I = randomShellableIdeal(R,m,k)
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.
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No claim is made on the distribution of the ideal.
The object randomShellableIdeal is a method function.