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SimplicialComplexes :: link

link -- link of a face in a simplicial complex

Synopsis

Usage:
link(D,f)
Inputs:
- D, a simplicial complex
- f, a ring element, a monomial representing a face of the simplicial complex D
Outputs:
- a simplicial complex, the link of f in D

Description

The link of a face f in D is the simplicial complex whose faces are the subsets g whose intersection with f is empty, where f ∪g is a face of D.

i1 : R = QQ[x0,x1,x2,x3,x4,x5,x6];

i2 : D = simplicialComplex {x0*x1*x3, x1*x3*x4, x1*x2*x4, x2*x4*x5,
                    x2*x3*x5, x3*x5*x6, x3*x4*x6, x0*x4*x6,
                    x0*x4*x5, x0*x1*x5, x1*x5*x6, x1*x2*x6,
                    x0*x2*x6, x0*x2*x3}

o2 = | x3x5x6 x1x5x6 x3x4x6 x0x4x6 x1x2x6 x0x2x6 x2x4x5 x0x4x5 x2x3x5 x0x1x5 x1x3x4 x1x2x4 x0x2x3 x0x1x3 |

o2 : SimplicialComplex

i3 : link(D,x0)

o3 = | x4x6 x2x6 x4x5 x1x5 x2x3 x1x3 |

o3 : SimplicialComplex

i4 : link(D,x0*x2)

o4 = | x6 x3 |

o4 : SimplicialComplex

See also

SimplicialComplexes -- simplicial complexes

Ways to use `link` :

link(SimplicialComplex,RingElement)