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# 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

## Description

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

## Ways to use idealFromShelling :

• "idealFromShelling(List)"
• "idealFromShelling(Ring,List)"

## For the programmer

The object idealFromShelling is .