4ti2

Solve algebraic, geometric, combinatorial problems on linear spaces

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 * an integer lattice basis * solutions of linear inequality and equation systems over the integers