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