Matroid 4.6.6

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

Basic invariants

Characteristic set	characteristic 0 and all primes `[0]`
Realizable	yes
Realizable char0	yes
Regular	yes
Binary	yes
Ternary	yes
Quaternary	yes
Graphic	yes

Status	computed_realization_space
Dimension of realization space	0
Expected dimension over ℤ	not computed
Components of realization space	1
Free realization space	yes
Principal ideal	yes
Birational type	rational how determined: birational type method: `rigid`
Birational type components	show [ { "dim": 0, "free_rank": 0, "torus_rank": 0, "core_dim": 0, "qbar_components": 1, "type": "rational", "reason": "rigid: unique realization over Q (integer matrix)" } ]
Good basis	not computed
Good basis v2	1,2,4,5

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	true
Simplicial arrangement	yes
Realization space: n qbar components	1

\(T = x^{4} + 2 x^{3} + 2 x^{2} y + x^{2} + 2 x y + y^{2}\)

Computed on the fly from the id.

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

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

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

rank 0 (1): {}
rank 1 (6): {1} {2} {3} {4} {5} {6}
rank 2 (11): {1,2,3} {1,4} {2,4} {3,4} {1,5} {2,5} {3,5} {1,6} {2,6} {3,6} {4,5,6}
rank 3 (6): {1,2,3,4} {1,2,3,5} {1,2,3,6} {1,4,5,6} {2,4,5,6} {3,4,5,6}
rank 4 (1): {1,2,3,4,5,6}

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

Dual (rank 2)

Revlex encoding in this labeling (not canonicalized, so not linked): 000******0***00

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

Loops: none. Parallel classes of size > 1: none.