isDecomposable -- determines whether a simplicial complex is k-decomposable

Synopsis

Usage:

isDecomposable(k, S)
Inputs:
- k, an integer,
- S, an abstract simplicial complex,
Outputs:
- B, a Boolean value, true if and only if $S$ is $k$-decomposable

Description

Definition 3.6 of [Wo] states that a simplicial complex $S$ is $k$-decomposable if $S$ is either a simplex or there exists a shedding face $F$ of $S$ of dimension at most $k$ such that both the face deletion and link of $S$ by $F$ are again $k$-decomposable.

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

i2 : isDecomposable(0, simplicialComplex {a*b*c*d*e*f})

o2 = true

i3 : isDecomposable(2, simplicialComplex {a*b*c, b*c*d, c*d*e})

o3 = true

The method checks the cache, if possible, to see if the complex is vertex-decomposable.

Ways to use isDecomposable :

isDecomposable(ZZ,SimplicialComplex)

For the programmer

The object isDecomposable is a method function.

isDecomposable -- determines whether a simplicial complex is k-decomposable

Synopsis

Description

See also

Ways to use isDecomposable :

For the programmer