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

""" 

Catalog of simplicial sets 

This provides pre-built simplicial sets: 

- the `n`-sphere and `n`-dimensional real projective space, both (in 

theory) for any positive integer `n`. In practice, as `n` increases, 

it takes longer to construct these simplicial sets. 

- the `n`-simplex and the horns obtained from it. As `n` increases, it 

takes *much* longer to construct these simplicial sets, because the 

number of nondegenerate simplices increases exponentially in `n`. 

For example, it is feasible to do 

``simplicial_sets.RealProjectiveSpace(100)`` since it only has 101 

nondegenerate simplices, but ``simplicial_sets.Simplex(20)`` is 

probably a bad idea. 

- `n`-dimensional complex projective space for `n \leq 4` 

- the classifying space of a finite multiplicative group or monoid 

- the torus and the Klein bottle 

- the point 

- the Hopf map: this is a pre-built morphism, from which one can 

extract its domain, codomain, mapping cone, etc. 

All of these examples are accessible by typing 

``simplicial_sets.NAME``, where ``NAME`` is the name of the 

example. Type ``simplicial_sets.[TAB]`` for a complete list. 

EXAMPLES:: 

sage: RP10 = simplicial_sets.RealProjectiveSpace(8) 

sage: RP10.homology() 

{0: 0, 1: C2, 2: 0, 3: C2, 4: 0, 5: C2, 6: 0, 7: C2, 8: 0} 

sage: eta = simplicial_sets.HopfMap() 

sage: S3 = eta.domain() 

sage: S2 = eta.codomain() 

sage: S3.wedge(S2).homology() 

{0: 0, 1: 0, 2: Z, 3: Z} 

""" 

from .simplicial_set_examples import (Sphere, ClassifyingSpace, 

RealProjectiveSpace, 

KleinBottle, Torus, 

Simplex, Horn, Point, 

ComplexProjectiveSpace, 

HopfMap)