Provided by:

4ti2_1.6.7+ds-2_amd64 **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