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 2 3 5 6 8 1 3 4 6 8 1 3 5 6 8
6 => {}
7 => {}
o6 : HashTable
|
It is assumed that the chains of the network define prime ideals.