Provided by: 4ti2_1.6.9+ds-5_amd64

**NAME**

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

**SYNOPSIS**

4ti2-circuits4ti2-genmodel[--quiet]foo.mod4ti2-gensymm[--quiet]abcdfoo4ti2-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]foo4ti2-hilbert[--quiet]foo4ti2-markov[--quiet|-q]foo4ti2-minimize[--quiet|-q]foo4ti2-normalform4ti2-output[--quiet][--binomials][--maple][--0-1][--transpose][--degree[N]][--positive][--3wayabc]foo4ti2-ppi4ti2-qsolve4ti2-rays4ti2-walk4ti2-zbasis4ti2-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 filefoo[.mat]containing the problem matrix. Related sets such as Graver basis or Markov basis are put intofoo.graandfoo.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 filefoo.varscontaining 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