ChordalNet -- a chordal network

Description

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

Examples

chordal networks examples -- a new representation of polynomial ideals

Overview of chordal networks methods

Methods to visualize a chordal network:

displayNet -- displays a chordal network using Graphivz
net -- print a chordal network
digraph(ChordalNet) -- digraph associated to 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:

rootCount -- counts the number of roots of a chordal network
dim(ChordalNet) -- dimension of a chordal network
codim(ChordalNet) -- dimension of a chordal network
codimCount -- codimension counts of the chains of a chordal network
topComponents(ChordalNet) -- top dimension of a chordal network
RingElement % ChordalNet -- ideal membership test
nextChain -- iterates over the chains of a chordal network
components(ChordalNet) -- components of a chordal network

Functions and methods returning an object of class ChordalNet :

"chordalNet(Ideal)" -- see chordalNet -- constructs a chordal network from a polynomial set
"chordalNet(Ideal,List)" -- see chordalNet -- constructs a chordal network from a polynomial set
"chordalNet(Ideal,String)" -- see chordalNet -- constructs a chordal network from a polynomial set
chordalNet(HashTable,HashTable,ElimTree,Digraph) -- construct chordal network from a digraph
RingMap ChordalNet -- apply ring map to a chordal network

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.