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