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):

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:

3 3
1 2 3
0 1 4
3 3 1

Then run:

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:

<command> --help

For example:

groebner --help

SLURM Job Script Example

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

#!/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