Examples of CW complexes¶
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sage.categories.examples.cw_complexes.
Example
¶
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class
sage.categories.examples.cw_complexes.
Surface
(bdy=1, 2, 1, 2)¶ Bases:
sage.structure.unique_representation.UniqueRepresentation
,sage.structure.parent.Parent
An example of a CW complex: a (2-dimensional) surface.
This class illustrates a minimal implementation of a CW complex.
EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example(); X An example of a CW complex: the surface given by the boundary map (1, 2, 1, 2) sage: X.category() Category of finite finite dimensional CW complexes
We conclude by running systematic tests on this manifold:
sage: TestSuite(X).run()
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class
Element
(parent, dim, name)¶ Bases:
sage.structure.element.Element
A cell in a CW complex.
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dimension
()¶ Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: f = X.an_element() sage: f.dimension() 2
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an_element
()¶ Return an element of the CW complex, as per
Sets.ParentMethods.an_element()
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.an_element() 2-cell f
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cells
()¶ Return the cells of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: C = X.cells() sage: sorted((d, C[d]) for d in C.keys()) [(0, (0-cell v,)), (1, (0-cell e1, 0-cell e2)), (2, (2-cell f,))]
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class