This repository contains the combinatorial patchworks listed in [1]. You can find direct links to the patchworks in the tables below. Each patchwork is available as a .pcom file, which can be opened using Polymake or Oscar.jl.
In Polymake
> polymake
polytope > $C = load("yourfile.pcom");In Oscar.jl
using Oscar
C = load("yourfile.pcom")You can also visualize the patchworks using the Patchworking GUI. Just click on the "Visual" link in the tables below, and it will open the corresponding patchwork in the visualization tool.
[1]
Z. Geiselmann, M. Joswig, L. Kastner, K. Mundinger,
S. Pokutta, C. Spiegel, M. Wack, M. Zimmer
121 patchworked curves of degree seven, tba
The degree-eight archive contains 2,367 unimodular .pcom
certificates for real schemes currently recorded as realizable by
combinatorial patchworking. Extract the archive with:
tar -xJf deg8.pcoms.txzWithin the archive, certificates are grouped under
deg8/oNN-pNN-nNN/, where o is the total number of ovals and (p,n) is
the positive/negative oval pair. Each filename encodes the realized type,
which is also stored in the certificate's TYPE field.
The folders below hold one patchwork for every real scheme of a maximal T-curve that a compatible collection of Harnack splits produces.
| degree | Harnack splits | compatible collections | real schemes | table |
|---|---|---|---|---|
| 8 | 873 | 105,949,232,275 | 38 | deg8 |
| 9 | 1,437 | 57,065,860,838,381 | 225 | deg9 |
| type | honeycomb |
|---|---|
| ⟨J⟩ | Link / Visual |
| ⟨J∪1⟩ | Link / Visual |
| ⟨J∪1⟨1⟩⟩ | Link / Visual |
| ⟨J∪2⟩ | Link / Visual |
| ⟨J∪3⟩ | Link / Visual |
| ⟨J∪4⟩ | Link / Visual |
| ⟨J∪5⟩ | Link / Visual |
| ⟨J∪6⟩ | Link / Visual |
| type | honeycomb |
|---|---|
| ⟨1⟩ | Link / Visual |
| ⟨1⟨1⟩⟩ | Link / Visual |
| ⟨2⟩ | Link / Visual |
| ⟨3⟩ | Link / Visual |
| ⟨4⟩ | Link / Visual |
| type | honeycomb |
|---|---|
| ⟨J⟩ | Link / Visual |
| ⟨J∪1⟩ | Link / Visual |
| type | honeycomb |
|---|---|
| ⟨1⟩ | Link / Visual |