  A characteristic pair is a pair (G,C) of polynomial sets in which G is a
reduced lexicographic Groebner basis, C is the minimal triangular set contained
in G, and C is normal. In this paper, we show that any finite polynomial set P
can be decomposed algorithmically into finitely many characteristic pairs with
associated zero relations, which provide representations for the zero set of P
in terms of those of Groebner bases and those of triangular sets. The algorithm
we propose for the decomposition makes use of the inherent connection between
Ritt characteristic sets and lexicographic Groebner bases and is based
essentially on the structural properties and the computation of lexicographic
Groebner bases. Several nice properties about the decomposition and the
resulting characteristic pairs, in particular relationships between the
Groebner basis and the triangular set in each pair, are established. Examples
are given to illustrate the algorithm and some of the properties.
