MULTIDIMENSIONAL GAUSS REDUCTION THEORY 
            FOR CONJUGACY CLASSES OF SL(n,Z).

In this paper we describe the set of conjugacy classes in the
group SL(n,Z). We expand geometric Gauss Reduction Theory that
solves the problem for SL(2,Z) to the multidimensional case.
Further we find complete invariant of classes in terms of
multidimensional Klein-Voronoi continued fractions, where
sigma-reduce Hessenberg matrices play the role of reduced
matrices.