isSheddingFace -- determines whether a face of a simplicial complex is a shedding face

Synopsis

Usage:

isSheddingFace(F, S)
Inputs:
- F, a ring element, a face of $S$
- S, an abstract simplicial complex,
Outputs:
- B, a Boolean value, true if and only if $F$ is a shedding face of $S$

Description

Definition 3.1 in [Wo] states that a face $F$ of a simplicial complex $S$ is a shedding face if every face $G$ of the star of $S$ by $F$ satisfies the exchange property, that is, for every vertex $v$ of $F$ there is a vertex $w$ of the face deletion of $S$ by $G$ such that $(G \cup w) \setminus v$ is a face of $S$.

i1 : R = QQ[a..e];

i2 : T = simplicialComplex {a*b*c, b*c*d, c*d*e};

i3 : isSheddingFace(b*d, T)

o3 = true

i4 : isSheddingFace(b*c*d, T)

o4 = false

Ways to use isSheddingFace :

isSheddingFace(RingElement,SimplicialComplex)

For the programmer

The object isSheddingFace is a method function.

isSheddingFace -- determines whether a face of a simplicial complex is a shedding face

Synopsis

Description

See also

Ways to use isSheddingFace :

For the programmer