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RandomIdeals :: randomShellableIdeal

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

Synopsis

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 )
                     0 2   0 3 4   1 2 3 4

o2 : MonomialIdeal of R

Caveat

No claim is made on the distribution of the ideal.

See also

Ways to use randomShellableIdeal :