Examples of CW complexes¶
- class sage.categories.examples.cw_complexes.Surface(bdy=(1, 2, 1, 2))[source]¶
- Bases: - UniqueRepresentation,- 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 - >>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example(); X An example of a CW complex: the surface given by the boundary map (1, 2, 1, 2) >>> X.category() Category of finite finite dimensional CW complexes - We conclude by running systematic tests on this manifold: - sage: TestSuite(X).run() - >>> from sage.all import * >>> TestSuite(X).run() - class Element(parent, dim, name)[source]¶
- Bases: - Element- A cell in a CW complex. - dimension()[source]¶
- 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 - >>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> f = X.an_element() >>> f.dimension() 2 
 
 - an_element()[source]¶
- 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 - >>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> X.an_element() 2-cell f 
 - cells()[source]¶
- 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,))] - >>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> C = X.cells() >>> sorted((d, C[d]) for d in C.keys()) [(0, (0-cell v,)), (1, (0-cell e1, 0-cell e2)), (2, (2-cell f,))]