del_restrictions=True):
+    def _del_derived(self, del_restrictions: bool = True):
         r"""
         Delete the derived quantities.
 

src/sage/manifolds/differentiable/manifold.py

@@ -440,23 +440,30 @@
 # ****************************************************************************
 
 from __future__ import annotations
-from typing import Optional, TYPE_CHECKING
-from sage.categories.manifolds import Manifolds
+
+from typing import TYPE_CHECKING, Optional, Union
+
 from sage.categories.homset import Hom
+from sage.categories.manifolds import Manifolds
+from sage.manifolds.differentiable.mixed_form_algebra import MixedFormAlgebra
+from sage.manifolds.differentiable.vectorframe import VectorFrame
+from sage.manifolds.manifold import TopologicalManifold
 from sage.rings.cc import CC
-from sage.rings.real_mpfr import RR
 from sage.rings.infinity import infinity, minus_infinity
 from sage.rings.integer import Integer
-from sage.manifolds.manifold import TopologicalManifold
-from sage.manifolds.differentiable.mixed_form_algebra import MixedFormAlgebra
+from sage.rings.real_mpfr import RR
 
 if TYPE_CHECKING:
     from sage.manifolds.differentiable.diff_map import DiffMap
     from sage.manifolds.differentiable.metric import PseudoRiemannianMetric
-    from sage.manifolds.differentiable.vectorfield_module import VectorFieldModule
+    from sage.manifolds.differentiable.vectorfield_module import (
+        VectorFieldFreeModule,
+        VectorFieldModule,
+    )
 
 ###############################################################################
 
+
 class DifferentiableManifold(TopologicalManifold):
     r"""
     Differentiable manifold over a topological field `K`.
@@ -1225,7 +1232,9 @@ def tensor_bundle(self, k, l, dest_map=None):
                                                            l, dest_map=dest_map)
         return self._tensor_bundles[dest_map][(k, l)]
 
-    def vector_field_module(self, dest_map: Optional[DiffMap] = None, force_free: bool = False) -> VectorFieldModule:
+    def vector_field_module(
+        self, dest_map: Optional[DiffMap] = None, force_free: bool = False
+    ) -> Union[VectorFieldModule, VectorFieldFreeModule]:
         r"""
         Return the set of vector fields defined on ``self``, possibly
         with values in another differentiable manifold, as a module over the
@@ -3029,7 +3038,7 @@ def set_change_of_frame(self, frame1, frame2, change_of_frame,
                 for sdom in self.open_supersets():
                     sdom._frame_changes[(frame2, frame1)] = change_of_frame.inverse()
 
-    def vector_frame(self, *args, **kwargs):
+    def vector_frame(self, *args, **kwargs) -> VectorFrame:
         r"""
         Define a vector frame on ``self``.
 

src/sage/manifolds/differentiable/tensorfield.py

@@ -51,10 +51,9 @@
 #  the License, or (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
-
 from __future__ import annotations
 
-from typing import TYPE_CHECKING, Optional, Tuple, Union
+from typing import TYPE_CHECKING, Optional, Tuple, TypeVar, Union
 
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
@@ -73,6 +72,9 @@
 
 
 TensorType = Tuple[int, int]
+T = TypeVar("T", bound="TensorField")
+
+
 class TensorField(ModuleElementWithMutability):
     r"""
     Tensor field along a differentiable manifold.
@@ -406,6 +408,12 @@ class TensorField(ModuleElementWithMutability):
 
     """
 
+    _name: Optional[str]
+    _latex_name: Optional[str]
+    _vmodule: VectorFieldModule
+    _domain: DifferentiableManifold
+    _ambient_domain: DifferentiableManifold
+
     def __init__(
         self,
         vector_field_module: VectorFieldModule,
@@ -616,7 +624,7 @@ def _latex_(self):
         else:
             return self._latex_name
 
-    def set_name(self, name=None, latex_name=None):
+    def set_name(self, name: Optional[str] = None, latex_name: Optional[str] = None):
         r"""
         Set (or change) the text name and LaTeX name of ``self``.
 
@@ -684,7 +692,7 @@ def _new_instance(self):
         return type(self)(self._vmodule, self._tensor_type, sym=self._sym,
                           antisym=self._antisym, parent=self.parent())
 
-    def _final_repr(self, description):
+    def _final_repr(self, description: str) -> str:
         r"""
         Part of string representation common to all derived classes of
         :class:`TensorField`.
@@ -1048,8 +1056,8 @@ def set_restriction(self, rst: TensorField):
         self._is_zero = False  # a priori
 
     def restrict(
-        self, subdomain: DifferentiableManifold, dest_map: Optional[DiffMap] = None
-    ) -> TensorField:
+        self: T, subdomain: DifferentiableManifold, dest_map: Optional[DiffMap] = None
+    ) -> T:
         r"""
         Return the restriction of ``self`` to some subdomain.
 

src/sage/manifolds/differentiable/tensorfield_paral.py

@@ -305,18 +305,22 @@
 
 from __future__ import annotations
 
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, Optional, Union
 
 from sage.manifolds.chart import Chart
+from sage.manifolds.differentiable.diff_map import DiffMap
+from sage.manifolds.differentiable.manifold import DifferentiableManifold
 from sage.manifolds.differentiable.tensorfield import TensorField
 from sage.parallel.decorate import parallel
 from sage.parallel.parallelism import Parallelism
+from sage.symbolic.expression import Expression
 from sage.symbolic.ring import SR
 from sage.tensor.modules.free_module_tensor import FreeModuleTensor
 
 if TYPE_CHECKING:
     from sage.tensor.modules.comp import Components
 
+
 class TensorFieldParal(FreeModuleTensor, TensorField):
     r"""
     Tensor field along a differentiable manifold, with values on a
@@ -713,7 +717,7 @@ def _init_derived(self):
         self._extensions_graph = {self._domain: self}
         self._restrictions_graph = {self._domain: self}
 
-    def _del_derived(self, del_restrictions=True):
+    def _del_derived(self, del_restrictions: bool = True):
         r"""
         Delete the derived quantities.
 
@@ -1517,7 +1521,7 @@ def paral_lie_deriv(a, b , coord_frame, chart_cp, local_list_ind):
 
     lie_der = lie_derivative
 
-    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.
 
@@ -1746,7 +1750,7 @@ def __call__(self, *args):
         # Call of the FreeModuleTensor version
         return FreeModuleTensor.__call__(self_r, *args_r)
 
-    def contract(self, *args):
+    def contract(self, *args: Union[int, TensorField]) -> TensorFieldParal:
         r"""
         Contraction with another tensor field, on one or more indices.
 
@@ -2265,7 +2269,7 @@ def along(self, mapping):
                 comp_resu._comp[ind] = val_resu
         return resu
 
-    def series_expansion(self, symbol, order):
+    def series_expansion(self, symbol: Expression, order: int) -> list[TensorFieldParal]:
         r"""
         Expand the tensor field in power series with respect to a small
         parameter.
@@ -2410,7 +2414,7 @@ def truncate(self, symbol, order):
         series = self.series_expansion(symbol, order)
         return sum(symbol**i * s for i, s in enumerate(series))
 
-    def set_calc_order(self, symbol, order, truncate=False):
+    def set_calc_order(self, symbol: Expression, order: int, truncate: bool = False):
         r"""
         Trigger a power series expansion with respect to a small parameter in
         computations involving the tensor field.

src/sage/manifolds/differentiable/vectorframe.py

@@ -462,7 +462,8 @@ def set_name(self, symbol, latex_symbol=None, indices=None,
             self._latex_name = r"\left({}, {}\right)".format(
                                     self._domain._latex_name, self._latex_name)
 
-#******************************************************************************
+# ******************************************************************************
+
 
 class VectorFrame(FreeModuleBasis):
     r"""

src/sage/manifolds/manifold.py

@@ -333,6 +333,10 @@
 from sage.categories.fields import Fields
 from sage.categories.homset import Hom
 from sage.categories.manifolds import Manifolds
+from sage.manifolds.chart import Chart
+from sage.manifolds.differentiable.chart import RealDiffChart
+from sage.manifolds.differentiable.scalarfield import DiffScalarField
+from sage.manifolds.scalarfield import ScalarField
 from sage.manifolds.structure import (
     DifferentialStructure,
     RealDifferentialStructure,
@@ -1206,7 +1210,7 @@ def index_generator(self, nb_indices):
                         ind[pos] = si
                         ret = 1
 
-    def atlas(self):
+    def atlas(self) -> list[Chart]:
         r"""
         Return the list of charts that have been defined on the manifold.
 
@@ -1458,8 +1462,13 @@ def is_manifestly_coordinate_domain(self):
         """
         return bool(self._covering_charts)
 
-    def chart(self, coordinates='', names=None, calc_method=None,
-              coord_restrictions=None):
+    def chart(
+        self,
+        coordinates: str = "",
+        names=None,
+        calc_method=None,
+        coord_restrictions=None,
+    ) -> Chart:
         r"""
         Define a chart, the domain of which is the manifold.
 
@@ -1939,8 +1948,9 @@ def scalar_field_algebra(self):
         """
         return self._scalar_field_algebra
 
-    def scalar_field(self, coord_expression=None, chart=None, name=None,
-                     latex_name=None):
+    def scalar_field(
+        self, coord_expression=None, chart=None, name=None, latex_name=None
+    ) -> ScalarField:
         r"""
         Define a scalar field on the manifold.
 

src/sage/manifolds/subset.py

@@ -151,7 +151,9 @@ class :class:`~sage.structure.parent.Parent`.
 
     Element = ManifoldPoint
 
-    def __init__(self, manifold, name, latex_name=None, category=None):
+    _name: str
+
+    def __init__(self, manifold, name: str, latex_name=None, category=None):
         r"""
         Construct a manifold subset.
 

src/sage/symbolic/function_factory.py

@@ -9,6 +9,8 @@
 #  version 2 or any later version.  The full text of the GPL is available at:
 #                  https://www.gnu.org/licenses/
 ###############################################################################
+from __future__ import annotations
+from typing import Union
 
 from sage.symbolic.function import (SymbolicFunction, sfunctions_funcs,
                                     unpickle_wrapper)
@@ -148,7 +150,7 @@ def unpickle_function(name, nargs, latex_name, conversions, evalf_params_first,
     return function_factory(*args)
 
 
-def function(s, **kwds):
+def function(s, **kwds) -> Union[SymbolicFunction, list[SymbolicFunction]]:
     r"""
     Create a formal symbolic function with the name *s*.
 

src/sage/tensor/modules/finite_rank_free_module.py

@@ -529,16 +529,20 @@ class :class:`~sage.modules.free_module.FreeModule_generic`
 #  the License, or (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 #******************************************************************************
+from __future__ import absolute_import
 
-from sage.misc.cachefunc import cached_method
-from sage.structure.unique_representation import UniqueRepresentation
-from sage.structure.parent import Parent
+from typing import Generator, Optional
+
+from sage.categories.fields import Fields
 from sage.categories.modules import Modules
 from sage.categories.rings import Rings
-from sage.categories.fields import Fields
+from sage.misc.cachefunc import cached_method
 from sage.rings.integer import Integer
+from sage.structure.parent import Parent
+from sage.structure.unique_representation import UniqueRepresentation
 from sage.tensor.modules.free_module_element import FiniteRankFreeModuleElement
 
+
 class FiniteRankFreeModule(UniqueRepresentation, Parent):
     r"""
     Free module of finite rank over a commutative ring.
@@ -749,6 +753,7 @@ class :class:`~sage.modules.module.Module`.
     """
 
     Element = FiniteRankFreeModuleElement
+    _sindex: int
 
     @staticmethod
     def __classcall_private__(cls, ring, rank, name=None, latex_name=None, start_index=0,
@@ -777,8 +782,16 @@ def __classcall_private__(cls, ring, rank, name=None, latex_name=None, start_ind
         return super(FiniteRankFreeModule, cls).__classcall__(
             cls, ring, rank, name, latex_name, start_index, output_formatter, category)
 
-    def __init__(self, ring, rank, name=None, latex_name=None, start_index=0,
-                 output_formatter=None, category=None):
+    def __init__(
+        self,
+        ring,
+        rank,
+        name=None,
+        latex_name=None,
+        start_index: int = 0,
+        output_formatter=None,
+        category=None,
+    ):
         r"""
         See :class:`FiniteRankFreeModule` for documentation and examples.
 
@@ -1963,7 +1976,7 @@ def _latex_(self):
         else:
             return self._latex_name
 
-    def rank(self):
+    def rank(self) -> int:
         r"""
         Return the rank of the free module ``self``.
 
@@ -2083,7 +2096,7 @@ def dual(self):
         """
         return self.dual_exterior_power(1)
 
-    def irange(self, start=None):
+    def irange(self, start: Optional[int] = None) -> Generator[int, None, None]:
         r"""
         Single index generator, labelling the elements of a basis of ``self``.
 

src/sage/tensor/modules/format_utilities.py

@@ -21,8 +21,10 @@
 #                  http://www.gnu.org/licenses/
 #******************************************************************************
 
+from sage.misc.latex import LatexExpr
 from sage.structure.sage_object import SageObject
 
+
 def is_atomic(expr, sep=['+', '-']):
     r"""
     Helper function to check whether some LaTeX expression is atomic.
@@ -295,7 +297,7 @@ class FormattedExpansion(SageObject):
         \frac{x}{2}
 
     """
-    def  __init__(self, txt=None, latex=None):
+    def __init__(self, txt=None, latex=None):
         r"""
         TESTS::
 
@@ -322,7 +324,7 @@ def _repr_(self):
         """
         return self._txt
 
-    def _latex_(self):
+    def _latex_(self) -> LatexExpr:
         r"""
         Return a LaTeX representation of ``self``.