Ehrhart series coefficients and quasi-period for random rational polytopes
- 1. Imperial College London
- 2. University of Nottingham
Description
Ehrhart series coefficients and quasi-period for random rational polytopes
A dataset of Ehrhart data for 84000 randomly generated rational polytopes, in dimensions 2 to 4, with quasi-periods 2 to 15.
The polytopes used to generate this data were produced by the following algorithm:
- Fix
a positive integer in . - Choose
uniformly at random. - Choose
lattice points uniformly at random in a box , where is chosen uniformly at random in . - Set
. If is not equal to then return to step 3. - Choose a lattice point
uniformly at random and replace with the translation . - Replace
with the dilation .
The final dataset was produced by first removing duplicate records, and then downsampling to a subset with 2000 datapoints for each pair
For details, see the paper:
Machine Learning the Dimension of a Polytope, Tom Coates, Johannes Hofscheier, and Alexander M. Kasprzyk, 2022.
If you make use of this data, please cite the above paper and the DOI for this data:
doi:10.5281/zenodo.6614829
quasiperiod.txt.gz
The file "quasiperiod.txt.gz" is a gzip-compressed plain text file containing key:value records with keys and values as described below, where each record is separated by a blank line. There are 84000 records in the file.
Example record
ULID: 01G57JBYP2ZW825E0NT4Q9JQNQ
Dimension: 2
Quasiperiod: 2
Volume: 97
EhrhartDelta: [1,50,195,289,192,49]
Ehrhart: [1,50,198,...]
LogEhrhart: [0.000000000000000000000000000000,3.91202300542814605861875078791,5.28826703069453523626966617327,...]
(The values for Ehrhart and LogEhrhart in the example have been truncated.)
For each polytope
ULID: A randomly generated string identifier for this record.
Dimension: A positive integer. The dimension
Quasiperiod: A positive integer. The quasi-period
Volume: A positive rational number. The lattice-normalised volume
EhrhartDelta: A sequence
Ehrhart: A sequence
LogEhrhart: A sequence
Files
quasiperiod.ipynb
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