next | previous | forward | backward | up | index | toc

# components(ChordalNet,ZZ) -- components of a chordal network

## Synopsis

• Function: components
• Usage:
components(N)
components(N,k)
• Inputs:
• Outputs:
• a list, of components of the network

## Description

Enumerates the (maximal) components of a chordal network. If the optional argument $k$ is given, then only the components in the top $k$ dimensions are computed.

 i1 : I = toLex edgeIdeal cycleGraph 8 o1 = ideal (x x , x x , x x , x x , x x , x x , x x , x x ) 1 2 2 3 3 4 4 5 5 6 6 7 1 8 7 8 o1 : Ideal of QQ[x ..x ] 1 8 i2 : N = chordalNet I; i3 : chordalTria N; i4 : codimCount N 7 6 5 4 o4 = t + 8t + 13t + 2t o4 : ZZ[t] i5 : components(N,1) o5 = HashTable{4 => {ideal (x , x , x , x ), ideal (x , x , x , x )}} 1 3 5 7 2 4 6 8 o5 : HashTable i6 : components(N) o6 = HashTable{4 => {ideal (x , x , x , x ), ideal (x , x , x , x )} } 1 3 5 7 2 4 6 8 5 => {ideal (x , x , x , x , x ), ideal (x , x , x , x , x ), ideal (x , x , x , x , x ), ideal (x , x , x , x , x ), ideal (x , x , x , x , x ), ideal (x , x , x , x , x ), ideal (x , x , x , x , x ), ideal (x , x , x , x , x )} 1 3 4 6 7 1 2 4 6 7 1 2 4 5 7 2 4 5 7 8 2 3 5 7 8 1 3 5 6 8 1 3 4 6 8 2 3 5 6 8 6 => {} 7 => {} o6 : HashTable

## Caveat

It is assumed that the chains of the network define prime ideals.