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# randomShellableIdeal -- Produces a ideal from a random shellable simplicial complex

- Usage:
    `I = randomShellableIdeal(R,m,k)`
- Inputs:
  - R, a ring, a polynomial ring
  - m, an integer, dimension of facets in shellable complex
  - k, an integer, the degree of the shellable complex
- Outputs:
  - I, a monomial ideal, the Stanley-Reisner ideal of a random shellable complex

## Description

The Stanley-Reisner ideal of a shellable simplicial complex is always Cohen-Macaulay; the converse is not true, although, to paraphrase Arnol'd, square-free monomial ideals that have a serious reason to be Cohen-Macaulay generally do come from shellable complexes.

The program makes a (Cohen-Macaulay) square-free monomial ideal from the Stanley-Reisner ideal of a random shellable simplicial complex. simplicial complex relies on the code for producing random shellable simplicial complexes; see randomShelling for a description.

    i1 : R = ZZ/101[x_0..x_4];

    i2 : I = randomShellableIdeal(R,2,6)

    o2 = monomialIdeal (x x x , x x x , x x x , x x x )
                         0 1 2   0 2 3   1 2 3   0 3 4

    o2 : MonomialIdeal of R

## Caveat

No claim is made on the distribution of the ideal.

## See also

- randomShelling -- produces a random chain of shellable complexes
- idealFromShelling -- Produces an ideal from a shelling
- idealChainFromShelling -- Produces chains of ideals from a shelling.
- randomShellableIdealChain -- Produces a chain of ideals from a random shelling

## Ways to use randomShellableIdeal:

- `randomShellableIdeal(Ring,ZZ,ZZ)`

## For the programmer

The object randomShellableIdeal is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomIdeals.m2:723:0.