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