Examples of manifolds¶
- sage.categories.examples.manifolds.Example¶
- class sage.categories.examples.manifolds.Plane(n=3, base_ring=None)¶
Bases:
sage.structure.unique_representation.UniqueRepresentation
,sage.structure.parent.Parent
An example of a manifold: the \(n\)-dimensional plane.
This class illustrates a minimal implementation of a manifold.
EXAMPLES:
sage: from sage.categories.manifolds import Manifolds sage: M = Manifolds(QQ).example(); M An example of a Rational Field manifold: the 3-dimensional plane sage: M.category() Category of manifolds over Rational Field
We conclude by running systematic tests on this manifold:
sage: TestSuite(M).run()
- Element¶
- an_element()¶
Return an element of the manifold, as per
Sets.ParentMethods.an_element()
.EXAMPLES:
sage: from sage.categories.manifolds import Manifolds sage: M = Manifolds(QQ).example() sage: M.an_element() (0, 0, 0)
- dimension()¶
Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.manifolds import Manifolds sage: M = Manifolds(QQ).example() sage: M.dimension() 3