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# kVar -- key in hash table gaussianRingData: labels of k variables

## Description

This key is present in every gaussianRingData that comes from a graph. It is equal to the value of the optional input gaussianRing(...,kVariableName=>...).

    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 : R1 = gaussianRing B

    o4 = R1

    o4 : PolynomialRing

    i5 : R2 = gaussianRing D

    o5 = R2

    o5 : PolynomialRing

    i6 : R3 = gaussianRing U

    o6 = R3

    o6 : PolynomialRing

    i7 : R4 = gaussianRing mixedGraph(U,B,D)

    o7 = R4

    o7 : PolynomialRing

    i8 : R1.gaussianRingData

    o8 = HashTable{compU => {}    }
                   compW => {4, 5}
                   kVar => k
                   lVar => l
                   nn => 2
                   pVar => p
                   sVar => s

    o8 : HashTable

    i9 : R2.gaussianRingData

    o9 = HashTable{compU => {}    }
                   compW => {1, 4}
                   kVar => k
                   lVar => l
                   nn => 2
                   pVar => p
                   sVar => s

    o9 : HashTable

    i10 : R3.gaussianRingData

    o10 = HashTable{kVar => k}
                    nn => 3
                    sVar => s

    o10 : HashTable

    i11 : R4.gaussianRingData

    o11 = HashTable{compU => {1, 2, 3}}
                    compW => {4, 5}
                    kVar => k
                    lVar => l
                    nn => 5
                    pVar => p
                    sVar => s

    o11 : HashTable

## See also

- kVariableName -- optional input to choose the variable names for concentration matrix in gaussianRing
- gaussianRingData -- hash table with main parameters of a gaussian ring
- pVar -- key in hash table gaussianRingData: labels of p variables
- lVar -- key in hash table gaussianRingData: labels of l variables
- sVar -- key in hash table gaussianRingData: labels of s variables
- compU -- key in hash table gaussianRingData: component of undirected edges in vertex set of a mixed graph
- 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 kVar is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GraphicalModels.m2:2953:0.