Examples of manifolds¶
- class sage.categories.examples.manifolds.Plane(n=3, base_ring=None)[source]¶
- Bases: - UniqueRepresentation,- 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 - >>> from sage.all import * >>> from sage.categories.manifolds import Manifolds >>> M = Manifolds(QQ).example(); M An example of a Rational Field manifold: the 3-dimensional plane >>> M.category() Category of manifolds over Rational Field - We conclude by running systematic tests on this manifold: - sage: TestSuite(M).run() - >>> from sage.all import * >>> TestSuite(M).run() - Element[source]¶
- alias of - ElementWrapper
 - an_element()[source]¶
- 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) - >>> from sage.all import * >>> from sage.categories.manifolds import Manifolds >>> M = Manifolds(QQ).example() >>> M.an_element() (0, 0, 0) 
 - dimension()[source]¶
- Return the dimension of - self.- EXAMPLES: - sage: from sage.categories.manifolds import Manifolds sage: M = Manifolds(QQ).example() sage: M.dimension() 3 - >>> from sage.all import * >>> from sage.categories.manifolds import Manifolds >>> M = Manifolds(QQ).example() >>> M.dimension() 3