Coverage for local/lib/python2.7/site-packages/sage/homology/simplicial_complexes_catalog.py : 100%

# -*- coding: utf-8 -*- 

""" 

Catalog of simplicial complexes 

There are two main types: manifolds and examples related to graph 

theory. 

For manifolds, there are functions defining the `n`-sphere for any 

`n`, the torus, `n`-dimensional real projective space for any `n`, the 

complex projective plane, surfaces of arbitrary genus, and some other 

manifolds, all as simplicial complexes. 

Aside from surfaces, this file also provides functions for 

constructing some other simplicial complexes: the simplicial complex 

of not-`i`-connected graphs on `n` vertices, the matching complex on n 

vertices, the chessboard complex for an `n` by `i` chessboard, and 

others. These provide examples of large simplicial complexes; for 

example, ``simplicial_complexes.NotIConnectedGraphs(7,2)`` has over a 

million simplices. 

All of these examples are accessible by typing 

``simplicial_complexes.NAME``, where ``NAME`` is the name of the example. 

- :meth:`~sage.homology.examples.BarnetteSphere` 

- :meth:`~sage.homology.examples.BrucknerGrunbaumSphere` 

- :meth:`~sage.homology.examples.ChessboardComplex` 

- :meth:`~sage.homology.examples.ComplexProjectivePlane` 

- :meth:`~sage.homology.examples.DunceHat` 

- :meth:`~sage.homology.examples.K3Surface` 

- :meth:`~sage.homology.examples.KleinBottle` 

- :meth:`~sage.homology.examples.MatchingComplex` 

- :meth:`~sage.homology.examples.MooreSpace` 

- :meth:`~sage.homology.examples.NotIConnectedGraphs` 

- :meth:`~sage.homology.examples.PoincareHomologyThreeSphere` 

- :meth:`~sage.homology.examples.PseudoQuaternionicProjectivePlane` 

- :meth:`~sage.homology.examples.RandomComplex` 

- :meth:`~sage.homology.examples.RandomTwoSphere` 

- :meth:`~sage.homology.examples.RealProjectivePlane` 

- :meth:`~sage.homology.examples.RealProjectiveSpace` 

- :meth:`~sage.homology.examples.RudinBall` 

- :meth:`~sage.homology.examples.ShiftedComplex` 

- :meth:`~sage.homology.examples.Simplex` 

- :meth:`~sage.homology.examples.Sphere` 

- :meth:`~sage.homology.examples.SumComplex` 

- :meth:`~sage.homology.examples.SurfaceOfGenus` 

- :meth:`~sage.homology.examples.Torus` 

- :meth:`~sage.homology.examples.ZieglerBall` 

You can also get a list by typing ``simplicial_complexes.`` and hitting the 

TAB key. 

EXAMPLES:: 

sage: S = simplicial_complexes.Sphere(2) # the 2-sphere 

sage: S.homology() 

{0: 0, 1: 0, 2: Z} 

sage: simplicial_complexes.SurfaceOfGenus(3) 

Triangulation of an orientable surface of genus 3 

sage: M4 = simplicial_complexes.MooreSpace(4) 

sage: M4.homology() 

{0: 0, 1: C4, 2: 0} 

sage: simplicial_complexes.MatchingComplex(6).homology() 

{0: 0, 1: Z^16, 2: 0} 

""" 

from sage.homology.examples import (Sphere, Simplex, Torus, ProjectivePlane, 

RealProjectivePlane, KleinBottle, SurfaceOfGenus, MooreSpace, 

ComplexProjectivePlane, PseudoQuaternionicProjectivePlane, 

PoincareHomologyThreeSphere, RealProjectiveSpace, K3Surface, 

BarnetteSphere, BrucknerGrunbaumSphere, NotIConnectedGraphs, 

MatchingComplex, ChessboardComplex, RandomComplex, SumComplex, 

RandomTwoSphere, ShiftedComplex, RudinBall, ZieglerBall, DunceHat)