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):

.. code-block:: bash

   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:

.. code-block:: text

   3 3
   1 2 3
   0 1 4
   3 3 1

Then run:

.. code-block:: 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:

.. code-block:: bash

   <command> --help

For example:

.. code-block:: bash

   groebner --help

SLURM Job Script Example
^^^^^^^^^^^^

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

.. code-block:: bash

   #!/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