# idealChainFromShelling -- Produces chains of ideals from a shelling.

## Synopsis

• Usage:
L = idealChainFromShelling(P)
L = idealChainFromShelling(R,P)
• Inputs:
• R, a ring, Polynomial ring
• P, a list, A (possibly impure) shelled simplicial complex, represented by a list of lists of integers. Each list of integers is a facet of the complex and the order is a shelling. If the ring R is specified, the output is a list of ideals in R; else it is a list of ideals in QQ[x_0..x_{n-1}], where n is the maximum number of elements in one of the lists of integers
• Outputs:
• L, a list, a list of ideals

## Description

Outputs the Stanley-Reisner ideal for each successive simplicial complex formed by truncating the shelling.

 i1 : P = {{1, 2, 4}, {0, 1, 4}, {0, 2, 4}, {0, 3, 4}}; i2 : idealChainFromShelling(P) o2 = {monomialIdeal (x , x ), monomialIdeal (x x , x ), monomialIdeal 0 3 0 2 3 ------------------------------------------------------------------------ (x x x , x ), monomialIdeal (x x x , x x , x x )} 0 1 2 3 0 1 2 1 3 2 3 o2 : List