#5386: [with patch, needs review] simplicial complexes and their homology
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Reporter: jhpalmieri | Owner: jhpalmieri
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.1
Component: misc | Keywords:
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The attached patch implements simplicial complexes, chain complexes, and
their homology. Some examples:
{{{
sage: S = SimplicialComplex(1, [[0], [1]]) # a two-point space
sage: S2 = S*S*S # its three-fold join with itself; i.e., a
2-sphere
sage: S2
Simplicial complex with 6 vertices and 8 facets
sage: S2.homology() # the reduced homology of S2
{0: 0, 1: 0, 2: Z}
sage: from sage.homology.examples import matching_complex
sage: M = matching_complex(8)
sage: sum(M.f_vector()) # total number of simplices in M
764
sage: M.homology(2)
Z^132
sage: from sage.homology.examples import torus, klein_bottle
sage: torus()
Simplicial complex with vertex set (0, 1, 2, 3, 4, 5, 6) and 14 facets
sage: klein_bottle()
Simplicial complex with 9 vertices and 18 facets
sage: klein_bottle().cohomology()
{0: 0, 1: Z, 2: C2}
sage: torus().product(klein_bottle())
Simplicial complex with 63 vertices and 1512 facets
}}}
The code could be made much faster, I think (for example, by writing some
of it in Cython); if anyone wants to undertake this, that would be great.
Otherwise, it might happen during Sage Days 15.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5386>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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