# Quatroid 66

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

[ ]:

]activate .

[ ]:

]instantiate

[ ]:

using Quatroids

[ ]:

QuatroidAnalysis()

[5]:

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

[5]:

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:

[6]:

shortDescription(Q)

[6]:

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:

[7]:

(Triples(Q), Sextuples(Q))

[7]:

([[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:

[8]:

MatroidNumber(Q)

[8]:

25

[9]:

AllMatroids[MatroidNumber(Q)]

[9]:

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:

[10]:

isBezoutian(Q)

[10]:

true


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

[11]:

isExhaustive(Q)

[11]:

true


This quatroid has a reduced base locus:

[12]:

ReducedBaseLocus(Q)

[12]:

true