# 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