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

- Function: components
- Usage:
    `components(N)`
    `components(N,k)`
- Inputs:
  - N, an instance of the type ChordalNet,
  - k, an integer, (optional)
- 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           1   3   4   6   8           2   3   5   6   8           1   3   5   6   8           2   3   5   7   8           2   4   5   7   8
                   6 => {}
                   7 => {}

    o6 : HashTable

## Caveat

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

## See also

- codimCount -- codimension counts of the chains of a chordal network
- nextChain -- iterates over the chains of a chordal network
- isPrimeSimple(ChordalNet) -- simple primality test of a chordal network

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Chordal/ChordalDoc.m2:1325:0.