Abstract of November 24th IMO Seminar by Raymond Hemmecke

Computation of Hilbert bases and Graver bases

In this talk we present an algorithm to compute Hilbert bases of cones given by Ax=0, x>=0. This algorithm is general enough to compute the union of such Hilbert bases, where the union is taken over a subset of the 2^n possible orthants of R^n. If we collect all 2^n Hilbert bases, we obtain the so-called Graver basis of A. The presented algorithm can also be used to exploit known bounds on variables. The full algorithmic power of this algorithm is currently being implemented by Matthias Walter as a "Jugend forscht" project. This short talk is mainly a preparation for the second talk on atomic fibers.