barycentricSubdivision -- the barycentric subdivision of a simplicial complex.

Usage:

barycentricSubdivision D

barycentricSubdivision F
Inputs:
- D, an abstract simplicial complex,
- F, a list, a list of facets defining a simplicial complex
Outputs:
- an abstract simplicial complex, the barycentric subdivision of a simplicial complex of D

Description

The following example uses the simplicial complex on four vertices composed of two disconnected edges.

i1 : S = QQ[a,b,c,d];

i2 : F = {a*b,c*d};

i3 : D = simplicialComplex F

o3 = simplicialComplex | cd ab |

o3 : SimplicialComplex

i4 : barycentricSubdivision D

o4 = simplicialComplex | v_0v_4v_6 v_0v_3v_6 v_0v_2v_5 v_0v_1v_5 |

o4 : SimplicialComplex

i5 : barycentricSubdivision F

o5 = simplicialComplex | v_0v_4v_6 v_0v_3v_6 v_0v_2v_5 v_0v_1v_5 |

o5 : SimplicialComplex

barycentricSubdivision(List)
barycentricSubdivision(SimplicialComplex)
barycentricSubdivision(SimplicialComplex,Ring) -- create the barycentric subdivision of a simplicial complex
barycentricSubdivision(SimplicialMap,Ring,Ring) -- create the map between barycentric subdivisions corresponding to a simplicial map

The source of this document is in ResolutionsOfStanleyReisnerRings.m2:329:0.