4ti21

Software package for algebraic, geometric and combinatorial problems on linear spaces

Usage

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

Overview

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

Releases

Unchanged in 5 releases since Debian 9 (Stretch).

9–13