chordalNet(HashTable,HashTable,ElimTree,Digraph) -- construct chordal network from a digraph

Synopsis

Function: chordalNet
Usage:

chordalNet(eqs,ranks,tree,DG)
Inputs:
- eqs, a hash table, indicating the equations/inequations of each node
- ranks, a hash table, indicating the rank of each node
- tree, an instance of the type ElimTree,
- DG, a digraph, whose vertices are labels (strings) of the nodes
Outputs:
- an instance of the type ChordalNet,

Description

This method constructs a chordal network from the digraph of its nodes.

i1 : R = QQ[a,b,c,d,MonomialOrder=>Lex];

i2 : DG = digraph {{"a0","b0"}, {"a0","b1"}, {"a1","b2"}, {"b0","c1"}, {"b1","c0"}, {"b2","c0"}, {"c0","d0"}, {"c1","d1"}}

o2 = Digraph{a0 => {b0, b1}}
             a1 => {b2}
             b0 => {c1}
             b1 => {c0}
             b2 => {c0}
             c0 => {d0}
             c1 => {d1}
             d0 => {}
             d1 => {}

o2 : Digraph

i3 : G = chordalGraph digraph hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}};

i4 : tree = elimTree G

o4 = ElimTree{a => b   }
              b => c
              c => d
              d => null

o4 : ElimTree

i5 : rnk = hashTable{"a0"=>a, "a1"=>a, "b0"=>b, "b1"=>b, "b2"=>b,
                     "c0"=>c, "d0"=>d, "c1"=>c, "d1"=>d};

i6 : eqs = hashTable{"a0" => ({a},{}), "a1" => ({},{}),
                     "b0" => ({b},{}), "b1" => ({},{}), "b2" => ({b},{}),
                     "c0" => ({c},{}), "c1" => ({},{}),
                     "d0" => ({},{}), "d1" => ({d},{}) };

i7 : chordalNet(eqs,rnk,tree,DG)

o7 = ChordalNet{ d => { , d}    }
                 b => {b,  , b}
                 a => {a,  }
                 c => { , c}

o7 : ChordalNet

Ways to use this method: