  Ritt-Wu's algorithm of characteristic sets is the most representative for
triangularizing sets of multivariate polynomials. Pseudo-division is the main
operation used in this algorithm. In this paper we present a new algorithmic
scheme for computing generalized characteristic sets by introducing other
admissible reductions than pseudo-division. A concrete subalgorithm is designed
to triangularize polynomial sets using selected admissible reductions and
several effective elimination strategies and to replace the algorithm of basic
sets (used in Ritt-Wu's algorithm). The proposed algorithm has been implemented
and experimental results show that it performs better than Ritt-Wu's algorithm
in terms of computing time and simplicity of output for a number of non-trivial
test examples.
