nextChain -- iterates over the chains of a chordal network

Synopsis

Usage:

C = nextChain(N)

C' = nextChain(C,N)

(C,data) = nextChain(cdim,N)

C' = nextChain(C,data,cdim,N)
Inputs:
- N, an instance of the type ChordalNet,
- C, an instance of the type ChordalNetChain, an initial chain (optional)
- cdim, an integer, codimension of the chain (optional)
- data, a sequence, cached data from previous computations (if codimension is specified)
Outputs:
- C', an instance of the type ChordalNetChain, the next chain of the chordal network, if any
- data, a sequence, cached data for future computations (if codimension is specified)

This method produces the chains of a chordal network one at a time. It can also iterate only over chains of a specified codimension.

Returns "null" if none.

i1 : I = toLex edgeIdeal cycleGraph 9;

o1 : Ideal of QQ[x ..x ]
                  1   9

i2 : N = chordalNet I;

i3 : chordalTria N;

i4 : codimCount N

      8     7      6     5
o4 = t  + 9t  + 20t  + 9t

o4 : ZZ[t]

i5 : nC = 0;

i6 : C = nextChain N;

i7 : while C=!=null do (C=nextChain(C,N); nC=nC+1;)

i8 : nC

o8 = 39

We can specify the codimension of the chains.

i9 : nC = 0;

i10 : (C,data) = nextChain(5,N);

i11 : while C=!=null do (C=nextChain(C,data,5,N); nC=nC+1;)

i12 : nC

o12 = 9