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 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/