  In the present paper, we study the finite type invariants of Gauss words. In
the Polyak algebra techniques, we reduce the determination of the group
structure to transformation of a matrix into its Smith normal form and we give
the simplified form of a universal finite type invariant by means of the
isomorphism of this transformation. The advantage of this process is that we
can implement it as a computer program. We obtain the universal finite type
invariant of degree 4, 5, and 6 explicitly. Moreover, as an application, we
give the complete classification of Gauss words of rank 4 and the partial
classification of Gauss words of rank 5 where the distinction of only one pair
remains.
