Coverage for local/lib/python2.7/site-packages/sage/categories/simplicial_complexes.py : 7%

""" 

Simplicial Complexes 

""" 

#***************************************************************************** 

# Copyright (C) 2015 Travis Scrimshaw <tscrim at ucdavis.edu> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

from sage.misc.abstract_method import abstract_method 

from sage.misc.cachefunc import cached_method 

from sage.categories.category_singleton import Category_singleton 

from sage.categories.category_with_axiom import CategoryWithAxiom 

#from sage.categories.cw_complexes import CWComplexes 

from sage.categories.sets_cat import Sets 

class SimplicialComplexes(Category_singleton): 

r""" 

The category of abstract simplicial complexes. 

An abstract simplicial complex `A` is a collection of sets `X` 

such that: 

- `\emptyset \in A`, 

- if `X \subset Y \in A`, then `X \in A`. 

.. TODO:: 

Implement the category of simplicial complexes considered 

as :class:`CW complexes <sage.categories.cw_complexes.CWComplexes>` 

and rename this to the category of ``AbstractSimplicialComplexes`` 

with appropriate functors. 

EXAMPLES:: 

sage: from sage.categories.simplicial_complexes import SimplicialComplexes 

sage: C = SimplicialComplexes(); C 

Category of simplicial complexes 

TESTS:: 

sage: TestSuite(C).run() 

""" 

@cached_method 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.simplicial_complexes import SimplicialComplexes 

sage: SimplicialComplexes().super_categories() 

[Category of sets] 

""" 

return [Sets()] 

class Finite(CategoryWithAxiom): 

""" 

Category of finite simplicial complexes. 

""" 

class ParentMethods: 

@cached_method 

def dimension(self): 

""" 

Return the dimension of ``self``. 

EXAMPLES:: 

sage: S = SimplicialComplex([[1,3,4], [1,2],[2,5],[4,5]]) 

sage: S.dimension() 

2 

""" 

return max(c.dimension() for c in self.facets()) 

class ParentMethods: 

@abstract_method 

def facets(self): 

""" 

Return the facets of ``self``. 

EXAMPLES:: 

sage: S = SimplicialComplex([[1,3,4], [1,2],[2,5],[4,5]]) 

sage: S.facets() 

{(1, 2), (1, 3, 4), (2, 5), (4, 5)} 

""" 

@abstract_method 

def faces(self): 

""" 

Return the faces of ``self``. 

EXAMPLES:: 

sage: S = SimplicialComplex([[1,3,4], [1,2],[2,5],[4,5]]) 

sage: S.faces() 

{-1: {()}, 

0: {(1,), (2,), (3,), (4,), (5,)}, 

1: {(1, 2), (1, 3), (1, 4), (2, 5), (3, 4), (4, 5)}, 

2: {(1, 3, 4)}} 

"""