DEBIAN

January 2015

Aliases: 4ti2-circuits(1), 4ti2-genmodel(1), 4ti2-gensymm(1), 4ti2-graver(1), 4ti2-groebner(1), 4ti2-hilbert(1), 4ti2-markov(1), 4ti2-minimize(1), 4ti2-normalform(1), 4ti2-output(1), 4ti2-ppi(1), 4ti2-qsolve(1), 4ti2-rays(1), 4ti2-walk(1), 4ti2-zbasis(1), 4ti2-zsolve(1)

### 4ti2

mathematical tool suite for problems on linear spaces -- tools

## 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