Matroid 2.7.17

A graph with this cycle matroid; edge labels are elements.

Basic invariants

Status	todo
Dimension of realization space	not computed
Expected dimension over ℤ	not computed
Components of realization space	not computed
Free realization space	not computed
Principal ideal	not computed
Birational type	not computed
Birational type components	not computed
Good basis	not computed
Good basis v2	not computed

Realization space: scheme simple core id	not computed
Smooth char 0	not computed
Singular primes	not computed
Realization space: smooth over ℚ	not computed
Realization space: smooth over ℤ	not computed
Realization space: is regular scheme	not computed
Realization space: singular fiber primes	not computed
Realization space: singular fiber characteristics	not computed
Realization space: characteristic dimensions	not computed
Realization space: characteristic dimension unexpected	not computed
Realization space: characteristic dimension varies	not computed

Char poly splits	not computed
Simplicial arrangement	yes
Realization space: n qbar components	1

\(T = x_{0}^{2} x_{1} + x_{0} x_{1}^{3} + 2 x_{0} x_{1}^{2} + x_{0} x_{1} + x_{1}^{5} + 2 x_{1}^{4} + 2 x_{1}^{3} + x_{1}^{2}\)

Computed on the fly from the id.

{2,5} {3,5} {4,5} {2,6} {3,6} {4,6} {2,7} {3,7} {4,7} {5,7} {6,7}

{1,2} {1,3} {2,3} {1,4} {2,4} {3,4} {1,5} {1,6} {5,6} {1,7}

{1} {2,3} {2,4} {3,4} {5,6} {2,5,7} {3,5,7} {4,5,7} {2,6,7} {3,6,7} {4,6,7}

{1,2,3,4} {1,5,6} {1,7}

Dual (rank 5)

Revlex encoding in this labeling (not canonicalized, so not linked): *****00***0***0000000

Bases: {1,3,4,6,7} {1,2,4,6,7} {1,2,3,6,7} {1,3,4,5,7} {1,2,4,5,7} {1,2,3,5,7} {1,3,4,5,6} {1,2,4,5,6} {1,2,3,5,6} {1,2,3,4,6} {1,2,3,4,5}

Loops: 1. Parallel classes of size > 1: {2,3,4} {5,6}.