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

       Ralf Hemmecke
       Raymond Hemmecke
       Matthias Koeppe
       Peter Malkin
       Matthias Walter

Debian                                            January 2015                                           4TI2(1)

       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

       The software package 4ti2 is a suite of  command-line  tools  for  addressing  algebraic,  geometric  and
       combinatorial problems on linear spaces.

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

       User's Guide for 4ti2
       http://www.4ti2.de/

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