Macaulay2 » Documentation
Packages » RandomIdeals :: isShelling
next | previous | forward | backward | up | index | toc

# isShelling -- determines whether a list represents a shelling of a simplicial complex.

- Usage:
    `b = isShelling(P)`
- Inputs:
  - P, a list, A list of lists of integers. Each list of integers is a facet of the complex and the order is a possible shelling.
- Outputs:
  - b, a Boolean value, true if and only if P is a shelling.

## Description

An ordering $F_1,..F_d$ of the facets of a simplicial complex $P$ is shellable if $(F_1 \cup .. \cup F_{k-1}) \cap F_k$ is pure of dim$F_k -1$ for all $k = 2,..,d$. Determines if a list of faces is a shelling order of the simplicial complex.

    i1 : P = {{1, 2, 3}, {1, 2, 5}};

    i2 : isShelling(P)

    o2 = true

    i3 : Q = {{1,2,3},{3,4,5},{2,3,4}};

    i4 : isShelling(Q)

    o4 = false

## Ways to use isShelling:

- `isShelling(List)`

## For the programmer

The object isShelling is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomIdeals.m2:557:0.