Examples of manifolds¶
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sage.categories.examples.manifolds.Example¶
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class
sage.categories.examples.manifolds.Plane(n=3, base_ring=None)¶ Bases:
sage.structure.unique_representation.UniqueRepresentation,sage.structure.parent.ParentAn 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()
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Element¶
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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)
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dimension()¶ Return the dimension of
self.EXAMPLES:
sage: from sage.categories.manifolds import Manifolds sage: M = Manifolds(QQ).example() sage: M.dimension() 3
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