4ti2¶

4ti2 is a software suite for algebraic, geometric, and combinatorial problems on linear spaces. It is available on the cluster via a module.

Loading the Module¶

To load 4ti2 version 1.6.11 and its required dependencies (GLPK and GMP):

Terminal

 module load 4ti2/1.6.11

This automatically loads the required modules:

glpk/5.0-6xtss3c
gmp/6.2.1

Once loaded, 4ti2 commands like zsolve, markov, groebner, and others become available in your shell.

Quick Example: Solving an Integer System¶

Create a file named matrix.mat with the following content:

Then run:

Terminal

```bash

zsolve matrix.mat ```

This computes the integer kernel of the matrix.

Common Commands in 4ti2¶

Some of the frequently used command-line tools in 4ti2 include:

zsolve – Solve systems of linear equations over integers
groebner – Compute toric Gröbner bases
markov – Compute Markov bases
hilbert – Compute Hilbert bases
homogenize – Homogenize a matrix
dual – Compute the dual of a matrix
graver – Compute Graver bases

You can get command-line help with:

Terminal

<command> --help

For example:

Terminal

```bash

groebner --help ```

SLURM Job Script Example¶

Here’s a sample SLURM batch script for using 4ti2 non-interactively:

Terminal

#!/bin/bash
#SBATCH --job-name=4ti2-test
#SBATCH --time=00:05:00
#SBATCH --mem=1G
#SBATCH --cpus-per-task=1
#SBATCH --output=4ti2-%j.out
module load 4ti2/1.6.11
echo "1 1" > test.mat
echo "1" >> test.mat
zsolve test.mat

Documentation and References¶

Official website: https://4ti2.github.io/

The software is useful for research in:

Integer programming
Algebraic statistics
Toric ideals
Gröbner and Markov bases