4ti2 - software package for algebraic, geometric and combinatorial problems on
linear spaces
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
The software package 4ti2 is a suite of command-line tools for addressing
algebraic, geometric and combinatorial problems on linear spaces.
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
User's Guide for 4ti2
http://www.4ti2.de/
Ralf Hemmecke
Raymond Hemmecke
Matthias Koeppe
Peter Malkin
Matthias Walter