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GraphicalModels :: compW

compW -- key in hash table gaussianRingData: component of bidirected edges in vertex set of a mixed graph

Description

This key is present in every gaussianRingData that comes from a graph of class MixedGraph. It is equal to the set of vertices that are incident to bidirected edges. For more details, check component W in partitionLMG.

i1 : U = graph {{1,2},{2,3}}

o1 = Graph{1 => {2}   }
           2 => {1, 3}
           3 => {2}

o1 : Graph
i2 : B = bigraph{{4,5}}

o2 = Bigraph{4 => {5}}
             5 => {4}

o2 : Bigraph
i3 : D = digraph {{1,4}}

o3 = Digraph{1 => {4}}
             4 => {}

o3 : Digraph
i4 : R = gaussianRing mixedGraph(U,B,D)

o4 = R

o4 : PolynomialRing
i5 : R.gaussianRingData

o5 = HashTable{compU => {1, 2, 3}}
               compW => {4, 5}
               kVar => k
               lVar => l
               nn => 5
               pVar => p
               sVar => s

o5 : HashTable

Since the gaussian rings of graphs of classes Digraph and Bigraph are created by first changing the class to MixedGraph, the key compW is also present in the gaussianRingData hashtables of these two classes of graphs and the corresponding value is computed according to the rules described in partitionLMG.

i6 : U = graph {{1,2},{2,3}}

o6 = Graph{1 => {2}   }
           2 => {1, 3}
           3 => {2}

o6 : Graph
i7 : B = bigraph{{4,5}}

o7 = Bigraph{4 => {5}}
             5 => {4}

o7 : Bigraph
i8 : D = digraph {{1,4}}

o8 = Digraph{1 => {4}}
             4 => {}

o8 : Digraph
i9 : R1 = gaussianRing B

o9 = R1

o9 : PolynomialRing
i10 : R2 = gaussianRing D

o10 = R2

o10 : PolynomialRing
i11 : R1.gaussianRingData

o11 = HashTable{compU => {}    }
                compW => {4, 5}
                kVar => k
                lVar => l
                nn => 2
                pVar => p
                sVar => s

o11 : HashTable
i12 : R2.gaussianRingData

o12 = HashTable{compU => {}    }
                compW => {1, 4}
                kVar => k
                lVar => l
                nn => 2
                pVar => p
                sVar => s

o12 : HashTable

See also

For the programmer

The object compW is a symbol.