Examples of manifolds#

sage.categories.examples.manifolds.Example[source]#: alias of Plane

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

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

Python

>>> 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

sage: TestSuite(M).run()

Python

>>> 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

sage: from sage.categories.manifolds import Manifolds
sage: M = Manifolds(QQ).example()
sage: M.an_element()
(0, 0, 0)

Python

>>> 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

sage: from sage.categories.manifolds import Manifolds
sage: M = Manifolds(QQ).example()
sage: M.dimension()
3

Python

>>> from sage.all import *
>>> from sage.categories.manifolds import Manifolds
>>> M = Manifolds(QQ).example()
>>> M.dimension()
3