## table of contents

- bullseye 1.6.9+ds-2
- testing 1.6.9+ds-5
- unstable 1.6.9+ds-5
- experimental 1.6.9+ds-6

4TI2(1) | General Commands Manual | 4TI2(1) |

# NAME¶

4ti2 - software package for algebraic, geometric and combinatorial problems on linear spaces

# 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|-aN]**

*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

# SEE ALSO¶

User's Guide for 4ti2 http://www.4ti2.de/

# AUTHORS¶

Ralf Hemmecke Raymond Hemmecke Matthias Koeppe Peter Malkin Matthias Walter

January 2015 | Debian |