---
name: "4ti2"
section: "1"
platform: "linux"
package: "4ti2"
version: "1.6.10+ds-1.1+b2"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/4ti2"
---

# 4ti2(1)

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

## 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 \[--quiet\|-q\] \[--force\|-f\] \[--saturation\|-s\] \[--project-and-lift\|-p\] \[--normal\|-n\] \[--weighted\|-w\] \[--gebauer-moeller\|-g\] \[--auto-reduce-freq=*N*\|-a*N*\]** *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
```

## SEE ALSO

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

## AUTHORS

```
Ralf Hemmecke
Raymond Hemmecke
Matthias Koeppe
Peter Malkin
Matthias Walter
```