## SYNOPSIS

**4ti2-circuits**

**4ti2-genmodel [--quiet]**

*foo.mod*

**4ti2-gensymm [--quiet]**

*a b c d*

*foo*

**4ti2-graver [--quiet]**

*foo[|.mat|.lat]*

**4ti2-groebner [--quiet|-q] [--force|-f] [--saturation|-s] [--project-and-lift|-p] [--normal|-n] [--weighted|-w] [--gebauer-moeller|-g] [--auto-reduce-freq=**

*N*

**|-a**

*N*

**]**

*foo*

**4ti2-hilbert [--quiet]**

*foo*

**4ti2-markov [--quiet|-q]**

*foo*

**4ti2-minimize [--quiet|-q]**

*foo*

**4ti2-normalform**

**4ti2-output [--quiet] [--binomials] [--maple] [--0-1] [--transpose] [--degree [**

*N*

**]] [--positive] [--3way**

*a b c*

**]**

*foo*

**4ti2-ppi**

**4ti2-qsolve**

**4ti2-rays**

**4ti2-walk**

**4ti2-zbasis**

**4ti2-zsolve**

## DESCRIPTION

The software package 4ti2 is a suite of command-line tools for addressing algebraic, geometric and combinatorial problems on linear spaces.## DATA STRUCTURE

The main concept of 4ti2 remains the same: a project is defined via a file*foo[.mat]*containing the problem matrix. Related sets such as Graver basis or Markov basis are put into

*foo.gra*and

*foo.mar*, respectively.

Input files and output files usually contain a matrix or a list of vectors (written as a matrix) in a standard encoding such as

2 4 1 1 1 1 1 2 3 4

There are only few exceptions, for example in a file
*foo.vars*
containing user specified variable names:

3 a b x

## AUTHORS

Ralf Hemmecke Raymond Hemmecke Matthias Koeppe Peter Malkin Matthias Walter