Manifold Structures¶
These classes encode the structure of a manifold.
AUTHORS:
- Travis Scrimshaw (2015-11-25): Initial version
- Eric Gourgoulhon (2015): add
DifferentialStructure
andRealDifferentialStructure
-
class
sage.manifolds.structure.
DifferentialStructure
¶ Bases:
sage.misc.fast_methods.Singleton
The structure of a differentiable manifold over a general topological field.
-
chart
¶ alias of
DiffChart
-
homset
¶ alias of
DifferentiableManifoldHomset
-
scalar_field_algebra
¶ alias of
DiffScalarFieldAlgebra
-
subcategory
(cat)¶ Return the subcategory of
cat
corresponding to the structure ofself
.EXAMPLE:
sage: from sage.manifolds.structure import DifferentialStructure sage: from sage.categories.manifolds import Manifolds sage: DifferentialStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
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-
class
sage.manifolds.structure.
RealDifferentialStructure
¶ Bases:
sage.misc.fast_methods.Singleton
The structure of a differentiable manifold over \(\RR\).
-
chart
¶ alias of
RealDiffChart
-
homset
¶ alias of
DifferentiableManifoldHomset
-
scalar_field_algebra
¶ alias of
DiffScalarFieldAlgebra
-
subcategory
(cat)¶ Return the subcategory of
cat
corresponding to the structure ofself
.EXAMPLE:
sage: from sage.manifolds.structure import DifferentialStructure sage: from sage.categories.manifolds import Manifolds sage: DifferentialStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
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-
class
sage.manifolds.structure.
RealTopologicalStructure
¶ Bases:
sage.misc.fast_methods.Singleton
The structure of a topological manifold over \(\RR\).
-
chart
¶ alias of
RealChart
-
homset
¶ alias of
TopologicalManifoldHomset
-
scalar_field_algebra
¶ alias of
ScalarFieldAlgebra
-
subcategory
(cat)¶ Return the subcategory of
cat
corresponding to the structure ofself
.EXAMPLES:
sage: from sage.manifolds.structure import RealTopologicalStructure sage: from sage.categories.manifolds import Manifolds sage: RealTopologicalStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
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-
class
sage.manifolds.structure.
TopologicalStructure
¶ Bases:
sage.misc.fast_methods.Singleton
The structure of a topological manifold over a general topological field.
-
chart
¶ alias of
Chart
-
homset
¶ alias of
TopologicalManifoldHomset
-
scalar_field_algebra
¶ alias of
ScalarFieldAlgebra
-
subcategory
(cat)¶ Return the subcategory of
cat
corresponding to the structure ofself
.EXAMPLES:
sage: from sage.manifolds.structure import TopologicalStructure sage: from sage.categories.manifolds import Manifolds sage: TopologicalStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-