idealFromShelling -- Produces an ideal from a shelling

Synopsis

Usage:

I = idealFromShelling(P)

I = idealFromShelling(S,P)
Inputs:
- S, a ring, (If omitted, it will use S=QQ[x_0..x_{n-1}] where n is the maximum integer in the lists of P.
- P, a list, A list of lists of integers. Each list of integers is a facet of the complex and the order is a shelling.
- S, a ring, (If omitted, it will use S=QQ[x_0..x_{n-1}] where n is the maximum integer in the lists of P.
Outputs:
- I, an ideal, generated by the monomials representing the minimal nonfaces of P

This gives the Stanley-Reisner ideal for the simplicial complex, that is the ideal generated by the monomials representing the minimal nonfaces of P.

i1 : S = QQ[x_0,x_1,x_2,x_3,x_4]

o1 = S

o1 : PolynomialRing

i2 : P =  {{1, 2, 4}, {0, 1, 4}, {0, 2, 4}, {0, 3, 4}};

i3 : idealFromShelling(S,P)

o3 = monomialIdeal (x x x , x x , x x )
                     0 1 2   1 3   2 3

o3 : MonomialIdeal of S