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

Synopsis

Usage:
boundary D
Function: boundary
Inputs:
- D, a simplicial complex
Outputs:
- a simplicial complex, the boundary simplicial complex, i.e. the subcomplex of D consisting of all nonmaximal faces of D

i1 : loadPackage "SimplicialComplexes";

The boundary of the standard 3-simplex is the 2-sphere.

i2 : R = ZZ[a..d];

i3 : simplex = simplicialComplex{a*b*c*d}

o3 = | abcd |

o3 : SimplicialComplex

i4 : sphere = boundary simplex

o4 = | bcd acd abd abc |

o4 : SimplicialComplex

i5 : fVector sphere

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

o5 : HashTable

i6 : fVector simplex

o6 = HashTable{-1 => 1}
               0 => 4
               1 => 6
               2 => 4
               3 => 1

o6 : HashTable

Facets may be of different dimensions.

i7 : R = ZZ[a..g];

i8 : D = simplicialComplex{a*b*c,a*d,d*f,g*c,e,f*g}

o8 = | fg cg df e ad abc |

o8 : SimplicialComplex

i9 : E = boundary D

o9 = | g f d bc ac ab |

o9 : SimplicialComplex

i10 : fVector D

o10 = HashTable{-1 => 1}
                0 => 7
                1 => 7
                2 => 1

o10 : HashTable

i11 : fVector E

o11 = HashTable{-1 => 1}
                0 => 6
                1 => 3

o11 : HashTable