Macaulay2 » Documentation
Packages » GraphicalModels :: compU
next | previous | forward | backward | up | index | toc

# compU -- key in hash table gaussianRingData: component of undirected 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 undirected edges. For more details, check component U 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 compU 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

- partitionLMG -- partition the vertices of a loopless mixed graph into adjacent to undirected edges and adjacent to bidirected edges
- gaussianRingData -- hash table with main parameters of a gaussian ring
- kVar -- key in hash table gaussianRingData: labels of k variables
- pVar -- key in hash table gaussianRingData: labels of p variables
- sVar -- key in hash table gaussianRingData: labels of s variables
- lVar -- key in hash table gaussianRingData: labels of l variables
- compW -- key in hash table gaussianRingData: component of bidirected edges in vertex set of a mixed graph
- nn -- key in hash table gaussianRingData: total number of variables

## For the programmer

The object compU is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GraphicalModels.m2:3109:0.