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SimplicialDecomposability :: isVertexDecomposable

isVertexDecomposable -- determines whether a simplicial complex is vertex-decomposable

Synopsis

Description

Vertex-decomposability is just zero-decomposability when $S$ is pure, see [PB]. When $S$ is non-pure, [BW-2] gives a generalisation: A complex $S$ is vertex decomposable if it is either a simplex or there exists a shedding vertex.

i1 : R = QQ[a..f];
i2 : isVertexDecomposable simplicialComplex {a*b*c*d*e}

o2 = true
i3 : isVertexDecomposable boundary simplicialComplex {a*b*c*d*e}

o3 = true
i4 : isVertexDecomposable simplicialComplex {a*b*c, c*d*e}

o4 = false
i5 : isVertexDecomposable simplicialComplex {a*b*c, c*d, d*e, e*f, d*f}

o5 = true

Whether the complex is vertex-decomposable is cached.

See also

Ways to use isVertexDecomposable :

For the programmer

The object isVertexDecomposable is a method function.