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star(SimplicialComplex,RingElement) -- make the star of a face



Given a subset $F$ of the vertices in an abstract simplicial complex $\Delta$, the star of $F$ is the set of faces $G$ in $\Delta$ such that the union of $G$ and $F$ is also a face in $\Delta$. This set forms a subcomplex of $\Delta$. When the subset $F$ is not face in $\Delta$, the star of $F$ is a void complex (having no facets).

The star of a subset $F$ may be the entire complex, a proper subcomplex, or the void complex.

i1 : S = ZZ[a..e];
i2 : Δ = simplicialComplex {a*b*c, c*d*e}

o2 = simplicialComplex | cde abc |

o2 : SimplicialComplex
i3 : star (Δ, c)

o3 = simplicialComplex | cde abc |

o3 : SimplicialComplex
i4 : assert (star (Δ, c) === Δ)
i5 : star (Δ, a*b)

o5 = simplicialComplex | abc |

o5 : SimplicialComplex
i6 : assert (star (Δ, a*b) === simplicialComplex {a*b*c})
i7 : star (Δ, a*d)

o7 = simplicialComplex 0

o7 : SimplicialComplex
i8 : assert (star (Δ, a*d) === simplicialComplex monomialIdeal 1_S)

See also

Ways to use this method: