next | previous | forward | backward | up | top | index | toc | Macaulay2 website
SimplicialComplexes :: boundary(SimplicialComplex)

boundary(SimplicialComplex) -- the boundary simplicial complex of D

Synopsis

Description

The boundary of the standard 3-simplex is the 2-sphere.
i1 : R = ZZ[a..d];
i2 : simplex = simplicialComplex{a*b*c*d}

o2 = | abcd |

o2 : SimplicialComplex
i3 : sphere = boundary simplex

o3 = | bcd acd abd abc |

o3 : SimplicialComplex
i4 : fVector sphere

o4 = HashTable{-1 => 1}
               0 => 4
               1 => 6
               2 => 4

o4 : HashTable
i5 : fVector simplex

o5 = HashTable{-1 => 1}
               0 => 4
               1 => 6
               2 => 4
               3 => 1

o5 : HashTable
Facets may be of different dimensions.
i6 : R = ZZ[a..g];
i7 : D = simplicialComplex{a*b*c,a*d,d*f,g*c,e,f*g}

o7 = | fg cg df e ad abc |

o7 : SimplicialComplex
i8 : E = boundary D

o8 = | g f d bc ac ab |

o8 : SimplicialComplex
i9 : fVector D

o9 = HashTable{-1 => 1}
               0 => 7
               1 => 7
               2 => 1

o9 : HashTable
i10 : fVector E

o10 = HashTable{-1 => 1}
                0 => 6
                1 => 3

o10 : HashTable

See also