Quatroid 66

We begin with the necessary setup steps from the README file. The output is supressed.

]activate .

]instantiate

using Quatroids

QuatroidAnalysis()

AllMatroids = GenerateAllMatroids();
AllQuatroids = GenerateAllCandidateQuatroids();
Q = AllQuatroids[66]

6-element Vector{Vector{Int64}}:
 [1, 2, 3]
 [1, 4, 5]
 [2, 4, 6]
 [3, 5, 7]
 [1, 2, 5, 6, 7, 8]
 [1, 3, 4, 6, 7, 8]

Structure

Sometimes its easier to use the quatroid’s short description:

shortDescription(Q)

2-element Vector{Vector{Any}}:
 [[1, 2, 3], [1, 4, 5], [2, 4, 6], [3, 5, 7]]
 [[1, 2, 5, 6, 7, 8], [1, 3, 4, 6, 7, 8]]

Retreive the triples and sextuples of the quatroid as follows:

(Triples(Q), Sextuples(Q))

([[1, 2, 3], [1, 4, 5], [2, 4, 6], [3, 5, 7]], [[1, 2, 5, 6, 7, 8], [1, 3, 4, 6, 7, 8]])

The index of the underlying matroid is found as follows, which we can then use to get the matroid itself:

MatroidNumber(Q)

25

AllMatroids[MatroidNumber(Q)]

4-element Vector{Vector{Int64}}:
 [1, 2, 3]
 [1, 4, 5]
 [2, 4, 6]
 [3, 5, 7]

This is indeed the correct underlying matroid, as can be seen from the picture at the top of this notebook.

Properties

This quatroid is Bezoutian:

isBezoutian(Q)

true

This quatroid is exhaustive, i.e. every point is involved in some condition:

isExhaustive(Q)

true

This quatroid has a reduced base locus:

ReducedBaseLocus(Q)

true