Simplicial Complexes¶
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class
sage.categories.simplicial_complexes.
SimplicialComplexes
(s=None)¶ Bases:
sage.categories.category_singleton.Category_singleton
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
CW complexes
and rename this to the category ofAbstractSimplicialComplexes
with appropriate functors.EXAMPLES:
sage: from sage.categories.simplicial_complexes import SimplicialComplexes sage: C = SimplicialComplexes(); C Category of simplicial complexes
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class
Connected
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom
The category of connected simplicial complexes.
EXAMPLES:
sage: from sage.categories.simplicial_complexes import SimplicialComplexes sage: C = SimplicialComplexes().Connected() sage: TestSuite(C).run()
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class
Finite
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom
Category of finite simplicial complexes.
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class
ParentMethods
¶ Bases:
object
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faces
()¶ 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)}}
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facets
()¶ Return the facets of
self
.EXAMPLES:
sage: S = SimplicialComplex([[1,3,4], [1,2],[2,5],[4,5]]) sage: sorted(S.facets()) [(1, 2), (1, 3, 4), (2, 5), (4, 5)]
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-
class
SubcategoryMethods
¶ Bases:
object
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Connected
()¶ Return the full subcategory of the connected objects of
self
.EXAMPLES:
sage: from sage.categories.simplicial_complexes import SimplicialComplexes sage: SimplicialComplexes().Connected() Category of connected simplicial complexes
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super_categories
()¶ Return the super categories of
self
.EXAMPLES:
sage: from sage.categories.simplicial_complexes import SimplicialComplexes sage: SimplicialComplexes().super_categories() [Category of sets]