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

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

See also

• idealFromShelling -- Produces an ideal from a shelling
• randomShellableIdealChain -- Produces a chain of ideals from a random shelling