# gaussianRingData -- hash table with main parameters of a gaussian ring

## Description

The contents of gaussianRingData depend on the type of gaussian ring.

First, we show an example of a gaussian ring with 5 variables

 i1 : R = gaussianRing 5 o1 = R o1 : PolynomialRing i2 : gaussianRingData o2 = gaussianRingData o2 : Symbol

In case of the gaussian ring of a graph, there are two options. First one, is when the graph is of class Graph .

 i3 : R=gaussianRing graph {{1,2},{2,3}} o3 = R o3 : PolynomialRing i4 : R.gaussianRingData o4 = HashTable{kVar => k} nn => 3 sVar => s o4 : HashTable

If the graph is of any other class -i.e., Bigraph, Digraph, MixedGraph - then it is internally converted to a MixedGraph and the gaussianRingData has the same structure.

 i5 : U = graph {{1,2},{2,3}} o5 = Graph{1 => {2} } 2 => {1, 3} 3 => {2} o5 : Graph i6 : B = bigraph{{4,5}} o6 = Bigraph{4 => {5}} 5 => {4} o6 : Bigraph i7 : D = digraph {{1,4}} o7 = Digraph{1 => {4}} 4 => {} o7 : Digraph i8 : R1 = gaussianRing B o8 = R1 o8 : PolynomialRing i9 : R2 = gaussianRing D o9 = R2 o9 : PolynomialRing i10 : R3 = gaussianRing mixedGraph(U,B,D) o10 = R3 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 i13 : R3.gaussianRingData o13 = HashTable{compU => {1, 2, 3}} compW => {4, 5} kVar => k lVar => l nn => 5 pVar => p sVar => s o13 : HashTable