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

# ChordalNet -- a chordal network

## Description

This type describes a chordal network representation of a polynomial ideal. The constructor of this type is chordalNet

### Overview of chordal networks methods

Methods to visualize a chordal network:
Methods to access properties of a chordal network:
• nodes -- list of nodes of a chordal network
• elimTree -- get the underlying elimination tree
• ring -- get the underlying ring
• isTriangular -- whether a chordal network is triangular
• structure -- either "Monomial", "Binomial" or "None"
Elimination routines using chordal structure:
• chordalElim -- performs elimination on the chordal network
• chordalTria -- makes a chordal network triangular
Methods for triangular chordal networks:

## Methods that use an object of class ChordalNet :

• chordalElim(ChordalNet) -- see chordalElim -- performs elimination on the chordal network
• net(ChordalNet)
• ring(ChordalNet)
• triaSystem(ChordalNet,ChordalNetChain) -- see ChordalNetChain -- a chain of a chordal network
• chordalTria(ChordalNet) -- see chordalTria -- makes a chordal network triangular
• codimCount(ChordalNet) -- see codimCount -- codimension counts of the chains of a chordal network
• components(ChordalNet) -- see components(ChordalNet,ZZ) -- components of a chordal network
• components(ChordalNet,ZZ) -- components of a chordal network
• digraph(ChordalNet) -- digraph associated to a chordal network
• codim(ChordalNet) -- see dim(ChordalNet) -- dimension of a chordal network
• dim(ChordalNet) -- dimension of a chordal network
• displayNet(ChordalNet) -- see displayNet -- displays a chordal network using Graphivz
• displayNet(Function,ChordalNet) -- see displayNet -- displays a chordal network using Graphivz
• displayNet(String,String,Function,ChordalNet) -- see displayNet -- displays a chordal network using Graphivz
• elimTree(ChordalNet) -- see ElimTree -- the elimination tree of a chordal graph
• isPrimeSimple(ChordalNet) -- simple primality test of a chordal network
• isTriangular(ChordalNet) -- see isTriangular -- whether a chordal network is triangular
• 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
• nodes(ChordalNet) -- see nodes -- list of nodes of a chordal network
• nodes(ChordalNet,RingElement) -- see nodes -- list of nodes of a chordal network
• reduceNet(ChordalNet) -- see reduceNet -- reduces a chordal network
• pseudoRemainder(RingElement,ChordalNet) -- see RingElement % ChordalNet -- ideal membership test
• RingElement % ChordalNet -- ideal membership test
• rootCount(ChordalNet) -- see rootCount -- counts the number of roots of a chordal network
• size(ChordalNet) -- size of a chordal network
• writeDotFile(String,Function,ChordalNet) -- writes a chordal network to a dot file

## For the programmer

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