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# ChordalNetChain -- a chain of a chordal network

## Description

This type represents a chain of a chordal network.

Let $N$ be a chordal network in variables $x_1,\dots,x_n$. A chain is a tuple $C = (N_1,...,N_n)$ of nodes of the network such that $rank N_i = x_i$, and the nodes are connected in the network.

The constructor of this type is nextChain.

Any chain has an associated triangular system, given by the union of the equations and inequations in each of the nodes. Such triangular system can be obtained with triaSystem(N,C). The command dim C computes the dimension of this system.

## See also

- nextChain -- iterates over the chains of a chordal network
- codimCount -- codimension counts of the chains of a chordal network
- TriaSystem -- a triangular system

## Functions and methods returning an object of class ChordalNetChain:

- `nextChain(ChordalNet)` -- see nextChain -- iterates over the chains of a chordal network
- `nextChain(ChordalNetChain,ChordalNet)` -- see nextChain -- iterates over the chains of a chordal network
- `nextChain(ChordalNetChain,Sequence,ZZ,ChordalNet)` -- see nextChain -- iterates over the chains of a chordal network
- `nextChain(ZZ,ChordalNet)` -- see nextChain -- iterates over the chains of a chordal network

## Methods that use an object of class ChordalNetChain:

- `codim(ChordalNetChain)`
- `dim(ChordalNetChain)`
- `triaSystem(ChordalNet,ChordalNetChain)`

## For the programmer

The object ChordalNetChain is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Chordal/ChordalDoc.m2:306:0.