4ti2 is a software package for algebraic, geometric and combinatorial problems
on linear spaces. It computes
* the circuits of a cone
* a problem matrix corresponding to graphical statistical models
* generators for the symmetry group acting on 4-way tables
* the Graver basis of a matrix or a given lattice
* a Groebner basis of the toric ideal of a matrix or, more general, of the
  lattice ideal of a lattice
* a Markov basis (generating set) of the toric ideal
* the minimal solution of an integer linear program or, more general, a lattice
  program, using a Groebner basis
* the normal form of a list of feasible points
* the primitive partition identities, that is, the Graver basis of [1 2 3 ... N]
* a generator description of a cone
* the extreme rays of a cone
* the minimal solution of an integer linear program or, more general, a lattice
  program using a Groebner basis
* an integer lattice basis
* solutions of linear inequality and equation systems over the integers

WWW: https://4ti2.github.io/