Computing all minimal Markov bases in Macaulay2

TL;DR

The paper presents the allMarkovBases package for Macaulay2, enabling the computation of all minimal Markov bases of a toric ideal by leveraging fiber graphs and related properties.

Contribution

It introduces a new Macaulay2 package that extends existing tools to compute all minimal Markov bases and related properties of toric ideals.

Findings

Successfully computes all minimal Markov bases for given toric ideals.

Identifies indispensable binomials and universal Markov basis using fiber graphs.

Enhances computational capabilities in algebraic statistics and combinatorics.

Abstract

We introduce the package allMarkovBases for Macaulay2, which is used to compute all minimal Markov bases of a given toric ideal. The package builds on functionality of 4ti2 by producing the fiber graph of the toric ideal. The package uses this graph to compute other properties of the toric ideal such as its indispensable set of binomials as well as its universal Markov basis.