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 |

- 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